Digital Design, 5th Edition Solution Manual
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1
SOLUTIONS MANUAL
DIGITAL
DESIGN
WITH
AN
INTRODUCTION
TO
THE
VERILOG
HDL
Fifth
Edition
M.
MORRIS
MANO
Professor
Emeritus
California
State
University,
Los
Angeles
MICHAEL
D.
CILETTI
Professor
Emeritus
University
of
Colorado,
Colorado
Springs
rev
02/14/2012
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
2
CHAPTER 1
1.1
Base-10:
Octal:
Hex:
Base-12
16 17
20 21
10 11
14 15
1.2
(a) 32,768
18
22
12
16
19
23
13
17
20
24
14
18
21
25
15
19
(b) 67,108,864
3
22 23 24 25
26 27 30 31
16 17 18 19
1A 1B 20 21
26 27 28 29 30
32 33 34 35 36
1A 1B 1C 1D 1E
22 23 24 25 26
31
37
1F
27
32
40
20
28
(c) 6,871,947,674
(4310)5 = 4 * 5 + 3 * 5 + 1 * 51 = 58010
1.3
2
(198)12 = 1 * 122 + 9 * 121 + 8 * 120 = 26010
1.4
1.5
(435)8
=
4
*
82
+
3
*
81
+
5
*
80
=
28510
(345)6
=
3
*
62
+
4
*
61
+
5
*
60
=
13710
16-bit binary: 1111_1111_1111_1111
Decimal equivalent:
216 -1 = 65,53510
Hexadecimal equivalent: FFFF16
Let b = base
(a) 14/2 = (b + 4)/2 = 5, so b = 6
(b) 54/4 = (5*b + 4)/4 = b + 3, so 5 * b = 52 – 4, and b = 8
(c) (2 *b + 4) + (b + 7) = 4b, so b = 11
1.6
(x – 3)(x – 6) = x2 –(6 + 3)x + 6*3 = x2 -11x + 22
Therefore: 6 + 3 = b + 1m, so b = 8
Also, 6*3 = (18)10 = (22)8
1.7
64CD16 = 0110_0100_1100_11012 = 110_010_011_001 _101 = (62315 )8
1.8
(a) Results of repeated division by 2 (quotients are followed by remainders):
43110 = 215(1); 107(1); 53(1); 26(1); 13(0); 6(1)
Answer: 1111_10102 = FA16
3(0)
1(1)
(b) Results of repeated division by 16:
43110 = 26(15); 1(10) (Faster)
Answer: FA = 1111_1010
1.9
(a) 10110.01012 = 16 + 4 + 2 + .25 + .0625 = 22.3125
(b) 16.516 = 16 + 6 + 5*(.0615) = 22.3125
(c) 26.248 = 2 * 8 + 6 + 2/8 + 4/64 = 22.3125
(d) DADA.B16 = 14*163 + 10*162 + 14*16 + 10 + 11/16 = 60,138.6875
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
3
(e) 1010.11012 = 8 + 2 + .5 + .25 + .0625 = 10.8125
1.10
(a) 1.100102 = 0001.10012 = 1.916 = 1 + 9/16 = 1.56310
(b) 110.0102 = 0110.01002 = 6.416 = 6 + 4/16 = 6.2510
1.11
Reason: 110.0102 is the same as 1.100102 shifted to the left by two places.
1011.11
101 | 111011.0000
101
01001
101
1001
101
1000
101
0110
The quotient is carried to two decimal places, giving 1011.11
Checking: 1110112 / 1012 = 5910 / 510 ≅ 1011.112 = 58.7510
1.12
(a) 10000 and 110111
1011
+101
10000 = 1610
1011
x101
1011
1011
110111 = 5510
(b) 62h and 958h
2Eh
+34 h
62h
1.13
0010_1110
0011_0100
0110_0010 = 9810
2Eh
x34h
B 38
2
8A
9 5 8h = 239210
(a) Convert 27.315 to binary:
27/2 =
13/2
6/2
3/2
½
Integer
Quotient
13
6
3
1
0
Remainder
+
+
+
+
+
½
½
0
½
½
Coefficient
a0 = 1
a1 = 1
a2 = 0
a3 = 1
a4 = 1
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
4
2710 = 110112
.315 x 2
.630 x 2
.26 x 2
.52 x 2
=
=
=
=
Integer
0
1
0
1
+
+
+
+
Fraction
.630
.26
.52
.04
Coefficient
a-1 = 0
a-2 = 1
a-3 = 0
a-4 = 1
.31510 ≅ .01012 = .25 + .0625 = .3125
27.315 ≅ 11011.01012
(b) 2/3 ≅ .6666666667
.6666_6666_67 x 2
.3333333334 x 2
.6666666668 x 2
.3333333336 x 2
.6666666672 x 2
.3333333344 x 2
.6666666688 x 2
.3333333376 x 2
Integer
= 1
= 0
= 1
= 0
= 1
= 0
= 1
= 0
+
+
+
+
+
+
+
+
Fraction
.3333_3333_34
.6666666668
.3333333336
.6666666672
.3333333344
.6666666688
.3333333376
.6666666752
Coefficient
a-1 = 1
a-2 = 0
a-3 = 1
a-4 = 0
a-5 = 1
a-6 = 0
a-7 = 1
a-8 = 0
.666666666710 ≅ .101010102 = .5 + .125 + .0313 + ..0078 = .664110
.101010102 = .1010_10102 = .AA16 = 10/16 + 10/256 = .664110 (Same as (b)).
1.14
`
1.15
(a)
0001_0000
1s comp: 1110_1111
2s comp: 1111_0000
(b)
0000_0000
1s comp: 1111_1111
2s comp: 0000_0000
(c)
1101_1010
1s comp: 0010_0101
2s comp: 0010_0110
(d)
1010_1010
1s comp: 0101_0101
2s comp: 0101_0110
(e)
1000_0101
1s comp: 0111_1010
2s comp: 0111_1011
(f)
1111_1111
1s comp: 0000_0000
2s comp: 0000_0001
(a)
25,478,036
9s comp: 74,521,963
10s comp: 74,521,964
(b)
63,325,600
9s comp: 36,674,399
10s comp: 36,674,400
(c)
25,000,000
9s comp: 74,999,999
10s comp: 75,000,000
(d)
00000000
9s comp: 99999999
10s comp: 100000000
1.16
15s comp:
16s comp:
1.17
C3DF
3C20
3C21
C3DF: 1100_0011_1101_1111
1s comp: 0011_1100_0010_0000
2s comp: 0011_1100_0010_0001 = 3C21
(a) 2,579 → 02,579 →97,420 (9s comp) → 97,421 (10s comp)
4637 – 2,579 = 2,579 + 97,421 = 205810
(b) 1800 → 01800 → 98199 (9s comp) → 98200 (10 comp)
125 – 1800 = 00125 + 98200 = 98325 (negative)
Magnitude: 1675
Result: 125 – 1800 = 1675
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
5
(c) 4,361 → 04361 → 95638 (9s comp) → 95639 (10s comp)
2043 – 4361 = 02043 + 95639 = 97682 (Negative)
Magnitude: 2318
Result: 2043 – 6152 = -2318
(d) 745 → 00745 → 99254 (9s comp) → 99255 (10s comp)
1631 -745 = 01631 + 99255 = 0886 (Positive)
Result: 1631 – 745 = 886
1.18
1.19
Note: Consider sign extension with 2s complement arithmetic.
(a)
0_10010
(b)
0_100110
1s comp: 1_01101
1s comp: 1_011001 with sign extension
2s comp: 1_01110
2s comp: 1_011010
0_10011
0_100010
Diff:
0_00001 (Positive)
1_111100 sign bit indicates that the result is negative
Check:19-18 = +1
0_000011 1s complement
0_000100 2s complement
000100 magnitude
Result: -4
Check: 34 -38 = -4
(c)
0_110101
(d)
1s comp: 1_001010
1s comp:
2s comp: 1_001011
2s comp:
0_001001
Diff:
1_010100 (negative)
0_101011 (1s comp)
0_101100 (2s complement)
101100 (magnitude)
-4410 (result)
0_010101
1_101010 with sign extension
1_101011
0_101000
0_010011 sign bit indicates that the result is positive
Result: 1910
Check: 40 – 21 = 1910
+9286 → 009286; +801 → 000801; -9286 → 990714; -801 → 999199
(a) (+9286) + (_801) = 009286 + 000801 = 010087
(b) (+9286) + (-801) = 009286 + 999199 = 008485
(c) (-9286) + (+801) = 990714 + 000801 = 991515
(d) (-9286) + (-801) = 990714 + 999199 = 989913
1.20
+49 → 0_110001 (Needs leading zero extension to indicate + value);
+29 → 0_011101 (Leading 0 indicates + value)
-49 → 1_001110 + 0_000001→ 1_001111
-29 → 1_100011 (sign extension indicates negative value)
(a) (+29) + (-49) = 0_011101 + 1_001111 = 1_101100 (1 indicates negative value.)
Magnitude = 0_010011 + 0_000001 = 0_010100 = 20; Result (+29) + (-49) = -20
(b) (-29) + (+49) = 1_100011 + 0_110001 = 0_010100 (0 indicates positive value)
(-29) + (+49) = +20
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
6
(c) Must increase word size by 1 (sign extension) to accomodate overflow of values:
(-29) + (-49) = 11_100011 + 11_001111 = 10_110010 (1 indicates negative result)
Magnitude: 01_001110 = 7810
Result: (-29) + (-49) = -7810
1.21
+9742 → 009742 → 990257 (9's comp) → 990258 (10s) comp
+641 → 000641 → 999358 (9's comp) → 999359 (10s) comp
(a) (+9742) + (+641) → 010383
(b) (+9742) + (-641) →009742 + 999359 = 009102
Result: (+9742) + (-641) = 9102
(c) -9742) + (+641) = 990258 + 000641 = 990899 (negative)
Magnitude: 009101
Result: (-9742) + (641) = -9101
(d) (-9742) + (-641) = 990258 + 999359 = 989617 (Negative)
Magnitude: 10383
Result: (-9742) + (-641) = -10383
1.22
6,514
BCD:
ASCII:
ASCII:
0110_0101_0001_0100
0_011_0110_0_011_0101_1_011_0001_1_011_0100
0011_0110_0011_0101_1011_0001_1011_0100
1.23
0111
0110
1101
0110
0001 0011
0001 0001
0001 0100
1.24
0001 ( 791)
1000 (+658)
1001
0100
1001 (1,449)
(a)
6
0
0
0
0
0
0
1
1
1
1
1.25
1001
0101
1110
0110
0100
3
0
0
0
1
1
1
0
0
0
1
(b)
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
Decimal
0
1
2
3
4 (or 0101)
5
6
7 (or 1001)
8
9
6
0
0
0
0
0
0
1
1
1
1
4
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
Decimal
0
1
2
3
4
5
6 (or 0110)
7
8
9
(a) 6,24810
(b)
BCD:
0110_0010_0100_1000
Excess-3: 1001_0101_0111_1011
(c)
(d)
2421:
6311:
0110_0010_0100_1110
1000_0010_0110_1011
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
1.26
7
6,248 9s Comp:
2421 code:
1s comp c:
6,2482421
1s comp c
3,751
0011_0111_0101_0001
1001_1101_1011_0001 (2421 code alternative #1)
0110_0010_0100_1110 (2421 code alternative #2)
1001_1101_1011_0001 Match
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
8
For a deck with 52 cards, we need 6 bits (25 = 32 < 52 < 64 = 26). Let the msb's select the suit (e.g.,
diamonds, hearts, clubs, spades are encoded respectively as 00, 01, 10, and 11. The remaining four bits
select the "number" of the card. Example: 0001 (ace) through 1011 (9), plus 101 through 1100 (jack,
queen, king). This a jack of spades might be coded as 11_1010. (Note: only 52 out of 64 patterns are
used.)
1.27
1.28
G
(dot)
(space)
B
o
o
l
e
11000111_11101111_01101000_01101110_00100000_11000100_11101111_11100101
1.29
Steve Jobs
1.30
73 F4 E5 76 E5 4A EF 62 73
73:
F4:
E5:
76:
E5:
4A:
EF:
62:
73:
0_111_0011
1_111_0100
1_110_0101
0_111_0110
1_110_0101
0_100_1010
1_110_1111
0_110_0010
0_111_0011
s
t
e
v
e
j
o
b
s
1.31
62 + 32 = 94 printing characters
1.32
bit 6 from the right
1.33
(a) 897
1.34
ASCII for decimal digits with even parity:
1.35
(b) 564
(0):
00110000
(4):
10110100
(8):
10111000
(1):
(5):
(9):
(c) 871
10110001
00110101
00111001
(d) 2,199
(2):
(6):
10110010
00110110
(3):
(7):
00110011
10110111
(a)
a b c
a
f
b
c
g
f
g
1.36
a
b
a
f
g
b
f
g
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
9
CHAPTER 2
2.1
(a)
xyz
x+y+z
000
001
010
011
100
101
110
111
0
1
1
1
1
1
1
1
(x + y + z)' x'
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
y'
z'
x' y' z'
xyz
(xyz)
(xyz)'
x'
y'
z'
x' + y' + z'
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
000
001
010
011
100
101
110
111
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
(b)
(c)
xyz
x + yz
(x + y)
(x + z)
(x + y)(x + z)
xyz
x(y + z)
xy
xz
xy + xz
000
001
010
011
100
101
110
111
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
000
001
010
011
100
101
110
111
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
(c)
(d)
xyz
x
y+z
x + (y + z)
(x + y)
(x + y) + z
xyz
yz
x(yz)
xy
000
001
010
011
100
101
110
111
0
0
0
0
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
000
001
010
011
100
101
110
111
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2.2
(xy)z
0
0
0
0
0
0
0
1
(a) xy + xy' = x(y + y') = x
(b) (x + y)(x + y') = x + yy' = x(x +y') + y(x + y') = xx + xy' + xy + yy' = x
(c) xyz + x'y + xyz' = xy(z + z') + x'y = xy + x'y = y
(d) (A + B)'(A' + B')' = (A'B')(A B) = (A'B')(BA) = A'(B'B)A = 0
(e) (a + b + c')(a'b' + c) = aa'b' + ac + ba'b' + bc + c'a'b' + c'c = ac + bc +a'b'c'
(f) a'bc + abc' + abc + a'bc' = a'b(c + c') + ab(c + c') = a'b + ab = (a' + a)b = b
2.3
(a) ABC + A'B + ABC' = AB + A'B = B
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
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rights
reserved.
10
(b) x'yz + xz = (x'y + x)z = z(x + x')(x + y) = z(x + y)
(c) (x + y)'(x' + y') = x'y'(x' + y') = x'y'
(d) xy + x(wz + wz') = x(y +wz + wz') = x(w + y)
(e) (BC' + A'D)(AB' + CD') = BC'AB' + BC'CD' + A'DAB' + A'DCD' = 0
(f) (a' + c')(a + b' + c') = a'a + a'b' + a'c' + c'a + c'b' + c'c' = a'b' + a'c' + ac' + b'c' = c' + b'(a' + c')
= c' + b'c' + a'b' = c' + a'b'
2.4
(a) A'C' + ABC + AC' = C' + ABC = (C + C')(C' + AB) = AB + C'
(b) (x'y' + z)' + z + xy + wz = (x'y')'z' + z + xy + wz =[ (x + y)z' + z] + xy + wz =
= (z + z')(z + x + y) + xy + wz = z + wz + x + xy + y = z(1 + w) + x(1 + y) + y = x + y + z
(c) A'B(D' + C'D) + B(A + A'CD) = B(A'D' + A'C'D + A + A'CD)
= B(A'D' + A + A'D(C + C') = B(A + A'(D' + D)) = B(A + A') = B
(d) (A' + C)(A' + C')(A + B + C'D) = (A' + CC')(A + B + C'D) = A'(A + B + C'D)
= AA' + A'B + A'C'D = A'(B + C'D)
(e) ABC'D + A'BD + ABCD = AB(C + C')D + A'BD = ABD + A'BD = BD
2.5
(a)
x
y
Fsimplified
F
(b)
x
y
Fsimplified
F
(c)
Digital
Design
With
An
Introduction
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Verilog
HDL
–
Solution
Manual.
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Mano.
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Copyright
2012,
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11
x
y
z
Fsimplified
F
(d)
A
B
0
Fsimplified
F
(e)
x
y
z
Fsimplified
F
(f)
Digital
Design
With
An
Introduction
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the
Verilog
HDL
–
Solution
Manual.
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Mano.
M.D.
Ciletti,
Copyright
2012,
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rights
reserved.
12
x
y
z
F
Fsimplified
2.6
(a)
A
B
C
F
Fsimplified
(b)
x
y
z
F
Fsimplified
(c)
x
y
F
Fsimplified
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
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rights
reserved.
13
(d)
w
x
y
z
F
Fsimplified
(e)
A
B
C
D
Fsimplified = 0
F
(f)
w
x
y
z
F
Fsimplified
2.7
(a)
A
B
C
D
F
Fsimplified
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
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14
(b)
w
x
y
z
F
Fsimplified
(c)
A
B
C
D
F
Fsimplified
(d)
A
B
C
D
F
Fsimplified
Digital
Design
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An
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HDL
–
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Ciletti,
Copyright
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15
(e)
A
B
C
D
F
Fsimplified
2.8
F' = (wx + yz)' = (wx)'(yz)' = (w' + x')(y' + z')
FF' = wx(w' + x')(y' + z') + yz(w' + x')(y' + z') = 0
F + F' = wx + yz + (wx + yz)' = A + A' = 1 with A = wx + yz
2.9
(a) F' = (xy' + x'y)' = (xy')'(x'y)' = (x' + y)(x + y') = xy + x'y'
(b) F' = [(a + c) (a + b')(a' + b + c')]' = (a + c)' + (a + b')' + (a' + b + c')'
=a'c' + a'b + ab'c
(c) F' = [z + z'(v'w + xy)]' = z'[z'(v'w + xy)]' = z'[z'v'w + xyz']'
= z'[(z'v'w)'(xyz')'] = z'[(z + v + w') +( x' + y' + z)]
= z'z + z'v + z'w' + z'x' + z'y' +z' z = z'(v + w' + x' + y')
2.10
2.11
(a) F1 + F2 = Σ m1i + Σm2i = Σ (m1i + m2i)
(b) F1 F2 = Σ mi Σmj where mi mj = 0 if i ≠ j and mi mj = 1 if i = j
(a) F(x, y, z) = Σ(1, 4, 5, 6, 7)
(b) F(a, b, c) = Σ(0, 2, 3, 7)
F = xy + xy' + y'z
2.12
F = bc + a'c'
xyz
F
abc
F
000
001
010
011
100
101
110
111
0
1
0
0
1
1
1
1
000
001
010
011
100
101
110
111
1
0
1
1
0
0
0
1
A = 1011_0001
B = 1010_1100
Digital
Design
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HDL
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16
(a)
(b)
(c)
(d)
(e)
2.13
A AND B = 1010_0000
A OR B = 1011_1101
A XOR B = 0001_1101
NOT A = 0100_1110
NOT B = 0101_0011
(a)
u
x
y
z
(u + x')
Y = [(u + x')(y' + z)]
(y' + z)
(b)
u x y
x
Y = (u xor y)' + x
(u xor y)'
(c)
u
x
y z
(u'+ x')
Y = (u'+ x')(y + z')
(y + z')
(d)
u x y
z
u(x xor z)
Y = u(x xor z) + y'
y'
(e)
u x y z
u
yz
Y = u + yz +uxy
uxy
(f)
Digital
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HDL
–
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17
u x
y
Y = u + x + x'(u + y')
x'(u + y')
(u + y')
2.14
(a)
x
y
z
F =xy + x'y' + y'z
(b)
x
y
z
F = xy + x'y' + y'z
= (x' + y')' + (x + y)' + (y + z')'
(c)
x
y
z
F = xy + x'y' + y'z
= [(xy)' (x'y')' (y'z)']'
(d)
x
y
z
F = xy + x'y' + y'z
= [(xy)' (x'y')' (y'z)']'
Digital
Design
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HDL
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18
(e)
x
y
z
F = xy + x'y' + y'z
= (x' + y')' + (x + y)' + (y + z')'
2.15
(a) T1 = A'B'C' + A'B'C + A'BC' = A'B'(C' + C) +A'C'(B' + B) = A'B' +A'C' = A'(B' + C')
(b) T2 =T1' = A'BC + AB'C' + AB'C + ABC' + ABC
= BC(A' + A) + AB'(C' + C) + AB(C' + C)
= BC + AB' + AB = BC + A(B' + B) = A + BC
∑ (3, 5, 6, 7) = Π (0,1, 2, 4)
T1 = A'B'C' + A'B'C + A'BC'
A'B'
A'C'
T2 = A'BC + AB'C' + AB'C + ABC' + ABC
AC'
AC
T1 = A'B' A'C' = A'(B' + C')
BC
T2 =AC' + BC + AC = A+ BC
2.16
(a) F(A, B, C) = A'B'C' + A'B'C + A'BC' + A'BC + AB'C' + AB'C + ABC' + ABC
= A'(B'C' + B'C + BC' + BC) + A((B'C' + B'C + BC' + BC)
= (A' + A)(B'C' + B'C + BC' + BC) = B'C' + B'C + BC' + BC
= B'(C' + C) + B(C' + C) = B' + B = 1
(b) F(x1, x2, x3, ..., xn) = Σmi has 2n/2 minterms with x1 and 2n/2 minterms with x'1, which can be factored
and removed as in (a). The remaining 2n-1 product terms will have 2n-1/2 minterms with x2 and 2n-1/2
minterms with x'2, which and be factored to remove x2 and x'2. continue this process until the last term is
left and xn + x'n = 1. Alternatively, by induction, F can be written as F = xnG + x'nG with G = 1. So F =
(xn + x'n)G = 1.
Digital
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Verilog
HDL
–
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19
2.17
(a) F = (b + cd)(c + bd) bc + bd + cd + bcd = Σ(3, 5, 6, 7, 11, 14, 15)
F'
=
Σ(0, 1, 2, 4, 8, 9, 10, 12, 13)
F = Π(0, 1, 2, 4, 8, 9, 10, 12, 13)
abcd
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
F
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
(b) (cd + b'c + bd')(b + d) = bcd + bd' + cd + b'cd = cd + bd'
= Σ (3, 4, 7, 11, 12,14, 15)
= Π (0, 1, 2, 5, 6, 8, 9, 10, 13)
abcd
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
F
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
(c) (c' + d)(b + c') = bc' + c' + bd + c'd = (c' + bd)
= Σ (0, 1, 4, 5, 7, 8, 12, 13, 15)
F = Π (2, 3, 6, 9, 10, 11, 14)
Digital
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HDL
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20
(d) bd' + acd' + ab'c + a'c' = Σ (0, 1, 4, 5, 10, 11, 14)
F' = Σ (2, 3, 6, 7, 8, 9, 12, 13, 15)
F = Π (02, 3, 6, 7, 8, 12, 13, 15)
abcd
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
F
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
Digital
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HDL
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21
2.18
(a)
(b)
wx y z
F
00 0 0
00 0 1
00 1 0
00 1 1
01 0 0
01 0 1
01 1 0
01 1 1
10 0 0
10 0 1
10 1 0
10 1 1
11 0 0
11 0 1
11 1 0
11 1 1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
1
x
y'
z
x'
y'
z
w'
x
y
w
x'
y
w
x
y
F = xy'z + x'y'z + w'xy + wx'y + wxy
F = Σ(1, 5, 6, 7, 9, 10 11, 13, 14, 15 )
5 - Three-input AND gates
2 - Three-input OR gates
Alternative: 1 - Five-input OR gate
4 - Inverters
F
(c)
F = xy'z + x'y'z + w'xy + wx'y + wxy = y'z + xy + wy = yʹ′z + y(w + x)
(d)
F = y'z + yw + yx) = Σ(1, 5, 9, 13 , 10, 11, 13, 15, 6, 7, 14, 15)
= Σ(1, 5, 6, 7, 9, 10, 11, 13, 14, 15)
(e)
y'
z
x
w
y
F
1 – Inverter, 2 – Two-input AND gates, 2 – Two-input OR gates
Digital
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HDL
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22
2.19
F = B'D + A'D + BD
2.20
ABCD
ABCD
ABCD
-B'-D
0001 = 1
0011 = 3
1001 = 9
1011 = 11
A'--D
0001 = 1
0011 = 3
0101 = 5
0111 = 7
-B-D
0101 = 5
0111 = 7
1101 = 13
1111 = 15
F = Σ(1, 3, 5, 7, 9, 11,13, 15) = Π(0, 2, 4, 6, 8, 10, 12, 14)
(a) F(A, B, C, D) = Σ(2, 4, 7, 10, 12, 14)
F'(A, B, C, D) = Σ(0, 1, 3, 5, 6, 8, 9, 11, 13, 15)
(b) F(x, y, z) = Π(3, 5, 7)
F' = Σ(3, 5, 7)
2.21
2.22
(a) F(x, y, z) = Σ(1, 3, 5) = Π(0, 2, 4, 6, 7)
(b) F(A, B, C, D) = Π(3, 5, 8, 11) = Σ(0, 1, 2, 4, 6, 7, 9, 10, 12, 13, 14, 15)
(a) (u + xw)(x + u'v) = ux + uu'v + xxw + xwu'v = ux + xw + xwu'v
= ux + xw = x(u + w)
= ux + xw (SOP form)
= x(u + w) (POS form)
(b) x' + x(x + y')(y + z') = x' + x(xy + xz' + y'y + y'z')
= x' + xy + xz' + xy'z' = x' + xy +xz' (SOP form)
= (x' + y + z') (POS form)
2.23
(a) B'C +AB + ACD
A
B
C
D
F
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23
(b) (A + B)(C + D)(A' + B + D)
A
B
C
D
F
(c) (AB + A'B')(CD' + C'D)
A
B
C
D
F
(d) A + CD + (A + D')(C' + D)
A
B
C
D
F
2.24
x ⊕ y = x'y + xy'
and (x ⊕ y)' = (x + y')(x' + y)
Dual of x'y + xy' = (x' + y)(x + y') = (x ⊕ y)'
2.25
(a) x| y = xy' ≠ y | x = x'y
(x | y) | z = xy'z' ≠ x | (y | z) = x(yz')' = xy' + xz
Not commutative
Not associative
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HDL
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24
(b) (x ⊕ y) = xy' + x'y = y ⊕ x = yx' + y'x
Commutative
(x ⊕ y) ⊕ z = ∑(1, 2, 4, 7) = x ⊕ (y ⊕ z)
Associative
2.26
NAND
(Positive logic)
Gate
xy
z
xy
z
xy
z
LL
LH
HL
HH
H
H
H
L
00
01
10
11
1
1
1
0
11
10
01
00
0
0
0
1
NOR
(Positive logic)
Gate
2.27
NOR
(Negative logic)
NAND
(Negative logic)
xy
z
xy
z
xy
z
LL
LH
HL
HH
H
L
L
L
00
01
10
11
1
0
0
0
11
10
01
00
0
1
1
1
f1 = a'b'c' + a'bc' + a'bc + ab'c' + abc = a'c' + bc + a'bc' + ab'c'
f2 = a'b'c' + a'b'c + a'bc + ab'c' + abc = a'b' + bc + ab'c'
a'
b'
a'
a'
b
c'
a'
b
c
a'
b
c
a
b
c
a'
b'
c
a'
b
c
a
b'
c
a'
c'
b
f1
f2
c
a'
b
c'
a
b'
c'
a'
b'
b
f1
f2
c
a
b'
c'
Digital
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2.28
25
(a) y = a(bcd)'e = a(b' + c' + d')e
y = a(b' + c' + d')e = ab’e + ac’e + ad’e
= Σ( 17, 19, 21, 23, 25, 27, 29)
a bcde
y
a bcde
y
0 0000
0 0001
0 0010
0 0011
0 0100
0 0101
0 0110
0 0111
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1 0000
1 0001
1 0010
1 0011
1 0100
1 0101
1 0110
1 0111
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0 1000
0 1001
0 1010
0 1011
0 1100
0 1101
0 1110
0 1111
1 1000
1 1001
1 1010
1 1011
1 1100
1 1101
1 1110
1 1111
(b) y1 = a ⊕ (c + d + e)= a'(c + d +e) + a(c'd'e') = a'c + a'd + a'e + ac'd'e'
y2 = b'(c + d + e)f = b'cf + b'df + b'ef
y1 = a (c + d + e) = a'(c + d +e) + a(c'd'e') = a'c + a'd + a'e + ac'd'e'
y2 = b'(c + d + e)f = b'cf + b'df + b'ef
a'-c--001000 = 8
001001 = 9
001010 = 10
001011 = 11
a'--d-000100 = 8
000101 = 9
000110 = 10
000111 = 11
a'---e000010 = 2
000011 = 3
000110 = 6
000111 = 7
001100 = 12
001101 = 13
001110 = 14
001111 = 15
001100 = 12
001101 = 13
001110 = 14
001111 = 15
001010 = 10
001011 = 11
001110 = 14
001111 = 15
011000 = 24
011001 = 25
011010 = 26
011011 = 27
010100 = 20
010101 = 21
010110 = 22
010111 = 23
010010 = 18
010011 = 19
010110 = 22
010111 = 23
011100 = 28
011101 = 29
011110 = 30
011111 = 31
011100 = 28
011101 = 29
011110 = 30
011111 = 31
011010 = 26
011001 = 27
011110 = 30
011111 = 31
a-c'd'e'100000 = 32
100001 = 33
110000 = 34
110001 = 35
-b' c--f
-b' -d-f
-b' --ef
001001 = 9
001011 = 11
001101 = 13
001111 = 15
101001 = 41
101011 = 43
101101 = 45
101111 = 47
001001 = 9
001011 = 11
001101 = 13
001111 = 15
101001 = 41
101011 = 43
101101 = 45
101111 = 47
000011 = 3
000111 = 7
001011 = 11
001111 = 15
100011 = 35
100111 = 39
101011 = 51
101111 = 55
Digital
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HDL
–
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Copyright
2012,
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26
y1 = Σ (2, 3, 6, 7, 8, 9, 10 ,11, 12, 13, 14, 15, 18, 19, 22, 23, 24, 25, 26, 27, 28,
29, 30, 31, 32, 33, 34, 35 )
y2 = Σ (3, 7, 9, 13, 15, 35, 39, 41, 43, 45, 47, 51, 55)
ab cdef
y1 y2
ab cdef
y1 y2
ab cdef
y1 y2
ab cdef
y1 y2
00 0000
00 0001
00 0010
00 0011
00 0100
00 0101
00 0110
00 0111
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
01 0000
01 0001
01 0010
01 0011
01 0100
01 0101
01 0110
01 0111
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
10 0000
10 0001
10 0010
10 0011
10 0100
10 0101
10 0110
10 0111
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
11 0000
11 0001
11 0010
11 0011
11 0100
11 0101
11 0110
11 0111
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
00 1000
00 1001
00 1010
00 1011
00 1100
00 1101
00 1110
00 1111
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
01 1000
01 1001
01 1010
01 1011
01 1100
01 1101
01 1110
01 1111
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
10 1000
10 1001
10 1010
10 1011
10 1100
10 1101
10 1110
10 1111
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
11 1000
11 1001
11 1010
11 1011
11 1100
11 1101
11 1110
11 1111
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Digital
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HDL
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27
Chapter 3
3.1
x
y
yz
00
01
m0
0
m1
m3
m2
m5
m7
m6
1
00
01
m0
1
1
y
yz
x
10
1
m4
x
11
0
x
1
00
01
m0
0
m1
1
1
1
m7
m5
m7
m6
1
1
1
y
yz
00
m2
1
m5
x
10
m3
1
m4
x
11
m2
z
F = z' + xy'
y
yz
m3
1
z
F = xy' + x'z'
x
10
m1
1
m4
1
11
01
m0
m1
m4
m5
0
m6
1
x
11
1
m2
1
1
m7
1
z
F = x' + y'z
10
m3
m6
1
z
F = x'z + yz + x'y
3.2
x
00
0
x
y
yz
1
m0
1
m4
m1
m5
11
m3
1
m7
1
00
01
11
m0
m1
m3
m4
m5
m7
0
x
1
0
m6
x
1
x
10
m2
1
1
1
m4
m5
1
x
11
m3
m7
1
m6
1
1
z
F = y + x'z
y
00
1
10
m2
1
yz
01
m0
m1
m4
m5
11
m3
1
10
m2
1
m7
1
1
m6
1
1
z
z
F = xy' + x'y
(c)
m1
0
1
m6
01
m0
(b)
y
yz
00
m2
1
y
yz
x
10
z
F = x'y' + xz
(a)
x
01
F=y+z
(d)
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28
x
y
yz
00
m0
0
11
10
m1
m3
m2
m5
m7
m6
1
m4
x
01
1
x
1
00
01
11
m0
m1
m3
m4
m5
m7
0
1
1
y
yz
x
10
m2
1
1
1
m6
1
1
1
z
z
F = z'
F=x+yz
(e)
(f)
3.3
x
00
0
x
y
yz
1
m0
1
m4
m3
m2
m5
m7
m6
1
1
1
x
0
01
m1
11
m3
1
m4
m5
1
m7
1
x
m2
1
1
m4
m1
1
m5
11
m3
m7
1
1
x
10
m2
1
m6
z
F = x'y' + yz + x'yz'
F = x' + yz
yz
00
1
01
11
m0
m1
m3
m4
m5
m7
10
m2
1
1
m6
1
z
F = x'yz + xy'z' + xy'z
F = x'yz + xy'
z
F = x'y + yz' + y'z'
F = = x' y + z'
(c)
m0
01
0
1
m6
00
(b)
10
1
y
yz
0
y
00
1
x
10
m1
yz
m0
x
11
z
F =xy + x'y'z' + x'yz'
F = xy + x' z'
(a)
x
01
(d)
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
29
3.4
AB
CD
y
yz
0
x
1
00
m0
01
m1
11
m3
1
10
m2
1
m4
m5
m7
m6
1
11
A
10
(a)
AB
F=y
m5
m7
m12
m13
m15
m14
m8
m9
m11
m10
1
C
00
00
01
11
A
10
01
11
m0
m1
m3
m4
m5
m7
m2
1
m6
1
m15
m14
m8
m9
m11
m10
1
B
1
1
1
11
w
10
01
11
m0
m1
m3
m4
m5
m7
B
10
m2
1
1
m6
m12
m13
m15
m14
m8
m9
m11
m10
1
1
D
(c)
1
y
00
01
m13
m6
1
yz
00
m12
1
wx
10
m2
D
F = BCD + A' BD'
(b)
CD
10
m3
z
11
m1
m4
01
1
01
m0
00
x
C
00
1
x
1
z
F =CD + ABD + ABC
(d)
F = w'x'y +wx
wx
yz
y
00
01
m0
11
m1
wx
10
m3
y
00
m2
00
01
11
10
m0
m1
m3
m2
m4
m5
m7
m6
m15
m14
00
m4
m5
m7
m6
01
01
m12
11
w
yz
m13
1
m15
1
m8
x
m14
m12
1
m9
11
m11
10
w
m10
1
m8
10
z
m9
x
1
m11
1
m10
1
F = wz' + xy'w
1
z
F = wx + wyz
(e)
m13
1
(f)
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
30
3.5
y
yz
wx
00
m0
01
m1
00
11
AB
10
m3
m4
m5
m0
11
m6
m13
1
m15
1
w
m9
m11
m5
11
A
m10
m13
1
m15
m14
1
m9
B
1
m11
z
m10
D
F =xz' + w'y'z+ wxy
(b)
y
yz
00
01
m0
m1
00
11
m3
1
m4
01
1
1
11
m8
m2
m0
m6
1
01
x
m14
m9
1
(c)
z
F = z + xw'
A
m10
m2
m5
m7
m6
1
1
m13
1
1
m15
1
m8
1
10
m3
11
m11
10
11
m1
1
m12
1
01
1
m4
1
m15
1
C
00
00
m7
m13
F = AC' + ABC' + ABD'
CD
AB
10
1
m5
m12
w
m6
10
(a)
wx
1
m7
1
m8
10
m2
1
m12
1
10
m3
01
x
m14
1
m8
m1
11
1
m4
1
m12
01
00
m7
1
00
m2
1
01
C
CD
m9
B
m14
1
m11
m10
10
1
D
F =BD + A'B + B' D'
or = BD + B'D' + A'D'
(d)
3.6
AB
CD
C
00
00
01
11
A
10
(a)
m0
1
m4
01
11
m1
m3
m2
m5
m7
m6
1
1
1
m13
m15
m14
m8
m9
m11
m10
1
1
yz
1
D
F = B' D' +A'BD + ABC'
y
00
00
01
m12
1
wx
10
B
11
w
10
(b)
01
m0
m1
m4
m5
1
1
1
11
m3
1
10
m2
m7
m6
m12
m13
m15
m14
m8
m9
m11
m10
1
1
1
1
x
1
z
F = xy' +x'z + wx'y
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
31
AB
CD
C
00
m0
01
m1
00
11
m3
m4
m5
m12
m0
m6
m15
B
m14
m9
A
m10
1
1
m6
1
m15
m14
m11
m10
B
1
m8
m9
10
1
D
F = C'D + A'BD + A'B'C'
(d)
F = A'BC' + B'C'D + ACD + AB'C
m2
m7
m13
D
(c)
10
m3
1
11
m11
1
11
1
m5
m12
1
m8
m1
01
11
10
01
1
m4
1
m13
C
00
00
m7
1
CD
m2
1
01
A
AB
10
3.7
wx
yz
y
00
m0
01
m1
00
m4
m5
11
AB
m8
m9
z
F = z + x'y
00
01
m1
m3
m5
m7
1
m12
m13
11
(c)
m9
1
wx
m11
1
m15
m14
1
B
1
m11
m10
1
1
y
01
m1
11
m3
10
m2
00
m4
01
m14
m6
D
F = AD' + C'D + BCD'
m0
1
m15
m7
1
m9
1
00
m2
1
m2
yz
m6
1
m8
1
m8
10
10
1
01
m13
(b)
11
1
m4
10
1
C
00
m5
m12
A
m10
10
m3
1
11
1
CD
A
x
11
1
m4
m14
m11
(a)
m1
01
1
1
m0
m6
m15
10
01
00
1
1
C
00
m0
1
m7
m13
CD
m2
1
1
m12
AB
10
m3
1
01
w
11
B
m12
1
m10
m5
1
m13
11
w
1
m8
1
10
D
F = B'D' + AC + A'BD + CD (or B'C)
(d)
m7
1
m9
m6
1
m15
1
m14
1
m11
x
1
m10
z
F = xw' + xz + xy
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
32
3.8
(a) F(x, y, z) = Σ(3, 5, 6, 7)
x
00
0
x
y
yz
1
01
11
m0
m1
m3
m4
m5
m7
1
1
1
10
m2
m6
1
z
(b) F = Σ(1, 3, 5, 9, 12, 13, 14)
AB
CD
C
00
00
01
11
A
10
01
m0
m1
m4
m5
1
1
11
m3
1
10
m2
m7
m6
m12
m13
m15
m14
m8
m9
m11
m10
1
1
1
B
1
D
(c)
F = Σ(0, 1, 2, 3, 11, 12, 14, 15)
y
wx
00
00
01
11
w
10
m0
1
m4
01
m1
1
11
m3
1
10
m2
1
m5
m7
m12
m13
m15
m14
m8
m9
m11
m10
1
m6
1
1
x
1
z
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
33
(d)
F = Σ(3, 4, 5, 7, 11, 12)
CD
AB
C
00
00
01
11
A
10
m0
m4
1
01
m1
m5
1
11
m3
m7
10
m2
1
m6
1
m12
m13
m15
m14
m8
m9
m11
m10
1
1
B
D
3.9
yz
wx
y
00
m0
00
01
01
m1
m3
m2
m5
m7
m6
1
1
1
m13
11
1
m8
01
m3
m4
m5
m7
m12
m13
1
1
m11
A
m10
1
1
m9
(b)
CD
11
m0
m1
m3
m4
m5
m7
00
1
11
m13
1
m8
10
1
wx
10
1
1
m1
m4
m5
1
D
m10
m3
1
B
m12
w
1
m8
10
m13
m6
m15
1
m9
1
10
m2
1
m7
1
11
m11
(c)
m0
11
01
1
1
01
00
1
m14
y
00
m6
m15
m9
yz
m2
1
m12
A
Essential: B'D', AC, A'BD
Non-essential: CD, B'C
F = B'D' + AC + A'BD + (CD OR B'C)
C
01
1
D
Essential: xz, x'z'
Non-essential: w'x, w'z'
F = xz + x'z' + (w'x or w'z')
01
m10
1
(a)
00
1
m11
1
B
m14
1
m8
10
1
m6
m15
11
1
10
m2
1
z
AB
11
m1
01
x
m14
1
m9
C
00
00
1
m15
CD
m0
1
m12
10
AB
10
1
m4
w
11
1
m11
1
m14
x
1
m10
1
z
(d)
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
34
Essential: BC', AC, A'B'D
Non-Essential: A'B
F = BC' + AC + A'B'D
AB
Essential: wy', xy, w'x'z
F = wy' + xy + w'x'z
CD
C
00
01
m0
00
11
m1
1
m3
m2
m7
m6
1
m4
m5
m12
m13
01
A
m8
10
01
m5
m12
m13
01
m2
m7
m6
1
1
1
m15
11
m11
m8
1
x
m14
1
w
m10
1
10
m3
1
m4
10
m9
m11
m10
1
1
z
D
11
m1
1
B
m14
1
m9
1
y
00
00
1
m15
1
yz
m0
1
1
11
wx
10
Essential: BD, B'C', C'D
F = BD + B'C' + C'D
Essential: x'z', w'y'z, xyz
F = x'z' + w'y'z + xyz
3.10
wx
yz
y
00
m0
00
01
m1
m3
m2
m5
m7
m6
1
m12
m8
10
m13
1
m15
m9
1
m11
1
C
00
00
01
m1
m3
m5
m7
m14
1
m12
1
m13
A
m15
1
m8
1
10
m9
m11
1
1
z
1
m6
1
11
m10
10
m2
1
01
x
11
1
m4
1
1
CD
m0
1
01
11
AB
10
1
m4
w
11
m14
m10
1
D
F = Σ(0, 2, 5, 7, 8, 10, 12, 13, 14, 15)
Essential: xz, wx, x'z'
F = xz + wx + x'z'
(a)
F = Σ(0, 2, 3, 5, 7, 8, 10, 11, 14, 15)
Essential: AC, B'D', CD, A'BD
F = AC + B'D' + CD + A'BD
B
1
(b)
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
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rights
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35
CD
AB
C
00
01
m0
m1
m4
m5
00
11
m3
1
01
1
m13
1
A
m8
m9
m11
10
m13
m8
m9
10
AB
(c)
CD
m0
00
01
m1
1
m4
11
m3
1
m5
m12
m13
wx
10
m9
1
m11
B
m10
1
(d)
y
00
01
m1
1
01
m14
yz
m4
F(A, B, C, D) = S(0, 1, 3, 7 8, 9, 10,13,15)
Essential: B'C', AB'D'
Non-essential: ABD, A'CD, BCD
F = B'C' + AB'D' +A'CD +ABD
(e)
00
11
m2
m7
m6
1
1
1
m13
1
m15
11
w
10
m3
1
m5
m12
1
1
m0
m2
D
m6
m15
1
m8
10
1
11
m10
1
F = Σ(0, 1, 4, 5, 6, 7, 9, 11, 14, 15)
Essential: w'y', xy, wx'z
Non-essential: wx, x'y'z, w'wz, w'x'z
F = w'y' + xy + wx'z
1
m7
01
A
C
00
1
m11
1
x
m14
z
F = Σ(1, 3, 4, 5, 10, 11, 12, 13, 14, 15)
Essential: AC, BC', A'B'D
Non-essential: AB, Aʹ′Bʹ′D, Bʹ′CD, Aʹ′Cʹ′D
F = AC + BCʹ′ + Aʹ′Bʹ′D
1
m15
D
m6
1
1
w
1
m2
m7
1
11
m10
1
m5
m12
1
10
m3
1
1
B
11
m1
1
01
m14
1
01
m4
m6
m15
1
y
00
00
1
m7
yz
m0
m2
1
m12
11
wx
10
1
m14
x
1
m8
m9
m11
10
m10
1
z
F = S(0, 1, 2, 4, 5, 6, 7, 10, 15)
Essential: w'y', w'z', xyz, x'yz'
Non-Essential: w'x
F = w'y' + w'z' + xyz + x'yz'
(f)
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
36
3.11
(a)
F(w,
x,
y,
z)
=
∑
(0,
1,
2,
5,
8,
10,
13)
y
yz
wx
00
m0
00
01
m1
1
m4
wx
10
m3
m2
m7
m6
1
m5
01
1
m13
11
m8
10
m9
m15
x
m14
m11
w
m10
1
F
=
x'z'
+
w'x'y'
+
xy'z
11
m1
m3
m4
m5
m7
1
m8
m6
1
m13
1
10
10
m2
1
11
1
01
m0
m12
z
00
01
1
w
y
yz
00
1
m12
11
m15
1
m9
m11
1
1
m14
x
1
m10
1
z
F'
=
yz
+
xy
+
xz'
+
wx'z
F
=
(y'
+
z')(x'
+
y')(x'
+
z)(w'
+x
+
z')
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
3.12
37
(a)
F = Π(1, 3, 5, 7, 13, 15)
F' = A'D + B'D
F = (A + Dʹ′)(Bʹ′ + Dʹ′)
F = C'D' + AB' + CD'
AB
CD
C
00
m0
01
m1
00
m4
m7
0
m12
m6
0
m13
m15
0
m8
m2
0
m5
11
10
m3
0
01
A
11
B
m14
0
m9
m11
m10
10
D
(b)
F = Π(1, 3, 6, 9, 11, 12, 14)
F' = B'D + BCD' + ABD'
F = (B + D')(B' + C' + D)(A' + B' + D)
F = BD + B'D' + A'C'D'
AB
CD
C
00
00
01
11
A
10
01
11
m1
m4
m5
m7
m6
m12
m13
m15
m14
m8
m9
m11
m10
0
m3
10
m0
0
0
0
0
m2
0
B
0
D
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
38
3.13
(a) F = x'z' + y'z' + yz' + xy = x'z' + z' + xy = z' + xy
x
y
yz
00
m0
0
11
m1
m3
10
m2
1
m4
x
01
1
m5
1
m7
m6
1
1
1
z
F' = x'z + y'z
F = (x + z')(y + z')
(b) F = ACD' + C'D + AB' + ABCD
AB
CD
C
00
m0
01
m1
00
m4
m5
m2
m7
m6
1
m12
m13
11
m15
1
m8
10
10
m3
1
01
A
11
m9
1
1
m11
1
1
m14
B
1
m10
1
D
F = AC + AB' + C'D
F' = A'C + A'D' + BC'D'
F = (A + C')(A + D)(B'+C + D)
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
39
(c)
F = (A' + B + D')(A' + B' + C')(A' + B' + C)(B' + C + D')
F' = AB'D + ABC + ABC' + BC'D
AB
CD
C
00
m0
01
m1
00
m4
m5
10
m3
0
01
m2
0
m7
m6
0
m12
11
A
11
m13
0
m8
m15
0
m9
m14
0
B
0
m11
m10
10
D
F' = AB + BC'D
F = (A' + B')(B' + C + D')
F = A'D' + A'BC + AB'
AB
CD
C
00
m0
00
m4
11
m5
m13
10
m2
0
m7
m15
0
m11
1
1
m6
1
0
m9
1
m3
0
0
m8
11
0
1
m12
10
m1
1
01
A
01
1
1
m14
B
0
m10
1
D
Digital
Design
With
An
Introduction
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HDL
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2012,
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40
(d)
F = BCD' + ABC' + ACD
AB
CD
C
00
01
11
AB
10
m0
m1
m3
m2
m4
m5
m7
m6
m12
m13
m15
m14
C
00
m0
00
00
01
1
m8
1
01
B
m9
11
0
0
10
m3
m2
0
0
m7
0
m13
m6
0
m15
m14
11
m11
10
m1
m5
m12
1
01
0
m4
1
11
A
CD
A
m10
1
B
0
m8
10
m9
0
m11
m10
0
D
0
D
F' = A'C' + A'D + B'C' + A'B' + ACD'\
F = (A + C)(A + D') (B + C)(A + B)(A' +C' + D)
3.14
AB
CD
C
00
m0
00
01
m1
1
m4
11
m3
m5
m7
m0
m6
01
m1
11
m3
m13
m15
m4
m14
B
m9
m11
10
m10
1
1
m5
11
A
m13
m9
0
m15
0
0
m6
0
0
m8
10
m7
0
m12
1
10
m2
0
01
11
m8
C
00
00
1
m12
CD
m2
1
01
A
AB
10
0
m14
B
0
m11
m10
0
D
D
SOP form (using 1s):
F = A'BC'D + AB'CD + A'B'C' + ACD'
F = A'B'C' + A'C'D + AB'C + ACD'
POS form (using 0s):
F' = AC' + A'C + A'C'D' + ABD
F = (A' + C)(A + C')(A + C + D)(A' + B' + D')
Alternative POS:
F' = AC' + A'C + A'C'D' + BCD
F = (A' + C)(A + C')(A + C + D)(B' + C' + D')
Digital
Design
With
An
Introduction
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Verilog
HDL
–
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Copyright
2012,
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41
3.15
AB
CD
C
00
m0
00
x
00
m0
0
11
m1
1
m4
x
01
m3
1
m7
1
A
m6
1
x
m3
m2
m5
m7
m6
x
1
m13
11
x
m8
m9
CD
m0
11
m1
m3
00
m4
m5
m2
m0
11
m15
1
m8
1
m9
10
B
A
m10
m5
m7
m15
m14
m9
m11
m10
x
B
1
D
3.16
x
m13
1
D
F = BC + CD + ABD' + A'BD
F = Σ(3, 5, 6, 7, 11, 12, 14, 15)
10
m2
m6
1
m8
10
m3
1
11
x
m1
11
1
m12
1
m11
x
01
m14
01
x
m4
1
C
00
m6
1
m13
m10
x
CD
00
m7
1
m12
A
AB
10
x
01
m11
F = A'D' + B'D' + BCD' + ABC'D
F = Σ(0, 2, 4, 6, 8, 10, 13, 14)
C
01
B
1
D
F=1
F = Σ(0,1, 2, 3, 4, 5, 6, 7)
00
m14
1
z
AB
m15
1
10
1
10
m1
x
m12
m2
x
m5
1
01
10
11
1
m4
y
yz
01
F = B'D' + C'D' + A'BC
F = F = Σ(0, 2, 4, 6, 7, 8, 10, 12)
(a)
AB
CD
C
00
m0
00
m4
m3
11
m5
m7
m13
m15
1
m9
m11
1
1
D
F = C + D'
F = (C'D)'
1
m6
1
1
m8
10
m2
1
1
m12
10
m1
11
1
01
A
01
1
m14
1
B
D'
C
F
m10
1
Digital
Design
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HDL
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42
(b)
AB
CD
C
00
01
m0
11
m1
00
1
m4
10
m3
m2
F = AD + B'D + CD
F = ((AD)' (B'D)' (CD)')'
1
m5
m7
m6
01
A
D
1
m12
m13
11
m15
1
A
m8
m9
m11
10
B
m14
B'
D
1
1
m10
F
C
D
1
D
(c)
F = (A' + C' + D')(A' + C')(C' + D')
F' = (A' + C' + D')' + (A' + C')' + (C' + D')'
F' = ACD + AC + CD
AB
CD
C
00
01
m0
00
m1
1
1
11
A
(d)
F
0
m11
1
B
m14
0
m9
1
C
1
m15
1
m8
10
m6
0
m13
1
1
m7
1
m12
m2
0
m5
F = C' + A'D'
F = (C(A + D))'
F = (C(A'D')')'
10
m3
1
m4
01
11
A'
D'
m10
0
0
D
AB
CD
C
00
m0
00
01
m12
m3
m13
m15
m9
1
m11
1
1
A
m6
1
1
F = A' + B + D'
F = (A(B')D)'
10
m2
1
m7
1
1
m8
11
1
m5
1
11
10
m1
1
m4
A
01
1
m14
B
B'
F
1
m10
D
1
D
Digital
Design
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An
Introduction
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HDL
–
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Copyright
2012,
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43
3.17
AB
CD
C
00
m0
00
01
11
m1
1
10
m3
1
m2
1
m4
m5
m7
m6
m12
m13
m15
m14
m8
m9
m11
m10
01
1
11
A
A'
B'
1
B
B'
C
F'
1
10
1
1
C
D'
D
F = A'B' + B'C + CD'
F = ((A + B)(B + C') (C' + D))'
F = ((A'B')'(B'C)'(CD')' )'
F' = (A'B')'(B'C)'(CD')'
3.18
F = (A ⊕ B)'(C ⊕ D) = (AB' + A'B)'(CD' + C'D)
= (AB + A'B')(CD' + C'D) = ABCD' + ABC'D + A'B'CD' + A'B'C'D
F' = (AB + A'B')' + (CD' + C'D)'
F' = ( (A' + B')' + (A + B)' )' + ( (C' + D)' + (C + D')' )'
AB
CD
C
00
m0
01
m1
00
11
m3
10
m2
1
A'
B'
1
m4
m5
m7
m6
m12
m13
m15
m14
m8
m9
m11
m10
A
B
01
11
A
1
1
10
B
F'
C'
D
C
D'
D
Digital
Design
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HDL
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44
3.19
(a) F = (w + zʹ′)(xʹ′ + zʹ′)(wʹ′ + xʹ′ + yʹ′)
yz
wx
y
00
00
01
11
w
10
m0
m4
1
1
m12
1
m8
1
01
11
10
m1
m3
m2
m5
m7
m6
m13
m15
m14
m9
1
m11
1
y
z
1
x
F
w
z
m10
1
w
x
1
z
(b)
wx
F = y'z' + wx' + w'z'
F =[(y + z)' + (w' + x)' + (w + z)']
F' =[(y + z)' + (w' + x)' + (w + z)']'
yz
y
00
m0
00
01
m1
11
m3
1
10
m2
y
z'
y'
z
1
m4
m5
m7
m6
m12
m13
m15
m14
m9
m11
01
11
w
1
m8
x
1
m10
F'
w
x'
w'
x
10
z
F = Σ(0, 3, 12, 15)
F' =y'z+yz' + w'x + wx' = [(y + z')(w + x')(w + x')(w' + x)]'
F = (y + z')' + (y' + z)' + (w + x')' + (w' + x)'
(c) F = [(x + y)(x' + z)]' = (x + y)' + (x' + z)'
F' = [(x + y)' + (x' + z)']'
x
y
x'
z
F'
Digital
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HDL
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3.20
45
Multi-level NOR:
F = ACD(B + C) + (BC' + DE')
F' = [ACD(B + C) + (BC' + DE')]'
F' = [(A' + C' + D')'(B + C) + (B' + C)' + (D' + E)']'
F' = [((A' + C' + D') + (B + C)' )' + (B' + C)' + (D' + E)']'
F' = [(A' + C' + D' + (B + C)')' + (B' + C)' + (D' + E)']'
A'
C'
D'
B
C
B'
C
F'
D'
E
Multi-level NAND:
F = CD(B + C)A + (BC' + DE')
F' = [CD(B + C)A]' [BC' + DE']'
F' = [CD(B'C')'A]' [BC' + DE']'
F' = [CD(B'C')'A]' [[ (BC')' (DE')]' ]'
B'
C'
A
C
D
F
B
C'
D
E'
3.21
F = w(x + y + z) + xyz
F' = [w(x + y + z)]'[xyz]' = [w(x'y'z')')]'(xyz)'
x
y
z
x'
y'
F
z'
w
Digital
Design
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HDL
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46
3.22
z
D
C
y
B
x
w
A
z
D
C
y
B
x
w
A
Digital
Design
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HDL
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47
3.23
AB
CD
C
00
m0
00
01
m5
m12
11
10
m3
m2
m7
m6
m15
m14
x
1
11
1
A
B'
x
m13
1
m8
10
m1
x
m4
A
01
B
C'
D
1
m9
m11
F
m10
x
1
D
F = B'D' + AD' + C'D'
F' = D + A'BC
F = [D + A'BC]' = [D + (A + B' + C')']'
3.24
F(A, B, C, D) = S(0, 4, 8, 9, 10, 11, 12, 14)
AB
CD
C
00
00
01
11
A
10
m0
01
11
10
m1
m3
m2
m5
m7
m6
m12
m13
m15
m14
m8
m9
m11
m10
m4
1
1
1
1
1
1
B
1
1
D
(a) F = C'D' + AB' + AD'
F' = (C'D')'(AB')'(AD')'
AND-NAND:
C'
D'
A
B'
F
A
D'
(b) F' = [C'D' + AB' + AD']'
AND-NOR:
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48
C'
D'
F’
A
B'
A
D'
(c) F = C'D' + AB' + AD' = (C + D)' + (A' + B)' + (A' + D)'
F' = (C'D')'(AB')'(AD')' = (C + D)(A' + B)(A' + D)
F = [ (C + D)(A' + B)(A' + D) ]'
OR-NAND:
C
D
F
A'
B
A'
D
(d) F = C'D' + AB' + AD' = (C + D)' + (A' + B)' + (A' + D)'
NOR-OR:
C
D
F
A'
B
A'
D
3.25
A
B
A
B
ABCD
C
D
A+B+C+D
C
D
AND-AND
AND
OR-OR
OR
A
B
(AB CD)'
C
D
A
B
(A + B + C + D)'
C
D
AND-NAND
NAND
OR-NOR
NOR
A
B
(A'B'C'D')'
C
D
A+B+C+D
NOR-NAND
OR
A
B
[(AB)' + (C' D')]'
C
D
NAND-NOR
ABCD
AND
Digital
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HDL
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49
A'B'
A
B
A
B
A'B'C'D'
C
D
NOR-AND
A' + B' + C' + D'
(A + B + C + D)'
C
D
C'D' (A + B + C + D)'
NOR
NAND-OR
NAND
The degenerate forms use 2-input gates to implement the functionality of 4-input gates.
3.26
g = (a + b +c' + d')(b' + c' + d)(a'+ c + d')
g' = a'b'cd + bcd' + ac'd
cd
c
ab
00
01
11
10
f = abc' + c'd + a'cd'+ b'cd'
ab
cd
c
00
00
01
11
a
10
01
m0
m1
m4
m5
m12
m8
1
11
10
m3
m2
m7
m6
m13
m15
m14
m9
m11
m10
1
1
1
1
1
00
1
01
b
11
a
1
10
m0
m4
1
1
m1
m5
1
1
m3
m7
0
1
m6
1
0
m12
m13
m15
m14
m8
m9
m11
m10
1
1
0
0
d
1
1
d
b
0
1
fg = ac'd + abc'd + b'cd'
3.27
m2
x⊕ y = x'y + xy'; Dual = (x' + y)(x + y') = (x⊕ y)'
3.28
x
y
x
y
P
z
(a) 3-bit odd parity generator
C
z
P
(b) 4-bit odd parity generator
Digital
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3.29
50
D=A⊕ B⊕C
E = A'BC + AB'C = (A ⊕ B)C
F = ABC' + (A' + B')C = ABC' + (AB)'C = (AB) ⊕ C
G = ABC
A
B
Half-Adder
S
C
A
B
C
Half-Adder
Half-Adder
AB
3.30
S
D=A
B
C
C
E = (A
B)C
S
F = (AB)
C
G = ABC
C
F = AB'CD' + A'BCD' + AB'C'D + A'BC'D
F = (A ⊕ B)CD' + (A ⊕ B) C'D = (A ⊕ B)(C ⊕ D)
A
B
F
C
D
3.31
Note: It is assumed that a complemented input is generated by another circuit that
is not part of the circuit that is to be described.
(a)
module Fig_3_20a_gates (F, A, B, C, C_bar, D);
output F;
input
A, B, C, C_bar, D;
wire
w1, w2, w3, w4;
and
(w1, C, D);
or
(w2, w1, B);
and
(w3, w2, A);
and
(w4, B, C_bar);
or
(F, w3, w4);
endmodule
(b)
module Fig_3_20b_gates (F, A, B, B_Bar, C, C_bar, D);
output F;
input
A, B, B_bar, C, C_bar, D;
wire
w1, w2, w3, w4;
not
(w1_bar, w1);
not
(w3_bar, w3);
not
(w4_bar, w4);
nand
(w1, C, D);
or
(w2, w1_bar, B);
nand
(w3, w2, A);
nand
(w4, B, C_bar);
or
(F, w3_bar, w4_bar);
endmodule
Digital
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HDL
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2012,
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51
(c)
module Fig_3_21a_gates (F, A, A_bar, B, B_bar, C, D_bar);
output F;
input A, A_bar, B, B_bar, C, D_bar;
wire
w1, w2, w3, w4;
and
(w1, A, B_bar);
and
(w2, A_bar, B);
or
(w3, w1, w2);
or
(w4, C, D_bar);
and
(F, w3, w4);
endmodule
(d)
module Fig_3_21b_gates (F, A, A_bar, B, B_bar, C_bar, D);
output F;
input
A, A_bar, B, B_bar, C_bar, D;
wire
w1, w2, w3, w4, F_bar;
nand
(w1, A, B_bar);
nand
(w2, A_bar, B);
not
(w1_bar, w1);
not
(w2_bar, w2);
or
(w3, w1_bar, w2_bar);
or
(w4, w5, w6);
not
(w5, C_bar);
not
(w6, D);
nand
(F_bar, w3, w4);
not
(F, F_bar);
endmodule
(e)
module Fig_3_24_gates (F, A, A_bar, B, B_bar, C, D_bar);
output F;
input
A, A_bar, B, B_bar, C, D_bar
wire
w1, w2, w3, w4, w5, w6, w7, w8, w7_bar, w8_bar;
not
(w1_bar, w1);
not
(w2_bar, w2);
not
(w3, E_bar);
nor
(w1, A, B);
nor
(W2, C, D);
and
(F, w1_bar, w2_bar, w3);
endmodule
(f)
module Fig_3_25_gates (F, A, A_bar, B, B_bar, C, D_bar);
output F;
input A, A_bar, B, B_bar, C, D_bar;
wire
w1, w1_bar, w2, w2_bar;
wire
w3, w4, w5, w6, w7, w8;
not
(w1, A_bar);
not
(w2, B);
not
(w3, A);
not
(w4, B_bar);
and
(w5, w1_bar, w2_bar));
and
(w6, w3, w4);
nor
(w7, w5, w6);
nor
(w8, c, d_bar);
and
(F, w7, w8);
endmodule
Digital
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HDL
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2012,
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3.32
52
Note: It is assumed that a complemented input is generated by another circuit that
is not part of the circuit that is to be described.
Note:
Because
the
signals
here
are
all
scalar–valued,
the
logical
operators
(!,
&&,
and
||)
are
equivalent
to
the
bitwise
operators
(~,
&,
|).
If
the
operands
are
vectors
the
bitwise
operators
produce
a
vector
result;
the
logical
operators
would
produce
a
sclara
result
(true
or
false).
(a)
module Fig_3_20a_CA (F, A, B, C, C_bar, D);
output F;
input
A, B, C, C_bar, D;
wire
w1, w2, w3, w4;
assign w1 = C && D;
assign w2 = w1 || B;
assign w3 = !(w2 && A);
assign w4 = !w3;
assign w5 = !(B && C_bar);
assign w5_bar = !w5;
assign F = w4 || w5_bar);
endmodule
(b)
module Fig_3_20b_CA (F, A, B, C, C_bar, D);
output F;
input
A, B, B_bar, C, C_bar, D;
wire
w2 = !w1;
wire
w3 = !B_bar;
wire
w4, w5, w5_bar, w6, w6_bar;
assign w1 = !(C && D);
assign w4 = w2 || w3;
assign w5 = !(w4 && A);
assign w5_bar = !w5;
assign w6 = !(B && C_bar);
assign w6_bar = !w6;
assign F = w5_bar || w6_bar;
endmodule
module Fig_3_21a_CA (F, A, A_bar, B, B_bar, C, D_bar);
output F;
input
A, A_bar, B, B_bar, C, D_bar;
wire
w1, w2, w3, w4;
assign w1 = A && B_bar;
assign w2 = A_bar && B;
assign w3 = w1 || w2);
assign w4 = C || D_bar;
assign F = w3 || w4;
endmodule
(c)
(d)
module Fig_3_21b_CA (F, A, A_bar, B, B_bar, C_bar, D);
output F;
input
A, A_bar, B, B_bar, C_bar, D;
wire
w1, w2, w1_bar, w2_bar, w3, w4, w5, w6, F_bar;
assign w1 = !(A && B_bar);
assign w2 = !(A_bar && B);
assign w1_bar = !w1;
assign w2_bar = !w2;
assign w3 = w1_bar || w2_bar;
assign w4 = !C_bar;
assign w5 = !D;
assign w6 = w4 || w5;
assign F_bar = !(w3 && w6);
assign F = !F_bar;
endmodule
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
3.33
53
(e)
module Fig_3_24_CA (F, A, B, C, D, E_bar);
output F;
input
A, B, C, D, E_bar;
wire
w1, w2, w1_bar, w2_bar, w3_bar;
assign w1 = !(A || B);
assign w1_bar = !w1;
assign w2 = !(C || D);
assign w2_bar = !w2;
assign w3 = !E_bar;
assign F = w1_bar && w2_bar && w3;
endmodule
(f)
module Fig_3_25_CA (F, A, A_bar, B, B_bar, C, D_bar);
output F;
input
A, A_bar, B, B_bar, C, D_bar
wire
w1, w2, w3, w4, w5, w6, w7, w8, w9, w10;
assign w1 = !A _bar;
assign w2 = !B;
assign w3 = w1 && w2;
assign w4 = !A;
assign w5 = !B_bar;
assign w6 = w4 && w5;
assign w7 = !(C || D_bar);
assign w8 = !(w3 || w6);
assign w9 = !w8;
assign w10 = !w7;
assign F = w9 && w10;
endmodule
(a)
Initially, with xy = 00, w1 = w2 = 1, w3 = w4 = 0 and F = 0. w1 should change to 0 3ns after xy
changes to 01. w4 should change to 1 6ns after xy changes to 01. F should change from 0 to 1 8ns
after w4 changes from 0 to 1, i.e., 14 ns after xy changes from 00 to 01.
w3
x
w1
6
F=x
y
3
3
8
w2
y
6
w4
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
54
(b)
`timescale 1ns/1ps
module Prob_3_33 (F, x, y);
wire w1, w2, w3, w4;
and #6 (w3, x, w1);
not #3 (w1, x);
and #6 (w4, y, w1);
not #3 (w2, y);
or #8 (F, w3, w4);
endmodule
module t_Prob_3_33 ();
reg x, y;
wire F;
Prob_3_33 M0 (F, x, y);
initial #200 $finish;
initial fork
x = 0;
y = 0;
#20 y = 1;
join
endmodule
(c) To simulate the circuit, it is assumed that the inputs xy = 00 have been applied sufficiently long for
the circuit to be stable before xy = 01 is applied. The testbench sets xy = 00 at t = 0 ns, and xy = 1 at t =
10 ns. The simulator assumes that xy = 00 has been applied long enough for the circuit to be in a stable
state at t = 0 ns, and shows F = 0 as the value of the output at t = 0. For illustration, the waveforms show
the response to xy = 01 applied at t = 10 ns.
Name
x
w1
y
w2
w3
w4
F
t = 10 ns
t = 24 ns
Note: input change occurs at t = 10 ns.
t = 16 ns
Δ = 14 ns
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
55
3.34
module Prob_3_34 (Out_1, Out_2, Out_3, A, B, C, D);
output Out_1, Out_2, Out_3;
input
A, B, C, D;
wire
A_bar, B_bar, C_bar, D_bar;
assign A_bar = !A;
assign B_Bar = !B;
assign C_bar = !C;
assign D_bar = !D;
assign Out_1 = (A + B_bar) && C_bar && ( C || D);
assign Out_2 = ( (C_bar && D) || (B && C && D) || (C && D_bar) ) && (A_bar || B);
assign Out_3 = (((A && B) || C) && D) || (B_bar && C);
endmodule
3.35
module Exmpl-3(A, B, C, D, F)
inputs A, B, C, Output D, F,
output B
and g1(A, B, B);
not (D, B, A),
OR (F, B; C);
endofmodule;
// Line 1
// Line 2
// Line 3
// Line 4
// Line 5
// Line 6
// Line 7
Line 1: Dash not allowed character in identifier; use underscore: Exmpl_3. Terminate line with semicolon
(;).
Line 2: inputs should be input (no s at the end). Change last comma (,) to semicolon (;). Output is
declared but does not appear in the port list, and should be followed by a comma if it is intended to
be in the list of inputs. If Output is a mispelling of output and is to declare output ports, C should
be followed by a semicolon (;) and F should be followed by a semicolon (;).
Line 3: B cannot be declared both as an input (Line 2) and output (Line 3). Terminate the line with a
semicolon (;).
Line 4: A cannot be an output of the primitive if it is an input to the module
Line 5: Too many entries for the not gate (may have only a single input, and a single output). Termiante
the line with a semicolon, not a comma.
Line 6: OR must be in lowercase: change to “or”. Replace semicolon by a comma (B,) in the list of ports.
Line 7: Remove semicolon (no semicolon after endmodule).
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
3.36
56
(a)
B
C
D
x
d
z
a
A
w
F
y
(b)
A1 A0 B1 B0
w1
w6
w2
w7
w3
w4
F1
F2
F3
w5
(c)
a
b
y1
y2
y3
Digital
Design
With
An
Introduction
to
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Verilog
HDL
–
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Manual.
M.
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M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
57
3.37
UDP_Majority_4 (y, a, b, c, d);
output
y;
input
a, b, c, d;
table
// a b c d : y
0 0 0 0 : 0;
0 0 0 1 : 0;
0 0 1 0 : 0;
0 0 1 1 : 0;
0 1 0 0 : 0;
0 1 0 1 : 0;
0 1 1 0 : 0;
0 1 1 1 : 1;
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1
endtable
endprimitive
:
:
:
:
:
:
:
:
0;
0;
0;
0;
0;
0;
1;
1;
3.38
module t_Circuit_with_UDP_02467;
wire E, F;
reg A, B, C, D;
Circuit_with_UDP_02467 m0 (E, F, A, B, C, D);
initial #100 $finish;
initial fork
A = 0; B = 0; C = 0; D = 0;
#40 A = 1;
#20 B = 1;
#40 B = 0;
#60 B = 1;
#10 C = 1; #20 C = 0; #30 C = 1; #40 C = 0; #50 C = 1; #60 C = 0; #70 C = 1;
#20 D = 1;
join
endmodule
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
58
// Verilog model: User-defined Primitive
primitive UDP_02467 (D, A, B, C);
output D;
input A, B, C;
// Truth table for D = f (A, B, C) = S (0, 2, 4, 6, 7);
table
// A B C : D // Column header comment
0 0 0 : 1;
0 0 1 : 0;
0 1 0 : 1;
0 1 1 : 0;
1 0 0 : 1;
1 0 1 : 0;
1 1 0 : 1;
1 1 1 : 1;
endtable
endprimitive
// Verilog model: Circuit instantiation of Circuit_UDP_02467
module Circuit_with_UDP_02467 (e, f, a, b, c, d);
output e, f;
input
a, b, c, d;
UDP_02467 M0 (e, a, b, c);
and
(f, e, d);
//Option gate instance name omitted
endmodule
A
10
20
30
40
50
60
70
80
10
20
30
40
50
60
70
80
10
20
30
40
50
60
70
80
10
20
30
40
50
60
70
80
10
20
30
40
50
60
70
80
10
20
30
40
50
60
70
80
t, ns
B
t, ns
C
t, ns
D
t, ns
E
t, ns
F
t, ns
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
59
3.39
a
0
0
1
1
b
0
1
0
1
s
0
1
1
0
c
0
0
0
1
s = a'b + ab' = a ^ b
c = ab = a && b
module Prob_3_39 (s, c, a, b);
input a, b;
output s, c;
xor (s, a, b);
and (c, a, b);
endmodule
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
60
CHAPTER 4
4.1
(a)
T1 = B'C, T2 = A'B, T3 = A + T1 = A + B'C,
T4 = D ⊕ T2 = D ⊕ (A'B) = A'BD' + D(A + B') = A'BD' + AD + B'D
F1 = T3 + T4 = A + B'C + A'BD' + AD + B'D
With A + AD = A and A + A'BD' = A + BD':
F1 = A + B'C + BD' + B'D
Alternative cover: F1 = A + CD' + BD' + B'D
F2 = T2 + D' = A'B + D'
AB
ABCD T1 T2 T3 T4
F1 F2
0000
0001
0010
0011
0100
0101
0110
0111
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1000
1001
1010
1011
1100
1101
1110
1111
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
CD
M0
00
11
M1
M3
M2
M5
M7
M6
01
M0
11
1
M13
1
M15
M4
1
M8
1
M9
M11
1
11
D
F2 = A'B + D'
M2
1
1
M5
M7
M6
M13
M15
M14
1
1
A
1
M8
10
M9
1
1
M11
1
B
1
M10
1
1
D
F1 = A + B'C+ B'D + BD'
AB
CD
C
00
01
M4
M5
M7
M6
M13
M15
M14
1
11
1
1
1
1
M8
10
M2
1
1
M12
A
M3
10
M1
01
B
11
M0
00
M10
1
10
M3
1
M12
1
M14
M1
11
1
01
1
1
M12
01
00
10
1
M4
10
01
C
00
C
00
A
CD
M9
1
1
M11
1
1
B
1
M10
1
D
F1 = A + CD' + B'D + BD'
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
61
4.2
[(A'D)' A']'= A + D
A'
A
F
B
C
BC + A'
BC
G
D
(A'D)' = A + D’
F = (A + D)(A' + BC) = A'D + ABC + BCD += A'D + ABC
F = (A + D')(A' +BC) = A'D' + ABC + BCD' = A'D' + ABC
AB
CD
C
00
00
01
11
A
10
01
m0
m1
m4
m5
11
m3
1
m7
1
AB
10
m2
1
01
m12
m13
m15
m14
m8
m9
m11
m10
1
B
1
C
00
00
m6
1
CD
11
A
10
m0
11
10
m1
m3
m2
m5
m7
m6
m12
m13
m15
m14
m8
m9
m11
m10
m4
D
1
1
1
1
1
B
1
D
G = A'D' + ABC + BCD' = A'D' + ABC
F = A'D + ABC + BCD = A'D + ABC
4.3
01
(a) Yi = (AiS' + BiS)E' for i = 0, 1, 2, 3
(b) 1024 rows and 14 columns
4.4
(a)
xyz
F
000
001
010
011
100
101
110
111
1
1
1
0
0
0
0
0
x
00
0
x
y
yz
1
m0
m4
1
01
m1
11
1
m5
10
m3
m2
m7
m6
1
x'
y'
F
x'
y'
z
F = x'y' + x'z'
Digital
Design
With
An
Introduction
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Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
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rights
reserved.
62
(b)
xyz
F
000
001
010
011
100
101
110
111
0
1
0
0
0
0
0
0
x
00
0
x
y
yz
1
01
m0
m1
m4
m5
11
m3
1
1
m7
1
10
m2
z
F
m6
1
z
F=z
4.5
xyz
ABC
000
001
010
011
100
101
110
111
010
011
100
101
001
010
011
100
x
00
0
x
A
yz
1
y
01
11
m0
m1
m3
m4
m5
m7
10
m2
1
x'
y
1
A
m6
1
y
z
z
A = x'y + yz
x
00
0
x
B
yz
1
m0
1
m4
y
01
m1
m5
11
1
1
10
m3
m2
m7
m6
y
00
0
x
1
z'
C
01
m0
m1
m4
m5
1
1
B
x
B = x'y' + y'z + xyz'
x
y'
z
1
z
yz
x
y'
y
11
m3
1
m7
10
m2
m6
1
x
z
C
z
C= x'z + xz'
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
63
4.6
xyz
F
000
001
010
011
100
101
110
111
0
0
0
1
0
1
1
1
x
00
0
x
A
yz
1
01
m0
m1
m4
m5
1
y
11
m3
m7
1
1
10
m2
m6
z
F = xz + yz + xy
1
x
z
y
z
x
y
F
module Prob_4_6 (output F, input x, y, z);
assign F = (x & z) | (y & z) | (x & y);
endmodule
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
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M.
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M.D.
Ciletti,
Copyright
2012,
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rights
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64
4.7
(a)
ABCD
0000
0001
0011
0010
0110
0111
0101
0100
wxyz
1100
1101
1111
1110
1010
1011
1001
1000
1000
1001
1010
1011
1100
1101
1110
1111
0000
0001
0010
0011
0100
0101
0110
0111
AB
CD
C
00
00
01
11
A
10
01
11
CD
10
m0
m1
m3
m2
m4
m5
m7
m6
m12
m13
m15
m14
m8
m9
m11
m10
1
1
1
1
1
00
01
B
1
1
11
A
1
10
D
CD
C
00
00
01
11
A
10
01
11
m1
m3
m4
m5
m7
m6
1
1
m2
1
m13
m15
m14
m8
m9
m11
m10
1
1
m4
1
m1
m5
1
11
10
m3
m7
m2
m6
1
1
m12
m13
m15
m14
m8
m9
m11
m10
1
1
1
CD
B
1
00
B
1
11
A
10
D
y = A'B'C A'BC' + ABC + AB'C'
= A'(A B) + A(B C)'
=A B C
= X C
C
00
01
m12
1
AB
10
m0
1
m0
01
D
x = AB' + A'B = A B
w=A
AB
C
00
01
m0
m1
m4
w
B
x
C
y
10
m3
m2
m5
m7
m6
m12
m13
m15
m14
m8
m9
m11
m10
1
1
1
1
z=A B
=y D
A
11
1
B
1
1
D
C
1
D
z
D
Digital
Design
With
An
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HDL
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Copyright
2012,
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65
(b)
module Prob_4_7(output w, x, y, z, input A, B, C, D);
always @ (A, B, C, D)
case ({A, B, C, D})
4'b0000:
{w, x, y, z} = 4'b0000;
4'b0001:
{w, x, y, z} = 4'b1111;
4'b0010:
{w, x, y, z} = 4'b1110;
4'b0011:
{w, x, y, z} = 4'b1101;
4'b0100:
{w, x, y, z} = 4'b1100;
4'b0101:
{w, x, y, z} = 4'b1011;
4'b0110:
{w, x, y, z} = 4'b1010;
4'b0111:
{w, x, y, z} = 4'b1001;
4'b1000:
4'b1001:
4'b1010:
4'b1011:
4'b1100:
4'b1101:
4'b1110:
4'b1111:
endcase
endmodule
{w, x, y, z} = 4'b1000;
{w, x, y, z} = 4'b0111;
{w, x, y, z} = 4'b0110;
{w, x, y, z} = 4'b0101;
{w, x, y, z} = 4'b0100;
{w, x, y, z} = 4'b0011;
{w, x, y, z} = 4'b0010;
{w, x, y, z} = 4'b0001;
Alternative
model:
module Prob_4_7(output w, x, y, z, input A, B, C, D);
assign w = A;
assign x = A ^ B);
assign y = x ^ C;
assign z = y ^ D;
endmodule
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
4.8
66
(a) The 8-4-2-1 code (Table 1.5) and the BCD code (Table 1.4) are identical for digits 0 – 9.
(b)
8421
Gray
ABCD wxyz
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
0000
0001
0011
0010
0110
0111
0101
0100
1100
1101
AB
CD
C
00
01
11
CD
10
m0
m1
m3
m2
m4
m5
m7
m6
m0
00
m4
01
m12
m13
m15
m14
B
11
m8
m5
10
m3
m2
m7
1
1
m6
1
1
m12
m13
m15
m14
m9
m11
1
A
m10
1
m8
m9
m11
m10
10
1
D
w = AB'C'
CD
B
01
11
m1
m3
m4
m5
m7
m6
m15
m14
1
m12
1
C
00
01
m0
m1
m4
m5
m12
m13
00
1
m13
CD
m2
1
01
AB
10
m0
00
1
D
x = AB'C' + A'B
C
00
m9
m11
m10
10
A
10
m3
m2
m7
m6
m15
m14
m11
m10
1
1
11
m8
11
1
01
B
11
A
m1
11
11
10
AB
01
00
01
A
C
00
1
B
1
m8
m9
10
D
y = A'BD' + A'B'D
D
z = A'C'D + BC'D + A'CD'
Digital
Design
With
An
Introduction
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the
Verilog
HDL
–
Solution
Manual.
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Copyright
2012,
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rights
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67
4.9
ABCD a b c
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
d
e f
g
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
AB
CD
C
00
m0
00
01
11
A
10
01
11
m1
m3
m4
m5
m7
m12
m13
m15
m14
m8
m9
m11
m10
1
1
1
1
m2
1
m6
1
CD
AB
10
1
00
1
C
00
01
B
11
A
10
m0
m4
1
01
m1
1
11
m3
10
m2
1
1
m5
m7
m12
m13
m15
m14
m8
m9
m11
m10
1
1
1
D
m6
1
B
D
a = A'C + A'BD + B'C'D' + AB'C'
b = A'B' + A'C'D' + A'CD + AB'C'
AB
CD
C
00
00
01
11
A
10
m0
m4
01
m1
1
m5
1
11
m3
1
m7
1
1
1
m2
m6
1
m13
m15
m14
m8
m9
m11
m10
1
C
00
00
m12
1
CD
AB
10
01
B
11
A
10
m0
01
11
10
m1
m3
m4
m5
m7
m6
m12
m13
m15
m14
m8
m9
m11
m10
1
1
1
1
D
m2
1
1
1
B
D
c = A'B + A'D + B'C'D' + AB'C'
d = A'CD' + A'B' C+ B'C'D' + AB'C' + A'BC'D
AB
CD
C
00
00
01
11
A
10
m0
01
11
m3
m2
m4
m5
m7
m6
m12
m13
m15
m14
m8
m9
m11
m10
1
1
D
e = A'CD' + B'C'D'
AB
10
m1
1
CD
00
00
1
C
01
B
11
A
10
m0
m4
1
1
01
11
m3
m2
m5
m7
m6
1
1
m13
m15
m14
m8
m9
m11
m10
1
D
f = A'BC' + A'C'D' + A'BD + AB'C'
C
00
00
m12
1
AB
10
m1
CD
01
B
11
A
10
01
11
10
m0
m1
m3
m4
m5
m7
m6
1
1
1
m2
1
1
m12
m13
m15
m14
m8
m9
m11
m10
1
1
D
g = A'CD' + A'B'C + A'BC' + AB'C'
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
B
68
4.10
ABCD wxyz
0000 0000
0001 1111
0010 1110
0011 1101
0100 1100
0101 1011
0110 1001
0111 1000
1000
1001
1010
1011
1100
1101
1110
1111
1000
0111
0110
0101
0100
0011
0010
0001
AB
CD
C
00
00
01
11
A
10
01
m0
m1
m4
m5
1
1
1
11
m3
m7
CD
10
m2
1
m6
1
1
m13
m15
m14
m8
m9
m11
m10
1
00
1
m12
01
B
11
A
10
D
w = A'(B + C + D) + AB'C'D'
= A (B + C + D)
AB
CD
00
01
11
A
10
01
m0
m1
m4
m5
m12
m8
11
m2
m7
m6
m13
m15
m14
m9
m11
m10
1
1
1
AB
10
m3
1
11
m1
m4
m5
m7
m6
m12
m13
m15
m14
m8
m9
m11
m10
1
1
1
1
m3
10
m0
m2
1
1
1
1
B
1
01
B
1
C
00
00
1
1
CD
11
A
10
01
11
m1
m4
m5
m12
m13
m15
m14
m8
m9
m11
m10
y = CD' + C'D = C
D
For a 5-bit 2's complementer with input E and output v:
1
1
1
1
m3
10
m0
D
v=E
01
D
x = B'(C + D) + CB'D'
= B (C + D)
C
00
C
00
m7
1
1
1
1
m2
m6
B
D
z=D
(A + B + C + D)
Digital
Design
With
An
Introduction
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Verilog
HDL
–
Solution
Manual.
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Ciletti,
Copyright
2012,
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rights
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69
4.11
(a)
A3
A2
A1
A0
1
x
x
y
Half Adder
Half Adder
S
C
x
y
Half Adder
S
C
x
y
Half Adder
S
C
y
S
C
Note: 5-bit output
(b)
A3
x
1
A2
B
x
y
Full Adder
D
1
A1
x
y
Full Adder
y
Full Adder
D
B
1
D
B
A0
1
x
y
Half Adder
B
D
Note: To decrement the 4-bit number, add -1 to the number. In 2's complement format ( add Fh ) to
the number. An attempt to decrement 0 will assert the borrow bit. For waveforms, see solution to
Problem 4.52.
4.12
(a)
x
0
0
1
1
y
0
1
0
1
B
0
1
0
0
D
0
1
1
0
(b)
x y Bin
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
B
0
1
1
1
0
0
0
1
D
0
1
1
0
1
0
0
1
D = x'y + xy'
B = x'y
Diff = x y z
Bout = x'y + x'z + yz
Digital
Design
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An
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HDL
–
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2012,
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70
4.13
4.14
Sum
C
V
(a)
1101
0
1
(b)
0001
1
1
(c)
0100
1
0
(d)
1011
0
1
(e)
1111
0
0
xor
AND OR
10
4.15
+ 5
+ 5
XOR
+ 10
= 30 ns
C4 = G3 + P3C3 = G3 + P3(G2 + P2G1 + P2P1G0 + P2P1P0C0)
= G3 + P3G2 + P3P2G1 + P3P2P1G0 + P3P2P1P0C0
4.16
(a)
(C'G'i + p'i)' = (Ci + Gi)Pi = GiPi + PiCi
= AiBi(Ai + Bi) + PiCi
= A iB i + P iC i = G i + P iC i
= AiBi + (Ai + Bi)Ci = AiBi + AiCi + BiCi = Ci+1
(PiG'i) ⊕ Ci = (Ai + Bi)(AiBi)' ⊕ Ci = (Ai + Bi)(A'i + B'i) ⊕ Ci
= (A'iBi + AiB'i) ⊕ Ci = Ai ⊕ Bi ⊕ Ci = Si
(b)
Output of NOR gate = (A0 + B0)' = P'0
Output of NAND gate = (A0B0)' = G'0
S1 = (P0G'0) ⊕ C0
C1 = (C'0G'0 + P'0)' as defined in part (a)
4.17
(a)
(C'iG'i + P'i)' = (Ci + Gi)Pi = GiPi + PiCi = AiBi(Ai + Bi) + PiCi
= A iB i + P iC i = G i + P iC i
= AiBi + (Ai + Bi)Ci = AiBi + AiCi + BiCi = Ci+1
(PiG'i)⊕Ci = (Ai + Bi)(AiBi)'⊕Ci = (Ai + Bi)(A'i + B'i)⊕Ci
= (A'iBi + AiB'i)⊕Ci = Ai⊕Bi⊕Ci = Si
(b)
Output of NOR gate = (A0 + B0)' = P'0
Output of NAND gate = (A0B0)' = G'0
S0 = (P0G'0)⊕C0
C1 = (C'0G'0 + P'0)'
as defined in part (a)
Digital
Design
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HDL
–
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Copyright
2012,
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rights
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71
4.18
Inputs Outputs
ABCD wxyz
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
AB
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000
CD
C
00
00
01
11
A
10
m0
1
m4
11
10
m1
1
11
m3
m2
m7
m6
00
01
m13
m15
m14
m8
m9
m11
m10
x
x
x
x
D
w = A'B'C'
C
01
11
10
1
00
1
01
m5
m7
m12
m13
m15
m14
m8
m9
m11
m10
x
x
10
CD
AB
m4
x
A
m2
m6
B
x
11
A
x
10
D
y=C
m0
m4
1
01
m1
m5
1
11
m3
10
m2
1
m7
1
m6
m12
m13
m15
m14
m8
m9
m11
m10
x
x
x
B
x
x
x
C
C
00
m0
m4
1
1
01
m1
m5
1
11
10
m3
m2
m7
m6
1
1
m12
m13
m15
m14
m8
m9
m11
m10
x
1
x
x
x
D
z = D'
C
00
D
x = BC' + B'C = B
m3
x
11
x
m1
1
B
x
m0
1
CD
AB
10
m12
00
01
01
m5
CD
00
d(A, b, c, d) = Σ(10, 11, 12, 13, 14, 15)
B
x
x
Digital
Design
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HDL
–
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2012,
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72
4.19
Mode = 0 FOR Add
Mode = 1 for Subtract
B3 B2 B1 B0
9's Complementer
(See Problem 4.18)
Select = 1
Select
Select = 0
Quadruple 2 x 1 MUX
A3 A2 A1 A0
Cin
BCD Adder (See Fig. 4.14)
Digital
Design
With
An
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HDL
–
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Copyright
2012,
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rights
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4.20
73
Combine the following circuit with the 4-bit binary multiplier circuit of Fig. 4.16.
C6
A3
B3
B2
Cout
D7
B1
C2
C1 C0
B0
4-bit Adder
D6
C5 C4 C3
D5
Augend
D4
D3
D2 D1 D0
4.21
A0
B0
A1
B1
A2
B2
x
A3
B3
x = (A0 B0)'(A1 B1)'(A2 B2)'(A3 B3)'
4.22
XS-3 Binary
ABCD wxyz
0011 0000
0100 0001
0101 0010
0110 0011
0111 0100
1000 0101
1001 0110
1010 0111
1011 1000
1100 1001
Digital
Design
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HDL
–
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2012,
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74
AB
CD
C
00
00
01
11
A
10
m0
x
m4
01
m1
x
m5
11
m3
x
m7
m6
00
01
m12
m13
m15
m14
m8
m9
m11
m10
1
x
CD
AB
10
x
1
B
x
11
A
10
D
w = AB + ACD
C
00
m0
X
01
m1
X
11
m3
m7
10
m2
m4
m5
m12
m13
m15
m14
m8
m9
m11
m10
x
1
1
1
x
m6
x
(NOR)
(NOR)
(NOR)
(NOR)
A1
A0
D0' = (A1'A0')'
D1' = (A1'A0)'
D2' = (A1A0')'
D0' = (A1A0)'
(NAND)
(NAND)
(NAND)
(NAND)
D0 = (A1 + A0 + E' )' = A'1A'0E
D1 = (A1 + A'0 + E' )' = A'1A0E
D2 = (A'1 + A0 + E' ) = A1A'0E
D3 = (A'1 + A'0 + E' )' = A1A0E
E
E
A1
1
D
x = B'C' + B'D' + BCD
y = C'D + CD'
z = D'
4.23
D0 = A1'A0' = (A1 + A0)'
D1 = A1'A0 = (A1 + A0')'
D2 = A1A0' = (A1' + A0)'
D3 = A1A0 = (A1' + A0)'
X
A0
D0' = (A1 + A0 + E' ) = (A'1A'0E)'
D0
D1' = (A1 + A'0 + E' ) = (A'1A0E)'
D1
D2' = (A1' + A0 + E' ) = (A1A0'E)'
D2
D3' = (A1' + A0' + E' ) = (A1A0E)'
D3
Digital
Design
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HDL
–
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Manual.
M.
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Copyright
2012,
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rights
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B
75
4.24
AB
CD
C
00
m0
Inputs: A, B, C, D
D0 = A'B'C'D'
D1 = A'B'C'D
D2 = B'CD'
D3 = B'CD
D4 = BC'D'
00
Outputs: D0, D1, ... D9
D5 = BC'D
D6 = BCD'
D7 = BCD
D8 = AD'
A
D9 = AD
D0
m4
01
D4
D8
11
m3
D1
D3
m7
D5
m13
x
m8
10
m1
m5
m12
11
01
m9
D9
10
D2
m6
D7
m15
x
x
x
m11
x
D6
m14
B
x
m10
x
D
Digital
Design
With
An
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HDL
–
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2012,
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76
4.25
A0
A1
A2
3x8
Decoder
8
D0 - D7
E
3x8
Decoder
8
D8 - D15
E
A3
0
20
2x4
Decoder
A4
21
E
1
2
3
3x8
Decoder
8
3x8
Decoder
8
2x4
Decoder
4
D16 - D23
E
E
D24 - D31
E
4.26
A0
20
A1
1
2
20
1
2
A2
2x4
Decoder
4
D4 - D7
E
0
20
2x4
Decoder
A3
D0 - D3
E
21
E
1
2
20
3
1
2
2x4
Decoder
4
2x4
Decoder
4
D8 - D11
E
E
20
1
2
D12 - D15
E
Digital
Design
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77
4.27
F1 = Σ(1, 4, 6)
0
1
2
2 3x8 2
3
21 Decoder
4
0
2
5
6
7
A
B
C
F2 = Σ(3, 5)
F3 = Σ(2, 4, 6, 7)
4.28
(a)
F1 = x(y + y')z + x'yz' =xyx + xy'z + x'yz' = Σ(2, 5, 7)
F2 = xy'z' + x'y = xy'z' + x'yz + x'yz' = Σ(2, 3, 4)
F3 = x'y'z' + xy(z + z') =x'y'z' + xyz + xyz' = Σ(0, 6, 7)
0
1
x
y
z
22 3 x 8 2
21 Decoder 3
4
20
5
6
7
F1 = Σ((2, 5, 7)
F1 = Σ((2, 3, 4)
F1 = Σ(0, 6, 7)
(b)
Digital
Design
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2012,
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78
4.29
D1D0
D3D2
00
Inputs
D3 D2 D1 D0
Outputs
x y V
0 0 0 0
x x x 1
x x 1 0
x 1 0 0
1 0 0 0
x
0
0
1
1
x
0
1
0
1
D1
01
m0
m1
m4
m5
00
1
01
0
1
1
1
1
1
m12
11
D3
11
m3
1
1
m8
10
1
m9
m6
1
1
m15
1
1
1
m7
m13
10
m2
m14
1
m11
1
D2
1
m10
1
1
D0
V = D0 + D1 + D2 + D3
D3D2
D1D0
00
m0
00
11
10
m1
m3
m2
m5
m7
m6
m13
m15
m14
m9
m11
m10
D3D2
x
m4
01
11
m0
D1
01
11
10
m1
m3
m2
m4
m5
m7
m6
m12
m13
m15
m14
m8
m9
m11
m10
x
1
01
D2
1
m8
D1D0
00
00
1
m12
10
01
1
11
D3
1
10
D2
1
1
1
D0
D0
x = D1'D0'
y = D0'D2' + D1D0'
D0
x
D1
y
D2
D2
D3
D1
D0
V
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
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rights
reserved.
79
4.30
Inputs
Outputs
D0 D1 D2 D3 D4 D5 D6 D7
x y z
V
0
1
x
x
x
x
x
x
x
x
0
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
x
x
x
x
x
x
0
0
0
1
x
x
x
x
x
0
0
0
0
1
x
x
x
x
0
0
0
0
0
1
x
x
x
0
0
0
0
0
0
1
x
x
0
0
0
0
0
0
0
1
x
0
0
0
0
0
0
0
0
1
If D2 = 1, D6 = 1, all others = 0
Output xyz = 100 and V = 1
4.31
s0
s1
s2
s3
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
s0
s1
s2
0
1
2
3
4
5
6
7
s0
s1
s2
0
1
2
3
4
5
6
7
x
0
0
1
1
0
0
0
1
x
0
1
0
1
0
1
0
1
8x1
MUX
s
0
1
2x1
MUX
y
8x1
MUX
Digital
Design
With
An
Introduction
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Verilog
HDL
–
Solution
Manual.
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Mano.
M.D.
Ciletti,
Copyright
2012,
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rights
reserved.
(a) F = Σ (0, 2, 5, 8, 10, 14)
Inputs
ABCD
000 0
000 1
001 0
001 1
010 0
010 1
011 0
011 1
100 0
100 1
101 0
101 1
110 0
110 1
111 0
111 1
Mux input line (ABC)
Value
4.32
80
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
F = Σ(0, 2, 5, 8, 10, 14)
1 F = D'
0
1
F = D'
0
0
F=D
1
0F=0
0
1
F = D'
0
1
F = D'
0
0F=0
0
1
F = D'
0
A
B
C
D
0
s0
s1
s2
0
1
2
3
4
5
6
7
8x1
MUX
Y
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
F
81
Inputs
ABCD
000 0
000 1
001 0
001 1
010 0
010 1
011 0
011 1
100 0
100 1
101 0
101 1
110 0
110 1
111 0
111 1
Mux input line (ABC)
Value
(b)
F = Π(2, 6, 11) = (A' +B' + C + D')(A' +B + C + D')(A +B' + C + D)
F' = (A' +B' + C + D')' + (A' +B + C + D')' + (A +B' + C + D)'
F' = (ABC'D) + (AB'C'D) + (A'BC'D') = Σ(13, 9, 4)
F = Σ(0, 1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 14, 15)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
1F = 1
1
1
F=1
1
0
F=D
1
1F = 1
1
1
F = D'
0
1
F=1
1
1F = D'
0
1
F=1
1
s0
s1
s2
0
1
2
3
4
5
6
7
A
B
C
D
1
8x1
MUX
F
Y
4.33
S(x, y, z) = Σ(1, 2, 4, 7)
C(x, y, z) = Σ(3, 5, 6, 7)
S
I0 I1 I2 I3
x'
0 1 2 3
4 5 6 7
x x' x' x
x
C
x'
x
0
1
2
3
x
Dual
4x1
MUX
I0 I1 I2 I3
0 1 2 3
4 5 6 7
0 x' x' 1
0
1
S
0
1
2
3
Y
C
y
z
Digital
Design
With
An
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HDL
–
Solution
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Mano.
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Ciletti,
Copyright
2012,
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rights
reserved.
82
4.34
(a)
A
B
C
D
F
AB
0
0
1
I5 = 1
1
0
I0 = D
0
1
I4 = D 1
1
I6 = D'
1
1
1
0
0
0
0
0
0
1
1
I3 = 1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
0
1
1
0
C
00
00
01
11
A
10
01
11
10
m0
m1
m4
m5
m7
m12
m13
m15
m14
m8
m9
m11
m10
1
1
1
m3
m2
m6
1
1
1
B
1
D
Other minterms = 0
since I1 = I2 = I7 = 0
CD
F(A, B, C, D) = Σ(1, 6, 7, 9, 10, 11, 12)
(b)
A
B
0
0
I2 = 0 0
0
0
I3 = 1
0
1
I7 = 1
1
I4 = D 1
1
0
I0 = D' 0
1
I6= D' 1
0
0
1
1
1
1
1
1
0
0
0
0
1
1
I1 = 0
C
1
1
0
0
1
1
1
1
0
0
0
0
0
0
D
0
1
0
1
0
1
0
1
0
1
0
1
0
1
F
0
0
0
0
1
1
1
1
0
1
1
0
1
0
AB
CD
C
00
00
01
11
A
10
m0
1
01
m1
1
11
m3
10
m2
m4
m5
m7
m12
m13
m15
m14
m8
m9
m11
m10
1
1
1
1
m6
1
B
1
D
F(A, B, C, D) = Σ(0, 1, 6, 7, 9, 13, 14, 15)
Other minterms = 0
since I1 = I2 = 0
4.35
(a)
Inputs
ABCD
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
F
0
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
AB = 00
F=D
A
B
AB = 01
F = C'D'
= (C + D)'
C
D
AB = 10
F = CD
s0
s1
0
1
2
3
4x1
MUX
Y
F
1
AB = 11
F=1
Digital
Design
With
An
Introduction
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Verilog
HDL
–
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Manual.
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Mano.
M.D.
Ciletti,
Copyright
2012,
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rights
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83
(b)
F = S(1, 2, 5, 7, 8, 10, 11, 13, 15)
Inputs
ABCD F2 = Σ(1, 2, 5, 7, 8, 10, 11, 13, 15)
A
0000 0
0001 1 AB = 00
B
0010 1 F = C'D + CD'
0011 0
C
0100 0
AB = 01
0101 1
F = C'D + CD = D
0110 0
D
0111 1
1000 1
1001 0
1010 1 AB = 10
1011 1 F = C'D' + C'D + CD = C'D' + D
1100 0
AB = 11
1101 1
F=D
1110 0
1111 1
4.36
4.37
s0
s1
0
1
4x1
MUX
Y
F2
2
3
module priority_encoder_gates (output x, y, V, input D0, D1, D2, D3); // V2001
wire w1, D2_not;
not (D2_not, D2);
or
(x, D2, D3);
or
(V, D0, D1, x);
and (w1, D2_not, D1);
or
(y, D3, w1);
endmodule
Note:
See
Problem
4.45
for
testbench)
module Add_Sub_4_bit (
output [3: 0] S,
output C,
input [3: 0] A, B,
input M
);
wire [3: 0] B_xor_M;
wire C1, C2, C3, C4;
assign C = C4;
// output carry
xor (B_xor_M[0], B[0], M);
xor (B_xor_M[1], B[1], M);
xor (B_xor_M[2], B[2], M);
xor (B_xor_M[3], B[3], M);
// Instantiate full adders
full_adder FA0 (S[0], C1, A[0], B_xor_M[0], M);
full_adder FA1 (S[1], C2, A[1], B_xor_M[1], C1);
full_adder FA2 (S[2], C3, A[2], B_xor_M[2], C2);
full_adder FA3 (S[3], C4, A[3], B_xor_M[3], C3);
endmodule
module full_adder (output S, C, input x, y, z); // See HDL Example 4.2
wire S1, C1, C2;
// instantiate half adders
half_adder HA1 (S1, C1, x, y);
half_adder HA2 (S, C2, S1, z);
or G1 (C, C2, C1);
endmodule
Digital
Design
With
An
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HDL
–
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M.
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Ciletti,
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2012,
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rights
reserved.
84
module half_adder (output S, C, input x, y);
xor (S, x, y);
and (C, x, y);
endmodule
// See HDL Example 4.2
module t_Add_Sub_4_bit ();
wire [3: 0] S;
wire C;
reg [3: 0] A, B;
reg M;
Add_Sub_4_bit M0 (S, C, A, B, M);
initial #100 $finish;
initial fork
#10 M = 0;
#10 A = 4'hA;
#10 B = 4'h5;
#50 M = 1;
#70 B = 4'h3;
join
endmodule
Name
0
50
A[3:0]
x
B[3:0]
x
100
a
5
3
M
S[3:0]
x
f
5
7
C
4.38
module quad_2x1_mux (
// V2001
input
[3: 0] A, B,
// 4-bit data channels
input
enable_bar, select, // enable_bar is active-low)
output [3: 0] Y
// 4-bit mux output
);
//assign Y = enable_bar ? 0 : (select ? B : A);
// Grounds output
assign Y = enable_bar ? 4'bzzzz : (select ? B : A); // Three-state output
endmodule
//
Note
that
this
mux
grounds
the
output
when
the
mux
is
not
active.
module t_quad_2x1_mux ();
reg
[3: 0] A, B, C;
reg
enable_bar, select;
wire [3: 0] Y;
// 4-bit data channels
// enable_bar is active-low)
// 4-bit mux
quad_2x1_mux M0 (A, B, enable_bar, select, Y);
initial #200 $finish;
initial fork
enable_bar = 1;
select = 1;
A = 4'hA;
B = 4'h5;
#10 select = 0;
// channel A
Digital
Design
With
An
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Verilog
HDL
–
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Manual.
M.
Mano.
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Ciletti,
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2012,
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rights
reserved.
85
#20 enable_bar = 0;
#30 A = 4'h0;
#40 A = 4'hF;
#50 enable_bar = 1;
#60 select = 1;
// channel B
#70 enable_bar = 0;
#80 B = 4'h00;
#90 B = 4'hA;
#100 B = 4'hF;
#110 enable_bar = 1;
#120 select = 0;
#130 select = 1;
#140 enable_bar = 1;
join
endmodule
Name
0
70
a
A[3:0]
140
0
f
5
B[3:0]
0
a
0
a
f
enable_bar
select
Y[3:0]
0
a
0
f
0
5
f
0
With three-state output:
Name
0
70
a
A[3:0]
140
0
f
5
B[3:0]
0
a
0
a
f
enable_bar
select
Y[3:0]
4.39
z
a
0
f
z
5
f
z
// Verilog 1995
module Compare (A, B, Y);
input [3: 0] A, B; // 4-bit data inputs.
output [5: 0] Y;
// 6-bit comparator output.
reg
[5: 0] Y;
// EQ, NE, GT, LT, GE, LE
always @ (A or B)
if (A==B)
Y = 6'b10_0011;
else if (A < B)
Y = 6'b01_0101;
else
Y = 6'b01_1010;
endmodule
// EQ, GE, LE
// NE, LT, LE
// NE, GT, GE
// Verilog 2001, 2005
module Compare (input [3: 0] A, B, output reg [5:0] Y);
always @ (A, B)
if (A==B)
Y = 6'b10_0011;
// EQ, GE, LE
else if (A < B)
Y = 6'b01_0101;
// NE, LT, LE
else
Y = 6'b01_1010;
// NE, GT, GE
endmodule
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
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Manual.
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M.D.
Ciletti,
Copyright
2012,
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rights
reserved.
86
4.40
module Prob_4_40 (
output [3: 0] sum_diff, output carry_borrow,
input [3: 0] A, B, input sel_diff
);
always @(sel_diff, A, B)
endmodule
{carry_borrow, sum_diff} = sel_diff ? A - B : A + B;
module t_Prob_4_40;
wire [3: 0] sum_diff;
wire carry_borrow;
reg [3:0] A, B;
reg sel_diff;
integer I, J, K;
Prob_4_40 M0 ( sum_diff, carry_borrow, A, B, sel_diff);
initial #4000 $finish;
initial begin
for (I = 0; I < 2; I = I + 1) begin
sel_diff = I;
for (J = 0; J < 16; J = J + 1) begin
A = J;
for (K = 0; K < 16; K = K + 1) begin B = K; #5 ; end
end
end
end
endmodule
4.41
module Prob_4_41 (
output reg [3: 0] sum_diff, output reg carry_borrow,
input [3: 0] A, B, input sel_diff
);
always @ (A, B, sel_diff)
{carry_borrow, sum_diff} = sel_diff ? A - B : A + B;
endmodule
module t_Prob_4_41;
wire [3: 0] sum_diff;
wire carry_borrow;
reg [3:0] A, B;
reg sel_diff;
integer I, J, K;
Prob_4_46 M0 ( sum_diff, carry_borrow, A, B, sel_diff);
initial #4000 $finish;
initial begin
for (I = 0; I < 2; I = I + 1) begin
sel_diff = I;
for (J = 0; J < 16; J = J + 1) begin
A = J;
for (K = 0; K < 16; K = K + 1) begin B = K; #5 ; end
end
end
end
endmodule
Digital
Design
With
An
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HDL
–
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2012,
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rights
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87
Name
780
810
840
870
sel_diff
9
A[3:0]
a
b
B[3:0]
c
d
e
f
0
1
2
3
4
5
6
7
8
9
a
b
c
d
e
f
0
1
2
sum_diff[3:0]
5
6
7
8
a
b
c
d
e
f
0
1
2
3
4
5
6
7
8
9
b
c
d
carry_borrow
Name
2064
2094
2124
2154
sel_diff
9
A[3:0]
B[3:0]
d
e
sum_diff[3:0]
c
b
a
f
0
a
b
1
2
3
4
5
6
7
8
9
a
b
c
d
e
9
8
7
6
5
4
3
2
1
0
f
e
d
c
f
0
b
1
2
a
9
carry_borrow
4.42
(a)
module Xs3_Gates (input A, B, C, D, output w, x, y, z);
wire B_bar, C_or_D_bar;
wire CD, C_or_D;
or
(C_or_D, C, D);
not (C_or_D_bar, C_or_D);
not (B_bar, B);
and (CD, C, D);
not (z, D);
or
(y, CD, C_or_D_bar);
and (w1, C_or_D_bar, B);
and (w2, B_bar, C_or_D);
and (w3, C_or_D, B);
or
(x, w1, w2);
or
(w, w3, A);
endmodule
(b)
module Xs3_Dataflow (input A, B, C, D, output w, x, y, z);
assign {w, x, y, z} = {A, B, C, D} + 4'b0011;
endmodule
(c)
module Xs3_Behavior_95 (A, B, C, D, w, x, y, z);
input
A, B, C, D;
output w, x, y, z;
reg w, x, y, z;
always @ (A or B or C or D) begin {w, x, y, z} = {A, B, C, D} + 4'b0011; end
endmodule
module Xs3_Behavior_01 (input A, B, C, D, output reg w, x, y, z);
Digital
Design
With
An
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HDL
–
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Ciletti,
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2012,
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rights
reserved.
88
always @ (A, B, C, D) begin {w, x, y, z} = {A, B,C, D} + 4'b0011; end
endmodule
module t_Xs3_Converters ();
reg A, B, C, D;
wire w_Gates, x_Gates, y_Gates, z_Gates;
wire w_Dataflow, x_Dataflow, y_Dataflow, z_Dataflow;
wire w_Behavior_95, x_Behavior_95, y_Behavior_95, z_Behavior_95;
wire w_Behavior_01, x_Behavior_01, y_Behavior_01, z_Behavior_01;
integer k;
wire [3: 0] BCD_value;
wire [3: 0] Xs3_Gates = {w_Gates, x_Gates, y_Gates, z_Gates};
wire [3: 0] Xs3_Dataflow = {w_Dataflow, x_Dataflow, y_Dataflow, z_Dataflow};
wire [3: 0] Xs3_Behavior_95 = {w_Behavior_95, x_Behavior_95, y_Behavior_95, z_Behavior_95};
wire [3: 0] Xs3_Behavior_01 = {w_Behavior_01, x_Behavior_01, y_Behavior_01, z_Behavior_01};
assign BCD_value = {A, B, C, D};
Xs3_Gates M0 (A, B, C, D, w_Gates, x_Gates, y_Gates, z_Gates);
Xs3_Dataflow M1 (A, B, C, D, w_Dataflow, x_Dataflow, y_Dataflow, z_Dataflow);
Xs3_Behavior_95 M2 (A, B, C, D, w_Behavior_95, x_Behavior_95, y_Behavior_95, z_Behavior_95);
Xs3_Behavior_01 M3 (A, B, C, D, w_Behavior_01, x_Behavior_01, y_Behavior_01, z_Behavior_01);
initial #200 $finish;
initial begin
k = 0;
repeat (10) begin {A, B, C, D} = k; #10 k = k + 1; end
end
endmodule
0
Name
30
60
90
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
Xs3_Gates[3:0]
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
Xs3_Gates[3:0]
3
4
5
6
7
8
9
a
b
c
Xs3_Dataflow[3:0]
3
4
5
6
7
8
9
a
b
c
Xs3_Behavior_95[3:0]
3
4
5
6
7
8
9
a
b
c
Xs3_Behavior_01[3:0]
3
4
5
6
7
8
9
a
b
c
k
A
B
C
D
BCD_value[3:0]
w_Gates
x_Gates
y_Gates
z_Gates
4.43
Two-channel mux with 2-bit data paths, enable, and three-state output.
4.44
module ALU (output reg [7: 0] y, input [7: 0] A, B, input [2: 0] Sel);
always @ (A, B, Sel) begin
y = 0;
case (Sel)
3'b000:
y = 8'b0;
3'b001:
y = A & B;
3'b010:
y = A | B;
3'b011:
y = A ^ B;
3'b100:
y = A + B;
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–
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2012,
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reserved.
89
3'b101:
3'b110:
3'b111:
endcase
end
y = A - B;
y = ~A;
y = 8'hFF;
endmodule
module t_ALU ();
wire[7: 0]y;
reg [7: 0] A, B;
reg [2: 0] Sel;
ALU M0 (y, A, B, Sel);
initial #200 $finish;
initial fork
#5 begin A = 8'hAA; B = 8'h55; end
// Expect y = 8'd0
#10 begin Sel = 3'b000; A = 8'hAA; B = 8'h55; end // y = 8'b000
#20 begin Sel = 3'b001; A = 8'hAA; B = 8'hAA; end // y = A & B
#30 begin Sel = 3'b001; A = 8'h55; B = 8'h55; end // y = A & B
#40 begin Sel = 3'b010; A = 8'h55; B = 8'h55; end // y = A | B
#50 begin Sel = 3'b010; A = 8'hAA; B = 8'hAA; end // y = A | B
#60 begin Sel = 3'b011; A = 8'h55; B = 8'h55; end // y = A ^ B
#70 begin Sel = 3'b011; A = 8'hAA; B = 8'h55; end // y = A ^ B
#80 begin Sel = 3'b100; A = 8'h55; B = 8'h00; end // y = A + B
#90 begin Sel = 3'b100; A = 8'hAA; B = 8'h55; end // y = A + B
#110 begin Sel = 3'b101; A = 8'hAA; B = 8'h55; end // y = A – B
#120 begin Sel = 3'b101; A = 8'h55; B = 8'hAA; end // y = A – B
#130 begin Sel = 3'b110; A = 8'hFF; end
// y = ~A
#140 begin Sel = 3'b110; A = 8'd0; end
// y = ~A
#150 begin Sel = 3'b110; A = 8'hFF; end
// y = ~A
#160 begin Sel = 3'b111; end
// y = 8'hFF
join
endmodule
Name
0
60
001
Sel[2:0]
aa
010
55
aa
B[7:0]
55
aa
55
aa
y[7:0]
00
aa
55
aa
A[7:0]
Expect y = 8'd0
Expect y = 8'hAA = 8'1010_1010
Expect y = 8'h55 = 8'b0101_0101
Expect y = 8'h55 = 8'b0101_0101
Expect y = 8'hAA = 8'b1010_1010
Expect y = 8'd0
Expect y = 8'hFF = 8'b1111_1111
Expect y = 8'h55 = 8'b0101_0101
Expect y = 8'hFF = 8'b1111_1111
Expect y = 8'h55 = 8'b0101_0101
Expect y = 8'hab = 8'b1010_1011
Expect y = 8'd0
Expect y = 8'hFF = 8'b1111_1111
Expect y = 8'd0
Expect y = 8'hFF = 8'b1111_1111
120
011
55
100
aa
55
00
ff
101
55
aa
00
55
55
180
ff
55
110
ff
111
00
ff
aa
55
ab
00
ff
00
ff
Note that the subtraction operator performs 2's complement subtraction. So 8'h55 – 8'hAA adds the 2's
complement of 8'hAA to 8'h55 and gets 8'hAB. The sign bit is not included in the model, but hand
calculation shows that the 9th bit is 1, indicating that the result of the operation is negative. The magnitude
of the result can be obtained by taking the 2's complement of 8'hAB.
4.45
module priority_encoder_beh (output reg X, Y, V, input D0, D1, D2, D3); // V2001
always @ (D0, D1, D2, D3) begin
X = 0;
Y = 0;
V = 0;
casex ({D0, D1, D2, D3})
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90
4'b0000:
4'b1000:
4'bx100:
4'bxx10:
4'bxxx1:
default:
endcase
end
endmodule
{X, Y, V} = 3'bxx0;
{X, Y, V} = 3'b001;
{X, Y, V} = 3'b011;
{X, Y, V} = 3'b101;
{X, Y, V} = 3'b111;
{X, Y, V} = 3'b000;
module t_priority_encoder_beh (); // V2001
wire X, Y, V;
reg D0, D1, D2, D3;
integer k;
priority_encoder_beh M0 (X, Y, V, D0, D1, D2, D3);
initial #200 $finish;
initial begin
k = 32'bx;
#10 for (k = 0; k <= 16; k = k + 1) #10 {D0, D1, D2, D3} = k;
end
endmodule
Name 0
k
60
0
1
2
3
4
5
120
6
7
8
9
10
11
12
180
13
14
15
16
17
D0
D1
D2
D3
X
Y
V
Digital
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reserved.
4.46
91
(a)
F = Σ(0, 2, 5, 7, 11, 14)
See code below.
(b) From prob 4.32:
F = Π (3, 8, 12) = (A' + B' + C + D)(A + B' + C' + D')(A + B + C' + D')
F' = ABC'D' + A'BCD + A'B'CD = Σ(12, 7, 3)
F = Σ(0, 1, 2, 4, 5, 6, 8, 9, 10, 11, 13, 14, 15)
module Prob_4_46a (output F, input A, B, C, D);
assign F = (~A&~B&~C&~D) | (~A&~B&C&~D) | (~A&B&~C&D) | (~A&B&C&D) | (A&~B&C&D) |
(A&B&C&~D);
endmodule
module Prob_4_46b (output F, input A, B, C, D);
assign F = (~A&~B&~C&~D) | (~A&~B&~C&D) | (~A&~B&C&~D) | (~A&B&~C&~D) | (~A&B&~C&D) |
(~A&B&C&~D) | (A&~B&~C&~D) | (A&~B&~C&D) | (A&~B&C&~D) | (A&~B&C&D) | (A&B&~C&D) |
(A&B&C&~D) | (A&B&C&D);
endmodule
module t_Prob_4_46a ();
wire F_a, F_b;
reg A, B, C, D;
integer k;
Prob_4_46a M0 (F_a, A, B, C, D);
Prob_4_46b M1 (F_b, A, B, C, D);
initial
#200
$finish;
initial begin
k = 0;
#10 repeat (15) begin {A, B, C, D} = k; #10 k = k + 1; end
end
endmodule
Name 0
k
60
0
1
2
3
4
5
120
6
7
8
9
10
11
12
180
13
14
15
16
17
D0
D1
D2
D3
X
Y
V
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92
4.47
module Add_Sub_4_bit_Dataflow (
output [3: 0]
S,
output
C, V,
input
[3: 0]
A, B,
input
M
);
wire
C3;
assign {C3, S[2: 0]} = A[2: 0] + ({M, M, M} ^ B[2: 0]) + M;
assign {C, S[3]} = A[3] + M ^ B[3] + C3;
assign V = C ^ C3;
endmodule
module t_Add_Sub_4_bit_Dataflow ();
wire [3: 0] S;
wire C, V;
reg [3: 0] A, B;
reg M;
Add_Sub_4_bit_Dataflow M0 (S, C, V, A, B, M);
initial #100 $finish;
initial fork
#10 M = 0;
#10 A = 4'hA;
#10 B = 4'h5;
#50 M = 1;
#70 B = 4'h3;
join
endmodule
Name
0
50
A[3:0]
x
B[3:0]
x
100
a
5
3
M
S[3:0]
x
f
5
7
C
4.48
module ALU_3state (output [7: 0] y_tri, input [7: 0] A, B, input [2: 0] Sel, input En);
reg [7: 0] y;
assign y_tri = En ? y: 8'bz;
always @ (A, B, Sel) begin
y = 0;
case (Sel)
3'b000:
y = 8'b0;
3'b001:
y = A & B;
3'b010:
y = A | B;
3'b011:
y = A ^ B;
3'b100:
y = A + B;
3'b101:
y = A - B;
3'b110:
y = ~A;
3'b111:
y = 8'hFF;
endcase
end
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93
endmodule
module t_ALU_3state ();
wire[7: 0] y;
reg [7: 0] A, B;
reg [2: 0] Sel;
reg En;
ALU_3state M0 (y, A, B, Sel, En);
initial #200 $finish;
initial fork
#5 En = 1;
#5 begin A = 8'hAA; B = 8'h55; end
// Expect y = 8'd0
#10 begin Sel = 3'b000; A = 8'hAA; B = 8'h55; end // y = 8'b000 Expect y = 8'd0
#20 begin Sel = 3'b001; A = 8'hAA; B = 8'hAA; end // y = A & B Expect y = 8'hAA = 8'1010_1010
#30 begin Sel = 3'b001; A = 8'h55; B = 8'h55; end // y = A & B Expect y = 8'h55 = 8'b0101_0101
#40 begin Sel = 3'b010; A = 8'h55; B = 8'h55; end // y = A | B Expect y = 8'h55 = 8'b0101_0101
#50 begin Sel = 3'b010; A = 8'hAA; B = 8'hAA; end // y = A | BExpect y = 8'hAA = 8'b1010_1010
#60 begin Sel = 3'b011; A = 8'h55; B = 8'h55; end // y = A ^ B
Expect y = 8'd0
#70 begin Sel = 3'b011; A = 8'hAA; B = 8'h55; end // y = A ^ B
Expect y = 8'hFF = 8'b1111_1111
#80 begin Sel = 3'b100; A = 8'h55; B = 8'h00; end // y = A + B Expect y = 8'h55 = 8'b0101_0101
#90 begin Sel = 3'b100; A = 8'hAA; B = 8'h55; end // y = A + B Expect y = 8'hFF = 8'b1111_1111
#100 En = 0;
#115 En = 1;
#110 begin Sel = 3'b101; A = 8'hAA; B = 8'h55; end // y = A – B
Expect y = 8'h55 = 8'b0101_0101
#120 begin Sel = 3'b101; A = 8'h55; B = 8'hAA; end // y = A – B
Expect y = 8'hab = 8'b1010_1011
#130 begin Sel = 3'b110; A = 8'hFF; end
// y = ~A
Expect y = 8'd0
#140 begin Sel = 3'b110; A = 8'd0; end
// y = ~A
Expect y = 8'hFF = 8'b1111_1111
#150 begin Sel = 3'b110; A = 8'hFF; end
// y = ~A
Expect y = 8'd0
#160 begin Sel = 3'b111; end
// y = 8'hFF Expect y = 8'hFF = 8'b1111_1111
join
endmodule
4.49
// See Problem 4.1
module Problem_4_49_Gates (output F1, F2, input A, B, C, D);
wire A_bar = !A;
wire B_bar = !B;
and (T1, B_bar, C);
and (T2, A_bar, B);
or (T3, A, T1);
xor (T4, T2, D);
or (F1, T3, T4);
or (F2, T2, D);
endmodule
module Problem_4_49_Boolean_1 (output F1, F2, input A, B, C, D);
wire A_bar = !A;
wire B_bar = !B;
wire T1 = B_bar && C;
wire T2 = A_bar && B;
wire T3 = A || T1;
wire T4 = T2 ^ D;
assign F1 = T3 || T4;
assign F2 = T2 || D;
endmodule
module Problem_4_49_Boolean_2(output F1, F2, input A, B, C, D);
assign F1 = A || (!B && C) || (B && (!D)) || (!B && D);
assign F2 = ((!A) && B) || D;
endmodule
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94
module t_Problem_4_49;
reg A, B, C, D;
wire F1_Gates, F2_Gates;
wire F1_Boolean_1, F2_Boolean_1;
wire F1_Boolean_2, F2_Boolean_2;
Problem_4_48_Gates
M0 (F1_Gates, F2_Gates, A, B, C, D);
Problem_4_48_Boolean_1
M1 (F1_Boolean_1, F2_Boolean_1, A, B, C, D);
Problem_4_48_Boolean_2
M2 (F1_Boolean_2, F2_Boolean_2, A, B, C, D);
initial #100 $finish;
integer K;
initial begin
for (K = 0; K < 16; K = K + 1) begin {A, B, C, D} = K; #5; end
end
endmodule
4.50
(a) 84-2-1 to BCD code converter
//
See
Problem
4.8
and
Table
1.5.
//
Verilog
1995
// module Prob_4_50a (Code_BCD, Code84_m2_m1);
// output [3: 0] Code_BCD;
// input [3:0];
// reg [3: 0] Code_BCD;
// ...
// Verilog 2001, 2005
module Prob_4_50a (output reg [3: 0] Code_BCD, input [3: 0] Code_84_m2_m1);
always @ (Code_84_m2_m1)
case (Code_84_m2_m1)
4'b0000: Code_BCD = 4'b0000;
4'b0111: Code_BCD = 4'b0001;
4'b0110: Code_BCD = 4'b0010;
4'b0101: Code_BCD = 4'b0011;
4'b0100: Code_BCD = 4'b0100;
4'b1011: Code_BCD = 4'b0101;
4'b1010: Code_BCD = 4'b0110;
4'b1001: Code_BCD = 4'b0111;
4'b1000: Code_BCD = 4'b1000;
4'b1111: Code_BCD = 4'b1001;
4'b0001: Code_BCD = 4'b1010;
4'b0010: Code_BCD = 4'b1011;
4'b0011: Code_BCD = 4'b1100;
4'b1100: Code_BCD= 4'b1101;
4'b1101: Code_BCD = 4'b1110;
4'b1110: Code_BCD = 4'b1111;
endcase
endmodule
// always @ (A or B or C or D)
// 0
// 1
// 2
// 3
// 4
// 5
// 6
// 7
// 8
// 9
// 10
// 11
// 12
// 13
// 14
// 15
module t_Prob_4_50a;
wire [3: 0] Code_BCD;
reg [3: 0]; Code_84_m2_m1;
integer
K;
Prob_4_50a M0 ( Code_BCD, Code_84_m2_m1); // Unit under test (UUT)
initial #100 $finish;
initial begin
for (K = 0; K < 16; K = K + 1) begin Code_84_m2_m1 = K; #5 ; end
end
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HDL
–
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2012,
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reserved.
95
endmodule
(b)
84-2-1 to Gray code converter
module Prob_4_50b (output reg [3: 0] Code_BCD, input [3: 0] Code_84_m2_m1);
always @ (Code_84_m2_m1)
case (Code_84_m2_m1)
4'b0000: Code_Gray = 4'b0000;
4'b0111: Code_Gray = 4'b0001;
4'b0110: Code_Gray = 4'b0011;
4'b0101: Code_Gray = 4'b0010;
4'b0100: Code_Gray = 4'b0110;
4'b1011: Code_Gray = 4'b0111;
4'b1010: Code_Gray = 4'b0101;
4'b1001: Code_Gray = 4'b0100;
4'b1000: Code_Gray = 4'b1100;
4'b1111: Code_Gray = 4'b1101;
4'b0001: Code_Gray = 4'b1111;
4'b0010: Code_Gray = 4'b1110;
4'b0011: Code_Gray = 4'b1010;
4'b1100: Code_Gray= 4'b1011;
4'b1101: Code_Gray = 4'b1001;
4'b1110: Code_Gray = 4'b1000;
endcase
endmodule
// 0
// 1
// 2
// 3
// 4
// 5
// 6
// 7
// 8
// 9
// 10
// 11
// 12
// 13
// 14
// 15
module t_Prob_4_50b;
wire [3: 0] Code_Gray;
reg [3: 0] Code_84_m2_m1;
integer
K;
Prob_4_50b M0 (Code_Gray, Code_84_m2_m1); // Unit under test (UUT)
initial #100 $finish;
initial begin
for (K = 0; K < 16; K = K + 1) begin Code_84_m2_m1 = K; #5 ; end
end
endmodule
4.51
Assume that that the LEDs are asserted when the output is high.
module Seven_Seg_Display_V2001 (
output reg [6: 0] Display,
input
[3: 0] BCD
);
//
parameter
parameter
parameter
parameter
parameter
parameter
BLANK
ZERO
ONE
TWO
THREE
FOUR
abc_defg
= 7'b000_0000;
= 7'b111_1110;
= 7'b011_0000;
= 7'b110_1101;
= 7'b111_1001;
= 7'b011_0011;
// h7e
// h30
// h6d
// h79
// h33
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96
parameter
parameter
parameter
parameter
parameter
FIVE
SIX
SEVEN
EIGHT
NINE
= 7'b101_1011;
= 7'b101_1111;
= 7'b111_0000;
= 7'b111_1111;
= 7'b111_1011;
// h5b
// h5f
// h70
// h7f
// h7b
always @ (BCD)
case (BCD)
0:
Display = ZERO;
1:
Display = ONE;
2:
Display = TWO;
3:
Display = THREE;
4:
Display = FOUR;
5:
Display = FIVE;
6:
Display = SIX;
7:
Display = SEVEN;
8:
Display = EIGHT;
9:
Display = NINE;
default: Display = BLANK;
endcase
endmodule
module t_Seven_Seg_Display_V2001 ();
wire [6: 0] Display;
reg [3: 0] BCD;
parameter
parameter
parameter
parameter
parameter
parameter
parameter
parameter
parameter
parameter
parameter
BLANK
ZERO
ONE
TWO
THREE
FOUR
FIVE
SIX
SEVEN
EIGHT
NINE
= 7'b000_0000;
= 7'b111_1110;
= 7'b011_0000;
= 7'b110_1101;
= 7'b111_1001;
= 7'b011_0011;
= 7'b101_1011;
= 7'b001_1111;
= 7'b111_0000;
= 7'b111_1111;
= 7'b111_1011;
// h7e
// h30
// h6d
// h79
// h33
// h5b
// h1f
// h70
// h7f
// h7b
initial #120 $finish;
initial fork
#10 BCD = 0;
#20 BCD = 1;
#30 BCD = 2;
#40 BCD = 3;
#50 BCD = 4;
#60 BCD = 5;
#70 BCD = 6;
#80 BCD = 7;
#90 BCD = 8;
#100 BCD = 9;
join
Seven_Seg_Display_V2001 M0 (Display, BCD);
endmodule
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97
Name
0
60
120
BCD[3:0]
x
0
1
2
3
4
5
6
7
8
9
Display[6:0]
xx
7e
30
6d
79
33
5b
5f
70
7f
7b
Alternative with continuous assignments (dataflow):
module Seven_Seg_Display_V2001_CA (
output
[6: 0] Display,
input
[3: 0] BCD
);
//
abc_defg
parameter BLANK
= 7'b000_0000;
parameter ZERO
= 7'b111_1110;
parameter ONE
= 7'b011_0000;
parameter TWO
= 7'b110_1101;
parameter THREE = 7'b111_1001;
parameter FOUR
= 7'b011_0011;
parameter FIVE
= 7'b101_1011;
parameter SIX
= 7'b101_1111;
parameter SEVEN = 7'b111_0000;
parameter EIGHT
= 7'b111_1111;
parameter NINE
= 7'b111_1011;
wire
A, B, C, D, a, b, c, d, e, f, g;
// h7e
// h30
// h6d
// h79
// h33
// h5b
// h5f
// h70
// h7f
// h7b
assign A = BCD[3];
assign B = BCD[2];
assign C = BCD[1];
assign D = BCD[0];
assign Display = {a,b,c,d,e,f,g};
assign a = (~A)&C | (~A)&B&D | (~B)&(~C)&(~D) | A & (~B)&(~C);
assign b = (~A)&(~B) | (~A)&(~C)&(~D) | (~A)&C&D | A&(~B)&(~C);
assign c = (~A)&B | (~A)&D | (~B)&(~C)&(~D) | A&(~B)&(~C);
assign d = (~A)&C&(~D) | (~A)&(~B)&C | (~B)&(~C)&(~D) | A&(~B)&(~C) | (~A)&B&(~C)&D;
assign e = (~A)&C&(~D) | (~B)&(~C)&(~D);
assign f = (~A)&B&(~C) | (~A)&(~C)&(~D) | (~A)&B&(~D) | A&(~B)&(~C);
assign g = (~A)&C&(~D) | (~A)&(~B)&C | (~A)&B&(~C) | A&(~B)&(~C);
endmodule
module t_Seven_Seg_Display_V2001_CA ();
wire [6: 0] Display;
reg
[3: 0] BCD;
parameter
BLANK
= 7'b000_0000;
parameter ZERO
= 7'b111_1110;
// h7e
parameter ONE
= 7'b011_0000;
// h30
parameter TWO
= 7'b110_1101;
// h6d
parameter THREE = 7'b111_1001;
// h79
parameter FOUR
= 7'b011_0011;
// h33
parameter FIVE
= 7'b101_1011;
// h5b
parameter SIX
= 7'b001_1111;
// h1f
parameter SEVEN = 7'b111_0000;
// h70
parameter EIGHT
= 7'b111_1111;
// h7f
parameter NINE
= 7'b111_1011;
// h7b
initial #120 $finish;
initial fork
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
98
#10 BCD = 0;
#20 BCD = 1;
#30 BCD = 2;
#40 BCD = 3;
#50 BCD = 4;
#60 BCD = 5;
#70 BCD = 6;
#80 BCD = 7;
#90 BCD = 8;
#100 BCD = 9;
join
Seven_Seg_Display_V2001_CA M0 (Display, BCD);
endmodule
Digital
Design
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An
Introduction
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the
Verilog
HDL
–
Solution
Manual.
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Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
4.52
99
(a) Incrementer for unsigned 4-bit numbers
module Problem_4_52a_Data_Flow (output [3: 0] sum, output carry, input [3: 0] A);
assign {carry, sum} = A + 1;
endmodule
module t_Problem_4_52a_Data_Flow;
wire [3: 0] sum;
wire
carry;
reg [3: 0] A;
Problem_4_52a_Data_Flow M0 (sum, carry, A);
initial # 100 $finish;
integer K;
initial begin
for (K = 0; K < 16; K = K + 1) begin A = K; #5; end
end
endmodule
(b) Decrementer for unsigned 4-bit numbers
module Problem_4_52b_Data_Flow (output [3: 0] diff, output borrow, input [3: 0] A);
assign {borrow, diff} = A - 1;
endmodule
module t_Problem_4_52b_Data_Flow;
wire [3: 0]
diff;
wire
borrow;
reg [3: 0]
A;
Problem_4_52b_Data_Flow M0 (diff, borrow, A);
initial # 100 $finish;
integer K;
initial begin
for (K = 0; K < 16; K = K + 1) begin A = K; #5; end
end
endmodule
Name
0
30
60
90
A[3:0]
0
1
2
3
4
5
6
7
8
9
a
b
c
d
e
f
diff[3:0]
f
0
1
2
3
4
5
6
7
8
9
a
b
c
d
e
borrow
Digital
Design
With
An
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4.53
100
// BCD Adder
module Problem_4_53_BCD_Adder (
output
Output_carry,
output [3: 0] Sum,
input [3: 0] Addend, Augend,
input
Carry_in);
supply0
gnd;
wire [3: 0] Z_Addend;
wire
Carry_out;
wire
C_out;
assign Z_Addend = {1'b0, Output_carry, Output_carry, 1'b0};
wire [3: 0] Z_sum;
and (w1, Z_sum[3], Z_sum[2]);
and (w2, Z_sum[3], Z_sum[1]);
or (Output_carry, Carry_out, w1, w2);
Adder_4_bit M0 (Carry_out, Z_sum, Addend, Augend, Carry_in);
Adder_4_bit M1 (C_out, Sum, Z_Addend, Z_sum, gnd);
endmodule
module Adder_4_bit (output carry, output [3:0] sum, input [3: 0] a, b, input c_in);
assign {carry, sum} = a + b + c_in;
endmodule
module t_Problem_4_53_Data_Flow;
wire [3: 0] Sum;
wire
Output_carry;
reg [3: 0]
Addend, Augend;
reg
Carry_in;
Problem_4_53_BCD_Adder M0 (Output_carry, Sum, Addend, Augend, Carry_in);
initial # 1500 $finish;
integer i, j, k;
initial begin
for (i = 0; i <= 1; i = i + 1) begin Carry_in = i; #5;
for (j = 0; j <= 9; j = j +1) begin Addend = j; #5;
for (k = 0; k <= 9; k = k + 1) begin Augend = k; #5;
end
end
end
end
endmodule
Name 68
98
158
1
Addend[3:0]
Augend[3:0]
128
188
2
1
2
3
4
5
6
7
8
2
3
4
5
6
7
8
9
9
3
0
1
2
3
4
5
6
7
8
2
3
4
5
6
7
8
9
0
9
0
1
2
3
4
5
3
4
5
6
7
8
Carry_in
Sum[3:0]
0
1
1
2
Output_carry
Digital
Design
With
An
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HDL
–
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Manual.
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Ciletti,
Copyright
2012,
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rights
reserved.
4.54
101
(a) 9s Complement of BCD
module Nines_Complementer (
// V2001
output reg [3: 0] Word_9s_Comp,
input
[3: 0] Word_BCD
);
always @ (Word_BCD) begin
Word_9s_Comp = 4'b0;
case (Word_BCD)
4'b0000: Word_9s_Comp = 4'b1001;
// 0 to 9
4'b0001: Word_9s_Comp = 4'b1000;
// 1 to 8
4'b0010: Word_9s_Comp = 4'b0111;
// 2 to 7
4'b0011: Word_9s_Comp = 4'b0110;
// 3 to 6
4'b0100: Word_9s_Comp = 4'b0101;
// 4 to 5
4'b0101: Word_9s_Comp = 4'b0100;
// 5 to 4
4'b0110: Word_9s_Comp = 4'b0011;
// 6 to 3
4'b0111: Word_9s_Comp = 4'b0010;
// 7 to 2
4'b1000: Word_9s_Comp = 4'b0001;
// 8 to 1
4'b1001: Word_9s_Comp = 4'b0000;
// 9 to 0
default: Word_9s_Comp = 4'b1111;
// Error detection
endcase
end
endmodule
module t_Nines_Complementer ();
wire [3: 0] Word_9s_Comp;
reg [3: 0] Word_BCD;
Nines_Complementer M0 (Word_9s_Comp, Word_BCD);
initial #11$finish;
initial fork
Word_BCD = 0;
#10 Word_BCD = 1;
#20 Word_BCD = 2;
#30 Word_BCD = 3;
#40 Word_BCD = 4;
#50 Word_BCD = 5;
#60 Word_BCD = 6;
#70 Word_BCD = 7;
#20 Word_BCD = 8;
#90 Word_BCD = 9;
#100 Word_BCD = 4'b1100;
join
endmodule
Name
Word_BCD[3:0]
Word_9s_Comp[3:0]
// Confirm error detection
0
60
0
1
2
3
4
5
6
7
9
9
8
7
6
5
4
3
2
0
Digital
Design
With
An
Introduction
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HDL
–
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Manual.
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Ciletti,
Copyright
2012,
All
rights
reserved.
102
(b) 9s complement of Gray Code
module Nines_Complementer (
// V2001
output reg [3: 0] Word_9s_Comp,
input
[3: 0] Word_Gray
);
always @ (Word_Gray) begin
Word_9s_Comp = 4'b0;
case (Word_BCD)
4'b0000: Word_9s_Comp = 4'b1101;
// 0 to 9
4'b0001: Word_9s_Comp = 4'b1100;
// 1 to 8
4'b0010: Word_9s_Comp = 4'b0100;
// 2 to 7
4'b0011: Word_9s_Comp = 4'b0101;
// 3 to 6
4'b0100: Word_9s_Comp = 4'b0111;
// 4 to 5
4'b0101: Word_9s_Comp = 4'b0110;
// 5 to 4
4'b0110: Word_9s_Comp = 4'b0010;
// 6 to 3
4'b0111: Word_9s_Comp = 4'b0011;
// 7 to 2
4'b1000: Word_9s_Comp = 4'b0001;
// 8 to 1
4'b1001: Word_9s_Comp = 4'b0000;
// 9 to 0
default: Word_9s_Comp = 4'b1111;
// Error detection
endcase
end
endmodule
module t_Nines_Complementer ();
wire [3: 0] Word_9s_Comp;
reg [3: 0] Word_Gray;
Nines_Complementer M0 (Word_9s_Comp, Word_Gray);
initial #11$finish;
initial fork
Word_Gray = 0;
#10 Word_Gray = 1;
#20 Word_Gray = 2;
#30 Word_Gray = 3;
#40 Word_Gray = 4;
#50 Word_Gray = 5;
#60 Word_Gray = 6;
#70 Word_Gray = 7;
#20 Word_Gray = 8;
#90 Word_Gray = 9;
#100 Word_Gray = 4'b1100;
join
endmodule
// Confirm error detection
Digital
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2012,
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103
4.55 From Problem 4.19:
Mode = 0 FOR Add
Mode = 1 for Subtract
B3 B2 B1 B0
9's Complementer
(See Problem 4.18)
Select = 1
Select
Select = 0
Quadruple 2 x 1 MUX
A3 A2 A1 A0
Cin
BCD Adder (See Fig. 4.14)
// BCD Adder – Subtractor
module Problem_4_55_BCD_Adder_Subtractor (
output [3: 0]
BCD_Sum_Diff,
output
Carry_Borrow,
input [3: 0]
B, A,
input
Mode
);
wire [3: 0] Word_9s_Comp, mux_out;
Nines_Complementer M0 (Word_9s_Comp, B);
Quad_2_x_1_mux
M2 (mux_out, Word_9s_Comp, B, Mode);
BCD_Adder
M1 (Carry_Borrow, BCD_Sum_Diff, mux_out, A, Mode);
endmodule
module Nines_Complementer (
// V2001
output reg [3: 0] Word_9s_Comp,
input
[3: 0] Word_BCD
);
always @ (Word_BCD) begin
Word_9s_Comp = 4'b0;
case (Word_BCD)
4'b0000: Word_9s_Comp = 4'b1001;
// 0 to 9
4'b0001: Word_9s_Comp = 4'b1000;
// 1 to 8
4'b0010: Word_9s_Comp = 4'b0111;
// 2 to 7
4'b0011: Word_9s_Comp = 4'b0110;
// 3 to 6
4'b0100: Word_9s_Comp = 4'b1001;
// 4 to 5
4'b0101: Word_9s_Comp = 4'b0100;
// 5 to 4
4'b0110: Word_9s_Comp = 4'b0011;
// 6 to 3
4'b0111: Word_9s_Comp = 4'b0010;
// 7 to 2
4'b1000: Word_9s_Comp = 4'b0001;
// 8 to 1
4'b1001: Word_9s_Comp = 4'b0000;
// 9 to 0
default: Word_9s_Comp = 4'b1111;
// Error detection
endcase
end
endmodule
Digital
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–
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2012,
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rights
reserved.
104
module Quad_2_x_1_mux (output reg [3: 0] mux_out, input [3: 0] b, a, input select);
always @ (a, b, select)
case (select)
0: mux_out = a;
1: mux_out = b;
endcase
endmodule
module BCD_Adder (
output
Output_carry,
output [3: 0] Sum,
input
[3: 0] Addend, Augend,
input
Carry_in);
supply0
gnd;
wire
[3: 0] Z_Addend;
wire
Carry_out;
wire
C_out;
assign Z_Addend = {1'b0, Output_carry, Output_carry, 1'b0};
wire [3: 0] Z_sum;
and (w1, Z_sum[3], Z_sum[2]);
and (w2, Z_sum[3], Z_sum[1]);
or (Output_carry, Carry_out, w1, w2);
Adder_4_bit M0 (Carry_out, Z_sum, Addend, Augend, Carry_in);
Adder_4_bit M1 (C_out, Sum, Z_Addend, Z_sum, gnd);
endmodule
module Adder_4_bit (output carry, output [3:0] sum, input [3: 0] a, b, input c_in);
assign {carry, sum} = a + b + c_in;
endmodule
module t_Problem_4_55_BCD_Adder_Subtractor();
wire [3: 0] BCD_Sum_Diff;
wire
Carry_Borrow;
reg [3: 0] B, A;
reg
Mode;
Problem_4_55_BCD_Adder_Subtractor M0 (BCD_Sum_Diff, Carry_Borrow, B, A, Mode);
initial #1000 $finish;
integer J, K, M;
initial begin
for (M = 0; M < 2; M = M + 1) begin
for (J = 0; J < 10; J = J + 1) begin
for (K = 0; K < 10; K = K + 1) begin
A = J; B = K; Mode = M; #5 ;
end
end
end
end
endmodule
Digital
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HDL
–
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2012,
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rights
reserved.
105
Name 258
288
318
348
0
M
5
A[3:0]
6
7
B[3:0]
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
Word_9s_Comp[3:0]
7
6
9
4
3
2
1
0
9
8
7
6
9
4
3
2
1
0
9
8
7
3
6
mux_out[3:0]
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
BCD_Sum_Diff[3:0]
7
8
9
0
1
2
3
4
6
7
8
9
0
1
2
3
4
5
7
8
9
0
Carry_Borrow
Note: For subtraction, Carry_Borrow = 1 indicates a positive result; Carry_Borrow = 0 indicates a
negative result.
Name
768
798
828
858
1
M
5
A[3:0]
6
7
B[3:0]
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
Word_9s_Comp[3:0]
9
4
3
2
1
0
9
8
7
6
9
4
3
2
1
0
9
8
7
6
9
4
mux_out[3:0]
9
4
3
2
1
0
9
8
7
6
9
4
3
2
1
0
9
8
7
6
9
4
BCD_Sum_Diff[3:0]
5
0
9
8
7
5
4
3
6
1
0
9
8
6
5
4
7
2
6
7
Carry_Borrow
Digital
Design
With
An
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HDL
–
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2012,
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rights
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106
4.56
assign
match
=
(A
==
B);
//
Assumes
reg
[3:
0]
A,
B;
4.57
// Priority encoder (See Problem 4.29)
// Caution: do not confuse logic value x with identifier x.
// Verilog 1995
module Prob_4_57 (x, y, v, D3, D2, D1, D0);
output x, y, v;
input
D3, D2, D1, D0;
reg
x, y, v;
...
// Verilog 2001, 2005
module Prob_4_57 (output reg x, y, v, input D3, D2, D1, D0);
always @ (D3, D2, D1, D0) begin // always @ (D3 or D2 or D1 or D0)
x = 0;
y = 0;
v = 0;
casex ({D3, D2, D1, D0})
4'b0000: {x, y, v} = 3'bxx0;
4'bxxx1: {x, y, v} = 3'b001;
4'bxx10: {x, y, v} = 3'b011;
4'bx100: {x, y, v} = 3'b101;
4'b1000: {x, y, v} = 3'b110;
endcase
end
endmodule
module t_Prob_4_57;
wire
x, y, v;
reg
D3, D2, D1, D0;
integer
K;
Prob_4_57 M0 (x, y, v, D3, D2, D1, D0);
initial #100 $finish;
initial begin
for (K = 0; K < 16; K = K + 1) begin {D3, D2, D1, D0} = K; #5 ; end
end
endmodule
Digital
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HDL
–
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2012,
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rights
reserved.
4.58
107
(a)
//module shift_right_by_3_V2001 (output [31: 0] sig_out, input [31: 0] sig_in);
// assign sig_out = sig_in >>> 3;
//endmodule
module shift_right_by_3_V1995 (output reg [31: 0] sig_out, input [31: 0] sig_in);
always @ (sig_in)
sig_out = {sig_in[31], sig_in[31], sig_in[31], sig_in[31: 3]};
endmodule
module t_shift_right_by_3 ();
wire [31: 0] sig_out_V1995;
wire [31: 0] sig_out_V2001;
reg [31: 0] sig_in;
//shift_right_by_3_V2001 M0 (sig_out_V2001, sig_in);
shift_right_by_3_V1995 M1 (sig_out_V1995, sig_in);
integer k;
initial #1000 $finish;
initial begin
sig_in = 32'hf000_0000;
#100 sig_in = 32'h8fff_ffff;
#500 sig_in = 32'h0fff_ffff;
end
endmodule
Name 609
619
629
sig_in[31:0]
00001111111111111111111111111111
sig_out_V1995[31:0]
00000001111111111111111111111111
Name 34
44
639
54
sig_in[31:0]
11110000000000000000000000000000
sig_out_V1995[31:0]
11111110000000000000000000000000
Digital
Design
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HDL
–
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2012,
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rights
reserved.
64
108
(b)
//module shift_left_by_3_V2001 (output [31: 0] sig_out, input [31: 0] sig_in);
assign sig_out = sig_in <<< 3;
//module shift_left_by_3_V1995 (output reg [31: 0] sig_out, input [31: 0] sig_in);
//always @ (sig_in)
// sig_out = {sig_in[31: 3], 3'b0};
endmodule
module t_shift_left_by_3 ();
wire [31: 0] sig_out_V1995;
wire [31: 0] sig_out_V2001;
reg [31: 0] sig_in;
shift_left_by_3_V2001 M0 (sig_out_V2001, sig_in);
integer k;
initial #1000 $finish;
initial begin
sig_in = 32'hf000_0000;
#100 sig_in = 32'h8fff_ffff;
#500 sig_in = 32'h0fff_ffff;
end
endmodule
Name 0
50
100
150
sig_in[31:0]
xxxxxxxx
0000000f
sig_out_V1995[31:0]
xxxxxxxx
00000078
Digital
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HDL
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2012,
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rights
reserved.
109
4.59
module BCD_to_Decimal (output reg [3: 0] Decimal_out, input [3: 0] BCD_in);
always @ (BCD_in) begin
Decimal_out = 0;
case (BCD_in)
4'b0000: Decimal_out = 0;
4'b0001: Decimal_out = 1;
4'b0010: Decimal_out = 2;
4'b0011: Decimal_out = 3;
4'b0100: Decimal_out = 4;
4'b0101: Decimal_out = 5;
4'b0110: Decimal_out = 6;
4'b0111: Decimal_out = 7;
4'b1000: Decimal_out = 8;
4'b1001: Decimal_out = 9;
default: Decimal_out = 4'bxxxx;
endcase
end
endmodule
Digital
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110
4.60
module Even_Parity_Checker_4 (output P, C, input x, y, z);
xor (w1, x, y);
xor (P, w1, z);
xor (C, w1, w2);
xor (w2, z, P);
endmodule
See Problem 4.62 for testbench and waveforms.
4.61
module Even_Parity_Checker_4 (output P, C, input x, y, z);
assign w1 = x ^ y;
assign P = w1 ^ z;
assign C = w1 ^ w2;
assign w2 = z ^ P;
endmodule
0
Name
140
280
420
x
y
z
P
C
Digital
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111
4.62
A0
A1
A2
3x8
Decoder
8
D0 - D7
E
3x8
Decoder
8
D8 - D15
E
A3
0
20
2x4
Decoder
A4
21
E
1
2
3
3x8
Decoder
8
3x8
Decoder
8
D16 - D23
E
E
D24 - D31
E
module Decoder_3x8 (output D7, D6, D5, D4, D3, D2, D1, D0, input in2, in1, in0, E);
not (in2_bar, in2);
not (in1_bar, in1);
not (in0_bar, in0);
and (D0, in2_bar, in1_bar, in0_bar, E);
and (D1, in2_bar, in1_bar, in0, E);
and (D2, in2_bar, in1, in0_bar, E);
and (D3, in2_bar, in1, in0, E);
and (D4, in2, in1_bar, in0_bar, E);
and (D5, in2, in1_bar, in0, E);
and (D6, in2, in1, in0_bar, E);
and (D7, in2, in1, in0, E);
endmodule
module Decoder_5x32 (
output D31, D30, D29, D28, D27, D26, D25, D24, D23, D22, D21, D20, D19, D18, D17, D16,
D15, D14, D13, D12, D11, D10, D9, D8, D7, D6, D5, D4, D3, D2, D1, D0,
input A4, A3, A2, A1, A0, E;
wire E3, E2, E1, E0;
Decoder_3x8 M0 (D7, D6, D5, D4, D3, D2, D1, D0, A2, aA1, A0, E0);
Decoder_3x8 M1 (D15, D14, D13, D12, D11, D10, D9, D8, A2, A1, A0, E1);
Decoder_3x8 M2 (D23, D22, D21, D20, D19, D18, D17, D16, in2, in1, in0, E2);
Decoder_3x8 M3 (D31, D30, D29, D28, D27, D26, D25, D24, A2, A1, A0, E3);
Decoder_2x4 M4 (E3, E2, E1, E0, A4, A3, E);
endmodule
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
112
4.63
A0
20
A1
1
2
20
1
2
A2
4
D0 - D3
E
2x4
Decoder
4
D4 - D7
E
0
20
2x4
Decoder
A3
2x4
Decoder
21
E
1
2
20
3
21
2x4
Decoder
4
2x4
Decoder
4
D8 - D11
E
E
20
21
D12 - D15
E
module Decoder_2x4 (output D3, D2, D1, D0, input in1, in0, E);
not (in1_bar, in1);
not (in0_bar, in0);
and (D0, in1_bar, in0_bar, E);
and (D1, in1_bar, in0, E);
and (D2, in1, in0_bar, E);
and (D3, in1, in0, E);
endmodule
module Decoder_4x16 (
output D15, D14, D13, D12, D11, D10, D9, D8, D7, D6, D5, D4, D3, D2, D1, D0,
input A3, A2, A1, A0, E);
wire E3, E2, E1, E0;
Decoder_2x4 M0 (output D3, D2, D1, D0, input in1, in0, E0);
Decoder_2x4 M1 (output D7, D6, D5, D4, input in1, in0, E1);
Decoder_2x4 M2 (output D11, D10, D9, D8, input in1, in0, E2);
Decoder_2x4 M3 (output D15, D14, D13, D12, input in1, in0, E3);
Decoder_2x4 M4 (output E3, E2, E1, E0, input A3, A2, E);
endmodule
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
113
4.64
Inputs
Outputs
D0 D1 D2 D3 D4 D5 D6 D7
x y z
V
0
1
x
x
x
x
x
x
x
x
0
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
x
x
x
x
x
x
0
0
0
1
x
x
x
x
x
0
0
0
0
1
x
x
x
x
0
0
0
0
0
1
x
x
x
0
0
0
0
0
0
1
x
x
0
0
0
0
0
0
0
1
x
0
0
0
0
0
0
0
0
1
If D2 = 1, D6 = 1, all others = 0
Output xyz = 100 and V = 1
x
0
0
1
1
0
0
0
1
x
0
1
0
1
0
1
0
1
module Prob_4_64 (output x, y, x, V, input, D0, D1, D2, D3, D4,D5 D6, D7);
always @( D0, D1, D2, D3, D4,D5 D6, D7)
case({D0, D1, D2, D3, D4,D5 D6, D7})
8'b0000_0000: {x, y, x, V} = 4'bxxx0;
8'b1000_0000: {x, y, x, V} = 4'b0001;
8'b0100_0000: {x, y, x, V} = 4'b0011;
8'b0010_0000: {x, y, x, V} = 4'b0101;
8'b0001_0000:
8'b0000_1000:
8'b0000_0100:
8'b0000_0010:
8'b0000_0001:
default:
endcase
endmodule
{x, y, x, V} = 4'b0111;
{x, y, x, V} = 4'b1001;
{x, y, x, V} = 4'b1011;
{x, y, x, V} = 4'b1001;
{x, y, x, V} = 4'b1111;
{x, y, x, V} = 4'b1010;
// Use for error detection
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
114
4.65
s0
s1
s2
s3
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
s0
s1
s2
0
1
2
3
4
5
6
7
s0
s1
s2
0
1
2
3
4
5
6
7
8x1
MUX
s
0
1
2x1
MUX
y
8x1
MUX
module Mux_2x1 (
output y_out,
input in1, in0, sel);
not (sel_bar, sel);
and (y0, in0, sel);
and (y1, in1, sel);
or (y_out, in0, in1, sel_bar
);
endmodule
module Mux_4x1 (
output y_out,
input in3, in2, in1, in0, sel1, sel0);
not (sel_1_bar, sel1);
and (s0, sel_1_bar, sel0);
and (s1, sel[1], sel0);
Mux_2x1 M0 (y_M0, in0, in1, s0);
Mux_2x1 M1 (y_M1, in2, in3, s1);
or (y_out, y_M0, y_M1
);
endmodule
module Mux_8x1 (
output y_out,
input in7, in6, in5, in4, in3, in2, in1, in0, sel2, sel1, sel0
);
Mux_4x1 M0 (y_M0, in3, in2, in1, in0, sel1, sel0);
Mux_4x1 M1 (y_M1, in7, in6, in5, in4, sl1, sel0);
Mux_2x1 M2 (y_out, y_M0, y_M1, sel2);
endmodule
module Mux_16x1 (
output y_out,
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
input in15, in14, in13, in12, in11, in10, in9, in8, in7, in6, in5, in4, in3, in2, in1, in0, sel3, sel2, sel1, sel0
);
Mux_8x1 M0 (y_M0, in7, in6, in5, in4, in3, in2, in1, in0, sel2, sel1, sel0);
Mux_8x1 M1 (y_M1, in15, in14, in13, in12, in11, in10, in9, in8, sel2, sel1, sel0);
Mux_2x1 M2 (y_out, y_M0, y_M1, sel3);
endmodule
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
115
116
CHAPTER 5
5.1
(a)
R = D'C
D
Q
CP
C
Q'
S = DC
(b)
R = (D + C')' =D' C
D
Q
C
Q'
s = (D' + C')' =D C
(c)
S = (DC)' =D' + C'
D
CP
Q
C
Q'
R = ((DC)' C)' =DC + C'
= (D + C') = (D'C)'
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
117
5.2
J
0
2x1
mux
D = JQ' + K'Q
Q
Y
K
D
s
5.3
Q
1
C
Q'(t + 1) = (JQ' + K'Q)' = (J' + Q)(K + Q') = J'Q' + KQ
J
00
m0
0
J
K
KQ
m4
1
0
1
01
m1
m5
11
m3
1
m7
1
10
m2
0
m6
0
0
1
Q
5.4
(a)
P
N
Q(t + 1)
0
0
1
1
0
1
0
1
0
Q(t)
Q'(t)
1
(b) P
N
Q(t)
Q(t + 1)
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
N
NQ
P
00
0
P
1
m0
m4
1
01
11
m1
m3
m5
m7
1
1
10
m2
m6
1
Q
Q(t+1) = PQ' + NQ
(c)
Q(t)
Q(t+1)
P
N
0
0
1
1
0
1
0
1
0
1
x
x
x
x
0
1
(d) Connect P and N together.
5.5
The truth table describes a combinational circuit.
The state table describes a sequential circuit.
The characteristic table describes the operation of a flip-flop.
The excitation table gives the values of flip-flop inputs for a given state transition.
The four equations correspond to the algebraic expression of the four tables.
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
118
5.6
x
y
xy' + xA
D
Q
D
Q
A, z
C
B
CP
(b)
(c)
A(t+1) = xy' + xB
B(t+1) = xA + xB'
z=A
00, 01
x
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
y
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
Output
B
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
Next
state
A
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
Inputs
Present
state
00, 01
A
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
z
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
B
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
00
0
01
0
11
10
00, 01
10,11
00, 01
10
1
11
1
10, 11
10, 11
y
0
1
0
1
0
1
0
1
Output
x
0
0
1
1
0
0
1
1
Next
state
Q
0
0
0
0
1
1
1
1
Inputs
Present
state
5.7
Q
0
0
0
1
0
1
1
1
S
0
1
1
0
1
0
0
1
00/0
01/0
10/1
01/0
10/0
11/1
11/0
0
1
00/1
S=x⊕y⊕Q
Q(t + 1) = xy + xQ + yQ
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
A counter with a repeated sequence of 00, 01, 10.
Present
state
Next
state
5.8
119
A B A B
FF
Inputs
TA TB
0
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
00
01
11
10
1
1
0
1
TA = A + B
TB = A' + B
Repeated sequence:
01 10
00
5.9
JA = x
JB = x
0
KA = B
KB = A'
0
00
01
A(t+1) = JAA' + KA'A = xA' + B'A
B(t+1) = JBB' + KB'B = xB' + AB
x
0
0
0
0
1
1
1
1
A
0
0
1
1
0
0
1
1
B xA' + B'A xB' + AB
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0,1
11
0
1
10
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
5.10
120
(a) JA = Bx + B'y'
KA = B'xy'
JB = A'x
KB = A + xy'
z = Axy + Bx'y'
(c)
Present
state
Inputs
Next
state
Output
(b)
A
B
x y
A B
z
FF
Inputs
JA KA JA JB
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
1
AB
xy
x
00
m0
01
11
m3
m2
m4
m5
m7
m6
m12
m13
m15
1
1
01
1
11
A
10
m1
00
1
m8
1
m9
10
1
1
m14
1
m11
1
B
1
m10
1
y
A(t+1) = Ax' + Bx + Ay + A'B'y'
AB
xy
x
00
m0
01
m1
11
m3
00
10
m2
1
m4
A 01
m5
1
m7
1
1
m6
1
m12
m13
m15
m14
m8
m9
m11
m10
B
11
10
y
B(t+1) = A'B'x + A'B'(x' + y)
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
121
5.11
(a)
Present
state:
Input:
Output:
Next
state:
00 00 01 00 01 11 00 01 11 10 00 01 11 10 10
0 1 0 1 1 0 1 1 1 0 1 1 1 1 0
0 0 1 0 0 1 0 0 0 1 0 0 0 0 1
00 01 00 01 11 00 01 11 10 00 01 11 10 10 00
(b)
State
labels:
a:
00,
b:
10,
c:
11,
d:
01
c
is
equivalent
to
b
d
is
equivalent
to
c
0/0
a
1/0
0/1
b
1/0
5.12
(c)
input
0
1
0
1
State
machine:
D-‐flop
with
direct
input
of
the
input
to
the
original
machine;
output
logic:
y
=
(!input)
&&
(state
==
b)
Present
state
a
b
d
f
g
state
0
0
1
1
next
st
0
1
0
1
Next state
0 1
f b
d a
g a
f b
g d
output
0
0
0
1
Output
0 1
0 0
0 0
1 0
1 1
0 1
Digital
Design
With
An
Introduction
to
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HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
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rights
reserved.
5.13
122
(a) State:
Input:
Output:
a
0
0
a
0
0
(b) State:
Input:
Output:
f b c e d g h g g h a
1 1 1 0 0 1 0 0 1 1
1 0 0 0 1 1 1 0 1 0
f b a b d g d g g d a
1 1 1 0 0 1 0 0 1 1
1 0 0 0 1 1 1 0 1 0
5.14
Next
state
x=0 x=1
Present
state
ABCDE
a
b
c
d
e
5.15
00001
00010
00100
01000
10000
00001
00100
00001
10000
00001
00010
01000
01000
01000
01000
Output
x=1 x=0
0
0
0
0
0
0
0
0
1
1
DQ = Qʹ′J + QKʹ′
Present
state
Q
0
0
0
0
1
1
1
1
Inputs
J K
0
0
1
1
0
0
1
1
Next
state
Q
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
Q
No change
Reset to 0
Set to 1
Complement
No change
Reset to 0
Set to 1
Complement
1
m4
1
11
m1
m3
m5
m7
1
10
m2
m6
1
1
Q(t+1) = DQ + Q'J + QK'
D
K
m0
01
K
J
5.16
00
0
Q
J
JK
clk
Q
Q
Q'
Q'
(a)
DA = Axʹ′ + Bx
DB = Aʹ′x + Bxʹ′
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
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rights
reserved.
123
Present
state
A B
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
Input
x
0
1
0
1
0
1
0
1
Next
state
A B
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
A
00
0
A
B
Bx
1
01
11
m0
m1
m3
m4
m5
m7
1
10
m2
1
m6
1
1
x
DA = Ax' + Bx
A
00
0
A
B
Bx
1
01
m0
m1
m4
m5
1
11
m3
10
m2
1
m7
m6
1
1
x
DB = A'x + Bx'
(b)
DA = A'x + Ax'
DB = AB + Bx'
Present
state
A B
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
Input
x
0
1
0
1
0
1
0
1
Next
state
A B
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
A
00
0
A
B
Bx
1
01
m0
m1
m4
m5
1
1
11
m3
10
m2
1
m7
m6
1
x
DA = A'x + Ax'
A
00
0
A
B
Bx
1
01
m0
m1
m4
m5
1
11
10
m3
m2
m7
m6
1
1
1
x
DB = AB + Bx'
5.17
The output is 0 for all 0 inputs until the first 1 occurs, at which time the output is 1. Thereafter, the output
is the complement of the input. The state diagram has two states. In state 0: output = input; in state 1:
output = input'.
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
124
D
x
Q
y
Present state
Input
Next state
Output
clk
A
0
0
1
1
x
0
1
0
1
A
0
1
1
1
y
0
1
1
0
reset_b
0/0
0/1
1/0
reset_b
0
1
1/1
DA = A + x
y = Ax' + A'x
5.18
Binary up-down counter with enable E.
Present
Next
state Input state
AB
x
AB
00
00
00
00
01
01
01
01
10
10
10
10
11
11
11
11
01
01
10
11
00
01
10
11
00
01
10
11
00
01
10
11
00
00
11
01
01
01
01
10
10
10
01
11
11
11
11
11
Flip-flop inputs
JA KA JB KB
0 x
0 x
1 x
0 x
0 x
0 x
0 x
1 x
x 0
x 0
x 1
x 0
x 0
x 0
1 0
x1
0
0
1
1
x
x
x
x
1
1
x
x
x
x
x
x
x
x
x
x
0
0
1
1
0
0
1
1
0
0
1
1
Digital
Design
With
An
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HDL
–
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Ciletti,
Copyright
2012,
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rights
reserved.
125
AB
Ex
E
00
00
01
11
A
10
01
11
10
m0
m1
m3
m2
m4
m5
m7
m6
m12
m13
m15
x
m8
x
x
m9
x
1
AB
1
Cx
00
01
m14
x
B
x
m11
m10
x
11
A
x
C
00
10
m0
m4
x
x
Ex
00
01
11
A
10
m0
m4
x
01
m1
m5
x
11
m3
m7
1
x
10
m2
m6
01
m14
m8
m9
m11
m10
1
E
x
11
A
1
x
JB = E
5.19
x
m7
10
m2
x
x
m6
x
m13
m15
m14
m8
m9
m11
m10
1
B
1
E
00
x
m15
x
x
Ex
00
m13
x
AB
1
m12
x
m5
m3
x
KA = (Bx + B'x')E
E
00
m1
11
m12
x
JA = (Bx + B'x')E
AB
01
10
m0
x
01
m1
x
11
m3
x
10
m2
m4
m5
m7
m12
m13
m15
m14
m8
m9
m11
m10
x
x
1
1
x
KB = E
(a) Unused states (see Fig. P5.19): 101, 110, 111.
x
m6
x
1
E
1
x
Present
Next
Input
Output
state
state
y
ABC
x
ABC
000
0
011
0
000
1
100
1
001
0
001
0
001
1
100
1
010
0
010
0
010
1
000
1
011
0
001
0
011
1
010
1
100
0
010
0
100
1
011
1
d(A, B, C, x) = Σ (10, 11, 12, 13, 14, 15)
Digital
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126
AB
Cx
C
00
00
01
11
A
10
01
m0
m1
m4
m5
1
11
m3
10
AB
Cx
1
00
m7
m6
01
m12
x
m8
m13
x
m9
m15
m14
x
B
x
m11
m10
x
11
A
x
C
00
m2
10
m0
m4
1
1
00
01
11
A
10
m0
1
m4
01
11
10
m1
m3
m2
m5
m7
m6
01
m14
m8
m9
m11
m10
1
x
m7
10
m2
m6
1
m15
m14
m8
m9
m11
m10
1
x
x
1
B
x
x
x
B
x
11
A
x
C
00
1
m15
x
m5
Cx
00
m13
x
AB
1
m12
x
m3
x
DB = A + C'x' + BCx
C
00
m1
m13
x
x
Cx
11
m12
DA = A'B'x
AB
01
10
01
m0
m1
m4
m5
11
m3
1
m7
1
1
1
10
m2
m6
m12
m13
m15
m14
m8
m9
m11
m10
x
x
DC = Cx'+ Ax +A'B'x'
x
x
x
x
y = A'x
B
x
x
The machine is self-correcting, i.e., the
unused states transition to known states.
111
101
0/0
1/0
0/0
1/0
011
110
0/0
1/0
010
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127
(b) With JK flip=flops, the state table is the same as in (a).
Flip-flop inputs
JA KA JB KB JC KC
0
1
0
1
0
0
0
0
x
x
x
x
x
x
x
x
x
x
1
1
1
0
0
0
x
x
x
x
1
1
x
x
x
x
0
1
1
0
x
x
1
0
x
x
0
0
x
x
0
1
x
x
0
1
x
x
0
1
x
x
JA = B'x
KA = 1
JB = A + C'x'
KB = C' x+ Cx'
JC = Ax + A'B'x' KC = x
y = A'x
The machine is self-correcting
because KA = 1.
5.20
From state table 5.4: TA (A, B, x) = Σ (2, 3, 6), TB(A, B, x) = Σ (0, 3, 4, 6).
A
00
0
A
B
Bx
1
01
11
m0
m1
m3
m4
m5
m7
1
A
10
m2
m6
1
00
0
1
A
B
Bx
1
m0
m4
x
TA = A'B + Bx'
5.21
1
1
01
11
m1
m3
m5
m7
1
10
m2
m6
1
x
TB = B'x' + A'x + A'Bx
The statements associated with an initial keyword execute once, in sequence, with the activity expiring
after the last statment competes execution; the statements assocated with the always keyword execute
repeatedly, subject to timing control (e.g, #10).
5.22
(a)
(b)
0
5.23
20
40
60
80
100
120
140
t
160
(a) RegA = 125, RegB = 125
(b) RegA = 125, RegB = 50 Note: Text has error, with RegB = 30 at page 526).
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128
5.24
(a)
module DFF (output reg Q, input D, clk, preset, clear);
always @ (posedge clk, negedge preset, negedge clear )
if (preset == 0) Q <= 1'b1;
else if (clear == 0) Q <= 1'b0;
else Q <= D;
endmodule
module t_DFF ();
wire Q;
reg clk, preset, clear;
reg D;
DFF M0 (Q, D, clk, preset, clear);
initial #160 $finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
#10 preset = 0;
#20 preset = 1;
#50 clear = 0;
#80 clear = 1;
#10 D = 1;
#100 D = 0;
#200 D = 1;
join
endmodule
Name
0
60
120
clk
preset
clear
D
Q
(b)
module
DFF
(output
reg
Q,
input
D,
clk,
preset,
clear);
always @ (posedge clk)
if (preset == 0) Q <= 1'b1;
else if (clear == 0) Q <= 1'b0;
else Q <= D;
endmodule
Name
0
60
120
clk
preset
clear
D
Q
Digital
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129
5.25
module Quad_Input_DFF (output reg Q, input D1, D2, D3, D4, s1, s0, clk, reset_b);
always @ (posedge clk, negedge reset_b)
if (reset_b == 1'b0) Q <= 0;
else case ({s1, s0})
2'b00: Q <= D1;
2'b01: Q <= D2;
2'b10: Q <= D3;
2'b11: Q <= D4;
endcase
endmodule
module t_Quad_Input_DFF ();
wire Q;
reg D1, D2, D3, D4, s1, s0, clk, reset_b;
Quad_Input_DFF M0 (Q, D1, D2, D3, D4, s1, s0, clk, reset_b);
initial #350 $finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
begin s1 = 0; s0 = 0; end
#40 begin s1 = 0; s0 = 1; end
#80 begin s1 =1; s0 = 0; end
#120 begin s1 = 1; s0 = 0; end
#160 begin s1 = 1; s0 = 1; end
join
initial fork
begin D1 = 0; forever #10 D1 = ~D1; end
begin D2 = 1; forever #20 D2 = ~D2; end
begin D3 = 0; forever #10 D3 = ~D3; end
begin D4 = 0; forever #20 D4 = ~D4; end
join
initial fork
#2 reset_b = 1;
#3 reset_b = 0;
#4 reset_b = 1;
join
endmodule
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130
5.26
(a)
Q(t + 1) = JQʹ′ + Kʹ′Q
When Q = 0, Q(t + 1) = J
When Q = 1, Q(t + 1) = Kʹ′
module JK_Behavior_a (output reg Q, input J, K, CLK, reset_b);
always @ (posedge CLK, negedge reset_b)
if
(reset_b
==
0)
Q
<=
0;
else
if (Q == 0)
Q <= J;
else
Q <= ~K;
endmodule
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131
(b)
module JK_Behavior_b (output reg Q, input J, K, CLK, reset_b);
always @ (posedge CLK, negedge reset_b)
if
(reset_b
==
0)
Q
<=
0;
else
case ({J, K})
2'b00: Q <= Q;
2'b01: Q <= 0;
2'b10: Q <= 1;
2'b11: Q <= ~Q;
endcase
endmodule
module t_Prob_5_26 ();
wire Q_a, Q_b;
reg J, K, clk, reset_b;
JK_Behavior_a M0 (Q_a, J, K, clk, reset_b);
JK_Behavior_b M1 (Q_b, J, K, clk, reset_b);
initial #100 $finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
#2 reset_b = 1;
#3 reset_b = 0;
// Initialize to s0
#4 reset_b = 1;
J =0; K = 0;
#20 begin J= 1; K = 0; end
#30 begin J = 1; K = 1; end
#40 begin J = 0; K = 1; end
#50 begin J = 1; K = 1; end
join
endmodule
Name
0
40
80
clk
reset_b
J
K
Q_a
Q_b
5.27
// Mealy FSM zero detector (See Fig. 5.16)
module Mealy_Zero_Detector (
output reg y_out,
input x_in, clock, reset
);
reg [1: 0] state, next_state;
parameter S0 = 2'b00, S1 = 2'b01, S2 = 2'b10, S3 = 2'b11;
always @ (posedge clock, negedge reset) // state transition
if (reset == 0) state <= S0;
else state <= next_state;
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132
always @ (state, x_in) // Form the next state
case (state)
S0: begin y_out = 0; if (x_in) next_state = S1; else next_state = S0; end
S1:
begin y_out = ~x_in; if (x_in)
next_state = S3; else next_state = S0; end
S2: begin y_out = ~x_in; if (~x_in) next_state = S0; else next_state = S2; end
S3:
begin y_out = ~x_in; if (x_in) next_state = S2; else next_state = S0; end
endcase
endmodule
module t_Mealy_Zero_Detector;
wire t_y_out;
reg t_x_in, t_clock, t_reset;
Mealy_Zero_Detector M0 (t_y_out, t_x_in, t_clock, t_reset);
initial #200 $finish;
initial begin t_clock = 0; forever #5 t_clock = ~t_clock; end
initial fork
t_reset = 0;
#2 t_reset = 1;
#87 t_reset = 0;
#89 t_reset = 1;
#10 t_x_in = 1;
#30 t_x_in = 0;
#40 t_x_in = 1;
#50 t_x_in = 0;
#52 t_x_in = 1;
#54 t_x_in = 0;
#70 t_x_in = 1;
#80 t_x_in = 1;
#70 t_x_in = 0;
#90 t_x_in = 1;
#100 t_x_in = 0;
#120 t_x_in = 1;
#160 t_x_in = 0;
#170 t_x_in = 1;
join
endmodule
Note: Simulation results match Fig. 5.22.
Name
6
46
86
126
166
t_clock
t_reset
state[1:0]
0
1
3
0
1
0
0
1
0
1
3
2
0
1
t_x_in
t_y_out
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5.28
133
(a)
module Prob_5_28a (output A, input x, y, clk, reset_b);
parameter s0 = 0, s1 = 1;
reg state, next_state;
assign A = state;
always @ (posedge clk, negedge reset_b)
if (reset_b == 0) state <= s0; else state <= next_state;
always @ (state, x, y) begin
next_state = s0;
case (state)
s0:
case ({x, y})
2'b00, 2'b11: next_state = s0;
2'b01, 2'b10: next_state = s1;
endcase
s1:
case ({x, y})
2'b00, 2'b11: next_state = s1;
2'b01, 2'b10: next_state = s0;
endcase
endcase
end
endmodule
module t_Prob_5_28a ();
wire A;
reg x, y, clk, reset_b;
Prob_5_28a M0 (A, x, y, clk, reset_b);
initial #350 $finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
#2 reset_b = 1;
#3 reset_b = 0;
// Initialize to s0
#4 reset_b = 1;
x =0; y = 0;
#20 begin x= 1; y = 1; end
#30 begin x = 0; y = 0; end
#40 begin x = 1; y = 0; end
#50 begin x = 0; y = 0; end
#60 begin x = 1; y = 1; end
#70 begin x = 1; y = 0; end
#80 begin x = 0; y = 1; end
join
endmodule
0
Name
80
clk
reset_b
x
y
A
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160
134
(b)
module Prob_5_28b (output A, input x, y, Clock, reset_b);
xor (w1, x, y);
xor (w2, w1, A);
DFF M0 (A, w2, Clock, reset_b);
endmodule
module DFF (output reg Q, input D, Clock, reset_b);
always @ (posedge Clock, negedge reset_b)
if (reset_b == 0) Q <= 0;
else Q <= D;
endmodule
module t_Prob_5_28b ();
wire A;
reg x, y, clk, reset_b;
Prob_5_28b M0 (A, x, y, clk, reset_b);
initial #350 $finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
#2 reset_b = 1;
#3 reset_b = 0;
// Initialize to s0
#4 reset_b = 1;
x =0; y = 0;
#20 begin x= 1; y = 1; end
#30 begin x = 0; y = 0; end
#40 begin x = 1; y = 0; end
#50 begin x = 0; y = 0; end
#60 begin x = 1; y = 1; end
#70 begin x = 1; y = 0; end
#80 begin x = 0; y = 1; end
join
endmodule
Name
0
60
120
180
Clock
reset_b
x
y
A
Digital
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135
(c)
See results of (b) and (c).
module t_Prob_5_28c ();
wire A_a, A_b;
reg x, y, clk, reset_b;
Prob_5_28a M0 (A_a, x, y, clk, reset_b);
Prob_5_28b M1 (A_b, x, y, clk, reset_b);
initial #350 $finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
#2 reset_b = 1;
#3 reset_b = 0;
// Initialize to s0
#4 reset_b = 1;
x =0; y = 0;
#20 begin x= 1; y = 1; end
#30 begin x = 0; y = 0; end
#40 begin x = 1; y = 0; end
#50 begin x = 0; y = 0; end
#60 begin x = 1; y = 1; end
#70 begin x = 1; y = 0; end
#80 begin x = 0; y = 1; end
join
endmodule
Name
0
60
120
180
clk
reset_b
x
y
A_a
A_b
5.29
module Prob_5_29 (output reg y_out, input x_in, clock, reset_b);
parameter s0 = 3'b000, s1 = 3'b001, s2 = 3'b010, s3 = 3'b011, s4 = 3'b100;
reg [2: 0] state, next_state;
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) state <= s0;
else state <= next_state;
always @ (state, x_in) begin
y_out = 0;
next_state = s0;
case (state)
s0:
if (x_in) begin next_state = s4; y_out = 1; end else begin next_state = s3; y_out = 0; end
s1:
if (x_in) begin next_state = s4; y_out = 1; end else begin next_state = s1; y_out = 0; end
s2:
if (x_in) begin next_state = s0; y_out = 1; end else begin next_state = s2; y_out = 0; end
s3:
if (x_in) begin next_state = s2; y_out = 1; end else begin next_state = s1; y_out = 0; end
s4:
if (x_in) begin next_state = s3; y_out = 0; end else begin next_state = s2; y_out = 0; end
default: next_state = 3'bxxx;
endcase
end
endmodule
module t_Prob_5_29 ();
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136
wire y_out;
reg x_in, clk, reset_b;
Prob_5_29 M0 (y_out, x_in, clk, reset_b);
initial #350$finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
#2 reset_b = 1;
#3 reset_b = 0;
// Initialize to s0
#4 reset_b = 1;
// Trace the state diagram and monitor y_out
x_in = 0;
// Drive from s0 to s3 to S1 and park
#40 x_in = 1;
// Drive to s4 to s3 to s2 to s0 to s4 and loop
#90 x_in = 0;
// Drive from s0 to s3 to s2 and part
#110 x_in = 1;
// Drive s0 to s4 etc
join
endmodule
0
40
80
Name
120
clk
reset_b
x_in
state[2:0]
3
1
4
3
2
0
4
2
0
y_out
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4
137
5.30
A
D
B
E
CLK
D
Q
CLK
C
CLK
5.31
module Seq_Ckt (input A, B, C, CLK, output reg Q);
reg E;
always @ (posedge CLK)
begin
Q = E && C;
E = A || B;
end
endmodule
Note: The statements must be written in an order than produces the effect of concurrent assignments.
Digital
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138
5.32
initial begin
enable = 0; A = 1; B = 0; C = 0; D = 1; E = 1; F = 1;
#10 A = 0; B = 1; C = 1;
#10 A = 1; B = 0; D = 1; E = 0;
#10 B = 1; E = 1; F = 0;
#10 enable = 1;
B = 0; D= 0; F =1;
#10 B = 1;
#10 B = 0; D = 1;
#10 B = 1;
end
initial fork
enable = 0; A = 1; B = 0; C = 0; D = 1; E = 1; F = 1;
#10 begin A = 0; B = 1; end
#20 begin A = 1; B = 0; D = 1; E = 0; end
#30 begin B = 1; E = 1; F = 0; end
#40 begin B = 0; D = 0; F = 1; end
#50 begin B = 1; end
#60 begin B = 0; D = 1; end
#70 begin B = 1; end
join
5.33
Signal transitions that are caused by input signals that change on the active edge of the clock race with the
clock itself to reach the affected flip-flops, and the outcome is indeterminate (unpredictable). Conversely,
changes caused by inputs that are synchronized to the inactive edge of the clock reach stability before the
active edge, with predictable outputs of the flip-flops that are affected by the inputs.
Digital
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rights
reserved.
5.34
139
Note: Problem statement should refer to Problem 5.2 instead of Fig 5.5.
module JK_flop_Prob_5_34 (output Q, input J, K, clk);
wire K_bar;
D_flop M0 (Q, D, clk);
Mux M1 (D, J, K_bar, Q);
Inverter M2 (K_bar, K);
endmodule
module D_flop (output reg Q, input D, clk);
always @ (posedge clk) Q <= D;
endmodule
module Inverter (output y_bar, input y);
assign y_bar = ~y;
endmodule
module Mux (output y, input a, b, select);
assign y = select ? a: b;
endmodule
module t_JK_flop_Prob_5_34 ();
wire Q;
reg J, K, clock;
JK_flop_Prob_5_34 M0 (Q, J, K, clock);
initial #500 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial fork
#10 begin J = 0; K = 0; end
// toggle Q unknown
#20 begin J = 0; K = 1; end
// set Q to 0
#30 begin J = 1; K = 0; end
// set q to 1
#40 begin J = 1; K = 1; end
// no change
#60 begin J = 0; K = 0; end
// toggle Q
join
endmodule
Name 0
30
60
90
clock
J
K
Q
Digital
Design
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140
5.35
From Problem 5.6:
x
y
xy' + xA
D
Q
D
Q
A, z
C
B
CP
(b)
(c)
A(t+1) = xy' + xB
B(t+1) = xA + xB'
z=A
00, 01
x
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
y
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
Output
B
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
Next
state
A
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
Inputs
Present
state
00, 01
A
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
z
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
B
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
00
0
01
0
11
10
00, 01
10,11
00, 01
10
1
11
1
10, 11
10, 11
module Prob_5_35 (output out_z, input in_x, in, in_y, clk, reset_b);
reg [1:0] state, next_state;
assign out_z = ((state == 2'b10) || (state == 2'b11));
always @ (posedge clk) if (reset_b == 1'b0) state <= 2'b00; else state <= next_state;
always @ (state, in_x, in_y)
case (state)
2'b00: if (({in_x, in_y} == 2'b00) || ({in_x, in_y} == 2'b01)) next_state = 2'b00;
else if ({in_x, in_y} == 2'b10) next_state = 2'b11;
else next_state = 2'b01;
2'b01: if (({in_x, in_y} == 2'b00) || ({in_x, in_y} == 2'b01)) next_state = 2'b00;
else if (({in_x, in_y} == 2'b10) || ({in_x, in_y} == 2'b11)) next_state = 2'b10;
2'b10: if (({in_x, in_y} == 2'b00) || ({in_x, in_y} == 2'b01)) next_state = 2'b00;
else if (({in_x, in_y} == 2'b10) || ({in_x, in_y} == 2'b11)) next_state = 2'b11;
2'b11: if (({in_x, in_y} == 2'b00) || ({in_x, in_y} == 2'b01)) next_state = 2'b00;
else if (({in_x, in_y} == 2'b10) || ({in_x, in_y} == 2'b11)) next_state = 2'b11;
endcase
endmodule
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141
module t_Prob_5_35 ();
wire out_z;
reg in_x, in, in_y, clk, reset_b;
Prob_5_35 M0 (out_z, in_x, in, in_y, clk, reset_b);
initial #250 $finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
reset_b = 0;
#20 reset_b = 1;
#50 {in_x, in_y} = 2'b00;
#60 {in_x, in_y} = 2'b01;
#70 {in_x, in_y} = 2'b11;
#90 {in_x, in_y} = 2'b00;
#110 {in_x, in_y} = 2'b11;
#120 {in_x, in_y} = 2'b01;
// Remain in 2'b00
// Remain in 2'b00
// Transition to 2'b01
// Transition to 2'b00
// Transition to 2'b01
// Transition to 2'b00
#130 {in_x, in_y} = 2'b11;
#140 {in_x, in_y} = 2'b10;
#150 {in_x, in_y} = 2'b00;
#160 {in_x, in_y} = 2'b11;
// Transition to 2'b01
// Transition to 2'b10
// Transition to 2'b00
// Transition to 2'b01
#170 {in_x, in_y} = 2'b11;
#180 {in_x, in_y} = 2'b01;
// Transition to 2'b10
// Transition to 2'b00
#190 {in_x, in_y} = 2'b11;
#200 {in_x, in_y} = 2'b11;
#210 {in_x, in_y} = 2'b11;
// Transition to 2'b01
// Transition to 2'b10
// Transition to 2'b11
#220 {in_x, in_y} = 2'b10;
#230 {in_x, in_y} = 2'b11;
join
endmodule
// Remain in 2'b11
// Remain in 2'b11
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5.36
142
Note: See Problem 5.8 (counter with repeated sequence: (A, B) = 00, 01, 10, 00 ....
// See Fig. P5.8
module Problem_5_36 (output A, B, input Clock, reset_b);
or (T_A, A, B);
or (T_B, A_b, B);
T_flop M0 (A, A_b, T_A, Clock, reset_b);
T_flop M1 (B, B_b, T_B, Clock, reset_b);
endmodule
module T_flop (output reg Q, output QB, input T, Clock, reset_b);
assign QB = ~ Q;
always @ (posedge Clock, negedge reset_b)
if (reset_b == 0) Q <= 0;
else if (T) Q <= ~Q;
endmodule
module t_Problem_5_36 ();
wire A, B;
reg Clock, reset_b;
Problem_5_36 M0 (A, B, Clock, reset_b);
initial #350$finish;
initial begin Clock = 0; forever #5 Clock = ~Clock; end
initial fork
#2 reset_b = 1;
#3 reset_b = 0;
#4 reset_b = 1;
join
endmodule
Name
0
30
60
90
Clock
reset_b
A
B
5.37
module Problem_5_37_Fig_5_25 (output reg y, input x_in, clock, reset_b);
parameter a = 3'b000, b = 3'b001, c = 3'b010, d = 3'b011, e = 3'b100, f = 3'b101, g = 3'b110;
reg [2: 0] state, next_state;
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) state <= a;
else state <= next_state;
always @ (state, x_in) begin
y = 0;
next_state = a;
case (state)
a:
begin y = 0; if (x_in == 0) next_state = a; else next_state = b; end
Digital
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143
b:
begin y = 0; if (x_in == 0) next_state = c; else next_state = d; end
c:
begin y = 0; if (x_in == 0) next_state = a; else next_state = d; end
d:
if (x_in == 0) begin y = 0; next_state = e; end
else begin y = 1; next_state = f; end
e:
if (x_in == 0) begin y = 0; next_state = a; end
else begin y = 1; next_state = f; end
f:
if (x_in == 0) begin y = 0; next_state = g; end
else begin y = 1; next_state = f; end
g:
if (x_in == 0) begin y = 0; next_state = a; end
else begin y = 1; next_state = f; end
default: next_state = a;
endcase
end
endmodule
module Problem_5_37_Fig_5_26 (output reg y, input x_in, clock, reset_b);
parameter a = 3'b000, b = 3'b001, c = 3'b010, d = 3'b011, e = 3'b100;
reg [2: 0] state, next_state;
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) state <= a;
else state <= next_state;
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144
always @ (state, x_in) begin
y = 0;
next_state = a;
case (state)
a:
begin y = 0; if (x_in == 0) next_state = a; else next_state = b; end
b:
begin y = 0; if (x_in == 0) next_state = c; else next_state = d; end
c:
begin y = 0; if (x_in == 0) next_state = a; else next_state = d; end
d:
if (x_in == 0) begin y = 0; next_state = e; end
else begin y = 1; next_state = d; end
e:
if (x_in == 0) begin y = 0; next_state = a; end
else begin y = 1; next_state = d; end
default:
endcase
end
endmodule
next_state = a;
module t_Problem_5_37 ();
wire y_Fig_5_25, y_Fig_5_26;
reg x_in, clock, reset_b;
Problem_5_37_Fig_5_25 M0 (y_Fig_5_25, x_in, clock, reset_b);
Problem_5_37_Fig_5_26 M1 (y_Fig_5_26, x_in, clock, reset_b);
wire [2: 0] state_25 = M0.state;
wire [2: 0] state_26 = M1.state;
initial #350 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial fork
x_in = 0;
#2 reset_b = 1;
#3 reset_b = 0;
#4 reset_b = 1;
#20 x_in = 1;
#40 x_in = 0; // abdea, abdea
#60 x_in = 1;
#100 x_in = 0; // abdf....fga, abd ... dea
#120 x_in = 1;
#160 x_in = 0;
#170 x_in = 1;
#200 x_in = 0; // abdf....fgf...fga, abd ...ded...ea
#220 x_in = 1;
#240 x_in = 0;
#250 x_in = 1; // abdef... // abded...
join
endmodule
Digital
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145
0
Name
110
220
clock
reset_b
x_in
state_25[2:0]
0
1 3 4
1 3
state_26[2:0]
0
1 3 4
1
5
3
6 0
4 0
3
5
3
5
6 0 1
4
5
3
4 0 1
4
3
y_Fig_5_25
y_Fig_5_26
5.38
(a)
module Prob_5_38a (input x_in, clock, reset_b);
parameter s0 = 2'b00, s1 = 2'b01, s2 = 2'b10, s3 = 2'b11;
reg [1: 0] state, next_state;
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) state <= s0;
else state <= next_state;
always @ (state, x_in) begin
next_state = s0;
case (state)
s0:
if (x_in == 0) next_state = s0;
else if (x_in == 1) next_state = s3;
s1:
if (x_in == 0) next_state = s1;
else if (x_in == 1) next_state = s2;
s2:
if (x_in == 0) next_state = s2;
else if (x_in == 1) next_state = s0;
s3:
if (x_in == 0) next_state = s3;
else if (x_in == 1) next_state = s1;
default:
next_state = s0;
endcase
end
endmodule
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146
module t_Prob_5_38a ();
reg x_in, clk, reset_b;
Prob_5_38a M0 ( x_in, clk, reset_b);
initial #350$finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
#2 reset_b = 1;
#3 reset_b = 0;
// Initialize to s0
#4 reset_b = 1;
#2 x_in = 0;
#20 x_in = 1;
#60 x_in = 0;
#80 x_in = 1;
#90 x_in = 0;
#110 x_in = 1;
#120 x_in = 0;
#140 x_in = 1;
#150 x_in = 0;
#170 x_in= 1;
join
endmodule
0
Name
60
120
180
clk
reset_b
x_in
state[1:0]
0
3
1
2
0
3
1
2
(b)
module Prob_5_38b (input x_in, clock, reset_b);
parameter s0 = 2'b00, s1 = 2'b01, s2 = 2'b10, s3 = 2'b11;
reg [1: 0] state, next_state;
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) state <= s0;
else state <= next_state;
always @ (state, x_in) begin
next_state = s0;
case (state)
s0:
if (x_in == 0) next_state = s0;
else if (x_in == 1) next_state = s3;
s1:
if (x_in == 0) next_state = s1;
else if (x_in == 1) next_state = s2;
s2:
if (x_in == 0) next_state = s2;
else if (x_in == 1) next_state = s0;
s3:
if (x_in == 0) next_state = s3;
else if (x_in == 1) next_state = s1;
default:
next_state = s0;
endcase
end
endmodule
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0
3
147
module t_Prob_5_38b ();
reg x_in, clk, reset_b;
Prob_5_38b M0 ( x_in, clk, reset_b);
initial #350$finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
#2 reset_b = 1;
#3 reset_b = 0;
// Initialize to s0
#4 reset_b = 1;
#2 x_in = 0;
#20 x_in = 1;
#60 x_in = 0;
#80 x_in = 1;
#90 x_in = 0;
#110 x_in = 1;
#120 x_in = 0;
#140 x_in = 1;
#150 x_in = 0;
#170 x_in= 1;
join
endmodule
Name
0
60
120
180
clk
reset_b
x_in
state[1:0]
0
3
1
2
0
3
1
2
0
3
1
5.39
module Serial_2s_Comp (output reg B_out, input B_in, clk, reset_b);
// See problem 5.17
parameter S_0 = 1'b0, S_1 = 1'b1;
reg state, next_state;
always @ (posedge clk, negedge reset_b) begin
if (reset_b == 0) state <= S_0;
else state <= next_state;
end
always @ (state, B_in) begin
B_out = 0;
case (state)
S_0: if (B_in == 0) begin next_state = S_0; B_out = 0; end
else if (B_in == 1) begin next_state = S_1; B_out = 1; end
S_1: begin next_state = S_1; B_out = ~B_in; end
default: next_state = S_0;
endcase
end
endmodule
module t_Serial_2s_Comp ();
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2
0
148
wire B_in, B_out;
reg clk, reset_b;
reg [15: 0] data;
assign B_in = data[0];
always @ (negedge clk, negedge reset_b)
if (reset_b == 0) data <= 16'ha5ac; else data <= data >> 1; // Sample bit stream
Serial_2s_Comp M0 (B_out, B_in, clk, reset_b);
initial #150 $finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
#10 reset_b = 0;
#12 reset_b = 1;
join
endmodule
Name
0
60
120
clk
reset_b
B_in
state
B_out
5.40
EF = 0x
s0
10
0x
10
11
11
11
11
s3
s1
10
0x
10
s2
0x
module Prob_5_40 (input E, F, clock, reset_b);
parameter s0 = 2'b00, s1 = 2'b01, s2 = 2'b10, s3 = 2'b11;
reg [1: 0] state, next_state;
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) state <= s0;
else state <= next_state;
always @ (state, E, F) begin
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149
next_state = s0;
case (state)
s0:
if (E == 0) next_state = s0;
else if (F == 1) next_state = s1; else next_state = s3;
s1:
if (E == 0) next_state = s1;
else if (F == 1) next_state = s2; else next_state = s0;
s2:
if (E == 0) next_state = s2;
else if (F == 1) next_state = s3; else next_state = s1;
s3:
if (E == 0) next_state = s3;
else if (F == 1) next_state = s0; else next_state = s2;
default: next_state = s0;
endcase
end
endmodule
module t_Prob_5_40 ();
reg E, F, clk, reset_b;
Prob_5_40 M0 ( E, F, clk, reset_b);
initial #350$finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
#2 reset_b = 1;
#3 reset_b = 0;
// Initialize to s0
#4 reset_b = 1;
#2 E = 0;
#20 begin E = 1; F = 1; end
#60 E = 0;
#80 E = 1;
#90 E = 0;
#110 E = 1;
#120 E = 0;
#140 E = 1;
#150 E = 0;
#170 E= 1;
#170 F = 0;
join
endmodule
Name
0
100
200
clk
reset_b
E
F
state[1:0]
0
1 2 3
0
1
2
3
2 1 0 3 2 1
5.41
module Prob_5_41 (output reg y_out, input x_in, clock, reset_b);
parameter s0 = 3'b000, s1 = 3'b001, s2 = 3'b010, s3 = 3'b011, s4 = 3'b100;
reg [2: 0] state, next_state;
Digital
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150
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) state <= s0;
else state <= next_state;
always @ (state, x_in) begin
y_out = 0;
next_state = s0;
case (state)
s0:
if (x_in) begin next_state = s4; y_out = 1; end else begin next_state = s3; y_out = 0; end
s1:
if (x_in) begin next_state = s4; y_out = 1; end else begin next_state = s1; y_out = 0; end
s2:
if (x_in) begin next_state = s0; y_out = 1; end else begin next_state = s2; y_out = 0; end
s3:
if (x_in) begin next_state = s2; y_out = 1; end else begin next_state = s1; y_out = 0; end
s4:
if (x_in) begin next_state = s3; y_out = 0; end else begin next_state = s2; y_out = 0; end
default: next_state = 3'bxxx;
endcase
end
endmodule
module t_Prob_5_41 ();
wire y_out;
reg x_in, clk, reset_b;
Prob_5_41 M0 (y_out, x_in, clk, reset_b);
initial #350$finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
#2 reset_b = 1;
#3 reset_b = 0;
// Initialize to s0
#4 reset_b = 1;
// Trace the state diagram and monitor y_out
x_in = 0;
// Drive from s0 to s3 to S1 and park
#40 x_in = 1;
// Drive to s4 to s3 to s2 to s0 to s4 and loop
#90 x_in = 0;
// Drive from s0 to s3 to s2 and part
#110 x_in = 1;
// Drive s0 to s4 etc
join
endmodule
0
40
80
Name
120
clk
reset_b
x_in
state[2:0]
3
1
4
3
2
0
4
2
0
y_out
Digital
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4
151
5.42
module Prob_5_42 (output A, B, B_bar, y, input x, clk, reset_b);
// See Fig. 5.29
wire w1, w2, w3, D1, D2;
and (w1, A, x);
and (w2, B, x);
or (D_A, w1, w2);
and (w3, B_bar, x);
and (y, A, B);
or (D_B, w1, w3);
DFF M0_A (A, D_A, clk, reset_b);
DFF M0_B (B, D_B, clk, reset_b);
not (B_bar, B);
endmodule
module DFF (output reg Q, input data, clk, reset_b);
always @ (posedge clk, negedge reset_b)
if (reset_b == 0) Q <= 0; else Q <= data;
endmodule
module t_Prob_5_42 ();
wire A, B, B_bar, y;
reg bit_in, clk, reset_b;
wire [1:0] state;
assign state = {A, B};
wire detect = y;
Prob_5_42 M0 (A, B, B_bar, y, bit_in, clk, reset_b);
// Patterns from Problem 5.45.
initial #350$finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
#2 reset_b = 1;
#3 reset_b = 0;
#4reset_b = 1;
// Trace the state diagram and monitor detect (assert in S3)
bit_in = 0;
// Park in S0
#20 bit_in = 1;
// Drive to S0
#30 bit_in = 0;
// Drive to S1 and back to S0 (2 clocks)
#50 bit_in = 1;
#70 bit_in = 0;
// Drive to S2 and back to S0 (3 clocks)
#80 bit_in = 1;
#130 bit_in = 0;// Drive to S3, park, then and back to S0
join
endmodule
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152
0
Name
50
100
150
reset_b
clk
A
B
B_bar
y
state[1:0]
x
0
1
0
1
2
0
1
2
3
0
detect
5.43
module Binary_Counter_3_bit (output [2: 0] count, input clk, reset_b)
always @ (posedge clk) if (reset_b == 0) count <= 0; else count <= next_count;
always @ (count) begin
case (state)
3'b000:
count = 3'b001;
3'b001:
count = 3'b010;
3'b010:
count = 3'b011;
3'b011:
count = 3'b100;
3'b100:
count = 3'b001;
3'b101:
count = 3'b010;
3'b110:
count = 3'b011;
3'b111:
count = 3'b100;
default: count = 3'b000;
endcase
end
endmodule
module t_Binary_Counter_3_bit ()
wire [2: 0] count;
reg clk, reset_b;
Binary_Counter_3_bit M0 ( count, clk, reset_b)
initial #150 $finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
reset = 1;
#10 reset = 0;
#12 reset = 1;
endmodule
Name
0
50
100
150
reset_b
clk
count[2:0]
x
0
1
2
3
4
5
6
7
0
1
2
3
4
5
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6
153
Alternative: structural model.
module Prob_5_41 (output A2, A1, A0, input T, clk, reset_bar);
wire toggle_A2;
T_flop M0 (A0, T, clk, reset_bar);
T_flop M1 (A1, A0, clk, reset_bar);
T_flop M2 (A2, toggle_A2, clk, reset_bar);
and (toggle_A2, A0, A1);
endmodule
module T_flop (output reg Q, input T, clk, reset_bar);
always @ (posedge clk, negedge reset_bar)
if (!reset_bar) Q <= 0; else if (T) Q <= ~Q; else Q <= Q;
endmodule
module t_Prob_5_41;
wire A2, A1, A0;
wire [2: 0] count = {A2, A1, A0};
reg T, clk, reset_bar;
Prob_5_41 M0 (A2, A1, A0, T, clk, reset_bar);
initial #200 $finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork reset_bar = 0; #2 reset_bar = 1; #40 reset_bar = 0; #42 reset_bar = 1; join
initial fork T = 0; #20 T = 1; #70 T = 0; #110 T = 1; join
endmodule
If the input to A0 is changed to 0 the counter counts incorrectly. It resumes a correct counting
sequence when T is changed back to 1.
Name
0
40
80
120
160
200
Default
clk
reset_bar
T
A2
A1
A0
count[2:0]
0
1
2 0
1
2
3
5
7
1
3
4
5
6
7
0
1
2
3
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154
5.44
module DFF_asynch_reset (output reg Q, input data, clk, reset);
always @ (posedge clk, posedge reset)
// Asynchronous reset
if (reset) Q <= 0; else Q <= data;
endmodule
module t_DFF_asynch_reset ();
reg data, clk, reset;
wire Q;
DFF_asynch_reset M0 (Q, data, clk, reset);
initial #150 $finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
reset = 0;
#7 reset = 1;
#41 reset = 0;
#82 reset = 1;
#97 reset = 0;
#12 data = 1;
#50 data = 0;
#60 data = 1;
#80 data = 0;
#90 data = 1;
#110 data = 0;
join
endmodule
Name
0
50
100
150
reset
clk
data
Q
5.45
module Seq_Detector_Prob_5_45 (output detect, input bit_in, clk, reset_b);
parameter S0 = 0, S1 = 1, S2 = 2, S3 = 3;
reg [1: 0] state, next_state;
assign detect = (state == S3);
always @ (posedge clk, negedge reset_b)
if (reset_b == 0) state <= S0; else state <= next_state;
always @ (state, bit_in) begin
next_state = S0;
case (state)
0:
if (bit_in) next_state = S1; else state = S0;
1:
if (bit_in) next_state = S2; else next_state = S0;
2:
if (bit_in) next_state = S3; else state = S0;
3:
if (bit_in) next_state = S3; else next_state = S0;
default: next_state = S0;
endcase
end
endmodule
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155
module t_Seq_Detector_Prob_5_45 ();
wire detect;
reg bit_in, clk, reset_b;
Seq_Detector_Prob_5_45 M0 (detect, bit_in, clk, reset_b);
initial #350$finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
#2 reset_b = 1;
#3 reset_b = 0;
#4reset_b = 1;
// Trace the state diagram and monitor detect (assert in S3)
bit_in = 0;
// Park in S0
#20 bit_in = 1;
// Drive to S0
#30 bit_in = 0;
// Drive to S1 and back to S0 (2 clocks)
#50 bit_in = 1;
#70 bit_in = 0;
// Drive to S2 and back to S0 (3 clocks)
#80 bit_in = 1;
#130 bit_in = 0;
// Drive to S3, park, then and back to S0
join
endmodule
Name
0
40
80
120
reset_b
clk
bit_in
state[1:0]
x
0
1
0
1
2
0
1
2
3
detect
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156
5.46
Pending simulation results
Assumption: Synchronous active-low reset
Moore machine
reset_b, x_in
01, 00, 10
y_out
000
0
11
001
1
010
1
1x
1x
011
1
1x
100
0
1x
101
0
xx
0x
0x
0x
0x
Verify that machine remains in state 000 while reset_b is asserted, independently of x_in.
Verify that machine makes transition from 000 to 001 if not reset_b and if x_in is asserted.
Verify that state transitions from 000 through 101 are correct.
Verify reset_b "on the fly."
Verify that y_out is asserted correctly.
module Prob_5_46 (output y_out, input x_in, clk, reset_b);
reg [2:0] state, next_state;
assign y_out = (state == 3'b001)||(state == 3'b010) || (state == 3'b011);
always @ (posedge clk)
if (reset_b == 1'b0) state <= 3'b000; else state <= next_state;
always @ (x_in, state) begin
next_state = 3'b000;
case (state)
3'b000:
if (x_in) next_state = 3'b001; else next_state = 3'b000;
3'b001:
next_state = 3'b010;
3'b010:
next_state = 3'b011;
3'b011:
next_state = 3'b100;
3'b100:
next_state = 3'b101;
3'b101:
next_state = 3'b000;
default: next_state = 3'b000;
endcase
end
endmodule
module t_Prob_5_46 ();
reg x_in, clk, reset_b;
wire y_out;
Prob_5_46 M0 (y_out, x_in, clk, reset_b);
initial #200 $finish;
initial begin clk = 0; forever #5 clk = !clk; end
initial fork
reset_b = 0;
#10 reset_b = 1;
#80 reset_b = 0;
#90 reset_b = 1;
x_in = 0;
#30 x_in = 1;
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157
#40 x_in = 1;
#50 x_in = 0;
#60 x_in = 1;
#70 x_in = 0;
#120 x_in = 1;
#130 x_in = 0;
join
endmodule
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158
5.47
Assume synchronous active-low reset.
module Prob_5_47 (output reg [3:0] y_out, input Run, clk, reset_b);
always @ (posedge clk)
if (reset_b == 1'b0) y_out <= 4'b000;
else if (Run && (y_out < 4'b1110)) y_out <= y_out + 2'b10;
else if (Run && (y_out == 4'b1110)) y_out <= 4'b0000;
else y_out <= y_out;
// redundant statement and may be omitted
endmodule
// Verify that counting is prevented while reset_b is asserted, independently of Run
// Verify that counting is initiated by Run if reset_b is de-asserted
// Verify reset on-the-fly
// Verify that deasserting Run suspends counting
// Verify wrap-around of counter.
module t_Prob_5_47 ();
reg Run, clk, reset_b;
wire [3:0] y_out;
Prob_5_47 M0 (y_out, Run, clk, reset_b);
initial #300 $finish;
initial begin clk = 0; forever #5 clk = !clk; end
initial fork
reset_b = 0;
#30 reset_b = 1;
Run = 1;
#30 Run = 0;
#50 Run = 1;
#70 Run = 0;
#90 reset_b = 0;
#120 reset_b = 1;
#150 Run = 1;
#180 Run = 0;
#200 Run = 1;
join
endmodule
// Attempt to run is overridden by reset_b
// Initiate counting
// Pause
// reset on-the-fly
// De-assert reset_b
// Resume counting
// Pause counting
// Resume counting
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159
5.48
Assume "a" is the reset state.
module Prob_5_48 (output reg y_out, input x_in, clk, reset_b);
parameter s_a = 2'd0;
parameter s_b = 2'd1;
parameter s_c = 2'd2;
parameter s_d = 2'd3;
reg [1: 0] state, next_state;
always @ (posedge clk)
if (reset_b == 1'b0) state <= s_a;
else state <= next_state;
always @ (state, x_in) begin
next_state = s_a;
y_out = 0;
case (state)
s_a: if (x_in == 1'b0) begin next_state = s_b; y_out = 1; end
else begin next_state = s_c; y_out = 0; end
s_b: if (x_in == 1'b0) begin next_state = s_c; y_out = 0; end
else begin next_state = s_d; y_out = 1; end
s_c: if (x_in == 1'b0) begin next_state = s_b; y_out = 0; end
else begin next_state = s_d; y_out = 1; end
s_d: if (x_in == 1'b0) begin next_state = s_c; y_out = 1; end
else begin next_state = s_a; y_out = 0; end
default: begin next_state = s_a; y_out = 0; end
endcase
end
endmodule
Verify reset action.
Verify state transitions.
Transition to a; hold x_in = 0 and get loop bc…
Transition to a; hold x_in = 1 and get loop acda…
Transitons to b; hold x_in = 1 and get loop bdacd…
Transition to d; hold x_in = 0 and get loop dcbc…
Confirm Mealy outputs at each state/input pair
Verify reset on-the-fly.
module t_Prob_5_48 ();
reg x_in, clk, reset_b;
wire y_out;
Prob_5_48 M0 (y_out, x_in, clk, reset_b);
initial #400 $finish;
initial begin clk = 0; forever #5 clk = !clk; end
initial fork
reset_b = 0;
#30 reset_b = 1;
#30 x_in = 0;
// loop abcbcbc…
#100 reset_b = 0;
#110 reset_b = 1;
#110 x_in = 1;
// loop acdacda…
#200 reset_b = 0;
#210 reset_b = 1;
#210 x_in = 0;
#220 x_in = 1;
// loop bdacdacd…
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#300 reset_b = 0;
#310 reset_b = 1;
#310 x_in = 1;
#330 x_in = 0;
join
endmodule
// loop acdcbcbc….
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161
5.49
Assume "a" is the reset state.
module Prob_5_49 (output reg y_out, input x_in, clk, reset_b);
parameter s_a = 2'd0;
parameter s_b = 2'd1;
parameter s_c = 2'd2;
parameter s_ =d 2'd3;
reg [1: 0] state, next_state;
always @ (posedge clk)
if (reset_b == 1'b0) state <= s_a;
else state <= next_state;
always @ (state, x_in) begin
next_state = s_a;
y_out = 1'b0;
case (state)
s_a: if (x_in == 1'b0) next_state = s_b;
else next_state = s_c;
s_b: begin y_out = 1'b1; if (x_in == 1'b0) next_state = s_c;
else next_state = s_d; end
s_c: begin y_out = 1'b1; if (x_in == 1'b0) next_state = s_b;
else next_state = s_d; end
s_d: if (x_in == 1'b0) next_state = s_c;
else next_state = s_a;
default: next_state = s_a;
endcase
end
endmodule
// Verify reset action.
// Verify state transitions.
// Transition to a; hold x_in = 0 and get loop abcbc…
// Transition to a; hold x_in = 1 and get loop acda…
// Transitons to b; hold x_in = 1 and get loop bdacd…
// Transition to d; hold x_in = 0 and get loop dcbc…
// Confirm Moore outputs at each state
// Verify reset on-the-fly.
module t_Prob_5_49 ();
reg x_in, Run, clk, reset_b;
wire y_out;
Prob_5_49 M0 (y_out, x_in, clk, reset_b);
initial #400 $finish;
initial begin clk = 0; forever #5 clk = !clk; end
initial fork
reset_b = 0;
#30 reset_b = 1;
#30 x_in = 0;
// loop abcbcbc…
#100 reset_b = 0;
#110 reset_b = 1;
#110 x_in = 1;
// loop acdacda…
#200 reset_b = 0;
#210 reset_b = 1;
#210 x_in = 0;
#220 x_in = 1;
// loop bdacdacd…
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#300 reset_b = 0;
#310 reset_b = 1;
#310 x_in = 1;
#330 x_in = 0;
join
endmodule
// loop acdcbcbc….
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163
5.50
The machine is to remain in its initial state until a second sample of the input is detected to be 1. A
flag will be set when the first sample is obtained. This will enable the machine to detect the presence
of the second sample while being in the initial state. The machine is to assert its output upon
detection of the second sample and to continue asserting the output until the fourth sample is detected.
Assumption: Synchronous active-low reset
Moore machine, links for reset on-the-fly are implicit and not shown
Set_flag
reset_b && x_in && !flag
!reset_b || !x_in
a
0
0
reset_b && x_in && flag
b
1
0
c
1
Clr_flag
Note: the output signal y_out is a Moore-type output. The control signals Set_flag and Clr_flag are
not.
module Prob_5_50 (output y_out, input x_in, clk, reset_b);
parameter s_a = 2'd0;
parameter s_b = 2'd1;
parameter s_c = 2'd2;
reg Set_flag;
reg Clr_flag;
reg [1:0] state, next_state;
assign y_out = (state == s_b) || (state == s_c) ;
always @ (posedge clk)
if (reset_b == 1'b0) state <= s_a;
else state <= next_state;
always @ (state, x_in, flag) begin
next_state = s_a;
Set_flag = 0;
Clr_flag = 0;
case (state)
s_a: if ((x_in == 1'b1) && (flag == 1'b0))
begin next_state = s_a; Set_flag = 1; end
else if ((x_in == 1'b1) && (flag == 1'b1))
begin next_state = s_b; Set_flag = 0; end
else if (x_in == 1'b0) next_state = s_a;
s_b: if (x_in == 1'b0) next_state = s_b;
else begin next_state = s_c; Clr_flag = 1; end
s_c: if (x_in == 1'b0) next_state = s_c;
else next_state = s_a;
default: begin next_state = s_a; Clr_flag = 1'b0; Set_flag = 1'b0; end
endcase
end
always @ (posedge clk)
if (reset_b == 1'b0) flag <= 0;
else if (Set_flag) flag <= 1'b1;
else if (Clr_flag) flag <= 1'b0;
endmodule
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164
// Verify reset action
// Verify detection of first input
// Verify wait for second input
// Verify transition at detection of second input
// Verify with between detection of input
// Verify transition to s_d at fourth detection of input
// Verify return to s_a and clearing of flag after fourth input
// Verify reset on-the-fly
module t_Prob_5_50 ();
wire y_out;
reg x_in, clk, reset_b;
Prob_5_50 M0 (y_out, x_in, clk, reset_b);
initial #500 $finish;
initial begin clk = 0; forever #5 clk = !clk; end
initial fork
reset_b = 1'b0;
#20 reset_b = 1;
#20 x_in = 1'b0;
#40 x_in = 1'b1;
#50 x_in = 1'b0;
#80 x_in = 1'b1;
#100 x_in = 0;
#150 x_in = 1'b1;
#160 x_in = 1'b0;
#200 x_in = 1'b1;
#230 reset_b = 1'b0;
#250 reset_b = 1'b1;
#300 x_in = 1'b0;
join
endmodule
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165
5.51
Assumption: Synchronous active-low reset
Moore machine, links for reset on-the-fly are implicit and not shown
reset_b 0
0
1
s0
0
0
1
s1
0
0
1
s2
1
s3
1
1
5.52
Assumption: Synchronous active-low reset
Moore/Mealy machine, links for reset on-the-fly are implicit and not shown
Mealy output
reset_b
0
0
0/1
0
1
s0
0
1
s1
0
1/0
s2
s3
1
1
5.53
Assumption: Synchronous active-low reset
Moore machine, links for reset on-the-fly are implicit and not shown
reset_b
0
0
1
s0
0
0
1
s1
0
0
1
s2
0
s3
1
1
5.54
Assumption: Synchronous active-low reset
Moore machine, links for reset on-the-fly are implicit and not shown
reset_b
s0
0
01, 10
01, 10
s1
0
00, 11
00, 11
01, 10
s2
1
00, 11
5.55
Assumption: Synchronous active-low reset
Mealy machine, links for reset on-the-fly are implicit and not shown
0/1
0/0
0/0
reset_b
0/0
s0
1/0
s1
1/0
s2
1/0
s3
1/1
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5.56
reset_b x_in
0
x
0
x
0
x
0
x
0
x
0
x
0
x
0
x
D2
0
0
0
0
1
1
1
1
D1
0
0
1
1
0
0
1
1
D0
0
1
0
1
0
1
0
1
nD2
0
0
0
0
0
0
0
0
nD1
0
0
0
0
0
0
0
0
nD0
0
0
0
0
0
0
0
0
1
1
1
0
1
x
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
x
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
x
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
x
1
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
For reset_b = 1:
nD2 = (x_in D2'D1D0') || (x_in' D2 D1' D0') || (x_in D2 D1' D0') || (x_in D2 D1 D0')
nD1 = (x_in D2' D1' D0') || (x_in' D2' D1 D0') || (x_in D2 D1' D0') || (x_in' D2 D1 D0')
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167
x_in D2
D1 D0
00
D1
01
11
x_in D2
10
m0
m1
m3
m2
m4
m5
m7
m6
m13
m15
m14
00
00
D1
01
1
m12
11
1
10
m0
m1
m3
m2
m4
m5
m7
m6
m12
m13
m15
m14
m8
m9
m11
m10
1
m9
m11
m10
1
01
D2
1
10
1
11
x_in
1
m8
10
1
D0
D0
nD2 = D2 D1'D0' + x_in D1 D0'
x_in
11
00
01
x_in
D1 D0
D2
D1
D0
nD1 = x_inD1' D0' + x_in' D1 D0'
Reset_b
Clk
D2
D
Clr
D2'
D1
D
Clr
D1'
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D2
168
5.57
Assume synchronous active-low reset. Assume that the counter is controlled by assertion of Run.
module Prob_5_57 (output reg [2:0] y_out, input Run, clk, reset_b);
always @ (posedge clk)
if (reset_b == 1'b0) y_out <= 3'b000;
else if (Run && (y_out < 3'b110)) y_out <= y_out + 3'b010;
else if (Run && (y_out == 3'b110)) y_out <= 3'b000;
else y_out <= y_out;
// redundant statement and may be omitted
endmodule
// Verify that counting is prevented while reset_b is asserted, independently of Run
// Verify that counting is initiated by Run if reset_b is de-asserted
// Verify reset on-the-fly
// Verify that deasserting Run suspends counting
// Verify wrap-around of counter.
module t_Prob_5_57 ();
reg Run, clk, reset_b;
wire [2:0] y_out;
Prob_5_57 M0 (y_out, Run, clk, reset_b);
initial #300 $finish;
initial begin clk = 0; forever #5 clk = !clk; end
initial fork
reset_b = 0;
#30 reset_b = 1;
Run = 1;
#30 Run = 0;
#50 Run = 1;
#70 Run = 0;
#90 reset_b = 0;
#120 reset_b = 1;
#150 Run = 1;
#180 Run = 0;
#200 Run = 1;
join
endmodule
// Attempt to run is overridden by reset_b
// Initiate counting
// Pause
// reset on-the-fly
// De-assert reset_b
// Resume counting
// Pause counting
// Resume counting
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169
5.58
module Prob_5_58 (output reg y_out, input x_in, clk, reset_b)
parameter s0 = 2'b00;
parameter s1 = 2'b01;
parameter s2= 2'b10;
parameter s3 = 2'b11;
reg [1:0] state, next_state;
always @ (posedge clk, negedge reset_b)
if (reset_b == 1'b0) state <= s0;
else state <= next_state;
always @(state, x_in) begin
y_out = 0;
next_state = s0;
case(state)
s0: if (x_in == 1'b0) next_state = s0; else if (x_in = 1'b1) next_state = s1;
s1: if (x_in == 1'b0) next_state = s0; else if (x_in = 1'b1) next_state = s2;
s2: if (x_in == 1'b0) next_state = s0; else if (x_in = 1'b1) next_state = s3;
s3: if (x_in == 1'b0) next_state = s0; else if (x_in = 1'b1) begin next_state = s3; y_out = 1; end
default: begin next_state = s0; y_out = 0; end
endcase
end
endmodule
module t_Prob_5_58 ();
wire y_out;
reg x_in, clk, reset_b;
Prob_5_58 M0 (y_out, x_in, clk, reset_b)
initial begin clk = 0; forever #5 clk = !clk; end
initial fork
reset_b = 0;
x_in = 0;
#20 reset_b = 1;
#40 reset_b = 1;
#50 x_in = 1;
#60 x_in = 0;
#80 x_in = 1;
#90 x+in = 0;
#110 x_in = 1;
#120 x_in = 1;
#150 x_in = 0;
#200 x_in = 1;
#210 reset_b = 0;
#240 reset_b = 1;
join
endmodule
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170
5.59
module Prob_5_59 (output reg [2: 0] count, input enable, clk, reset_b);
always @ (posedge clk)
if (reset_b == 1'b0) count <= 3'b000;
else if (enable) case (count)
3'b000:
count <= 3'b010;
3'b010:
count <= 3'b100;
3'b100:
count <= 3'b110;
3'b110:
count <= 3'b000;
default: count <= 3'b111;
// Use for error detection
endcase
endmodule
module t_Prob_5_59 ();
wire [2:0] count;
reg enable, clk, reset_b;
Prob_5_59 M0 (count, enable, clk, reset_b);
initial #200 $finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
reset_b = 0;
#10 reset_b = 1;
#100 reset_b = 0;
#130 reset_b = 1;
enable = 0;
#30 enable = 1;
#60 enable = 0;
#90 enable = 1;
join
endmodule
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171
5.60
Assume synchronous active-low reset. Assume that counting is controlled by Run.
module Prob_5_60 (output reg [3:0] y_out, input Run, clk, reset_b);
always @ (posedge clk)
if (reset_b == 1'b0) y_out <= 4'b000;
else if (Run && (y_out < 4'b1001)) y_out <= y_out + 4'b0001;
else if (Run && (y_out == 4'b1001)) y_out <= 4'b0000;500
else y_out <= y_out;
// redundant statement and may be omitted
endmodule
// Verify that counting is prevented while reset_b is asserted, independently of Run
// Verify that counting is initiated by Run if reset_b is de-asserted
// Verify reset on-the-fly
// Verify that deasserting Run suspends counting
// Verify wrap-around of counter.
module t_Prob_5_60 ();
reg Run, clk, reset_b;
wire [3:0] y_out;
Prob_5_60 M0 (y_out, Run, clk, reset_b);
initial #500 $finish;
initial begin clk = 0; forever #5 clk = !clk; end
initial fork
reset_b = 0;
#30 reset_b = 1;
Run = 1;
#30 Run = 0;
#50 Run = 1;
#70 Run = 0;
#90 reset_b = 0;
#120 reset_b = 1;
#150 Run = 1;
#180 Run = 0;
#200 Run = 1;
join
endmodule
// Attempt to run is overridden by reset_b
// Initiate counting
// Pause
// reset on-the-fly
// De-assert reset_b
// Resume counting
// Pause counting
// Resume counting
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172
CHAPTER 6
6.1
The structure shown below gates the clock through a nand gate. In practice, the circuit can exhibit two
problems if the load signal is asynchronous: (1) the gated clock arrives in the setup interval of the clock
of the flip-flop, causing metastability, and (2) the load signal truncates the width of the clock pulse.
Additionally, the propagation delay through the nand gate might compromise the synchronicity of the
overall circuit.
Connect to the
clock input of each
flip-flop.
Load
Clock
6.2
Modify Fig. 6.2, with each stage replicating the first stage shown below:
load
clear
D
Q
A0
I0
clk
Load
0
0
1
6.3
Clear
0
1
x
D
A0
0
I0
Operation
No change
Clear to 0
Load input
Note: In this design, clear has priority over load.
Serial data is transferred one bit at a time, in sequence. Parallel data is transferred n bits at a time (n > 1),
concurrently.
A shift register can convert serial data into parallel data by first shifting one bit a time into the register
and then taking the parallel data from the register outputs.
A shift register with parallel load can convert parallel data to a serial format by first loading the data in
parallel and then shifting the bits one at a time.
6.4
0110 => 0011, 0001, 1000, 1100, 1110, 0111, 1011
6.5
(a) See Fig. 11.19: IC 74194
(b) See Fig. 11.20. Connect two 74194 ICs to form an 8-bit register.
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6.6
173
First stage of register:
shift
load
serial input
D
I0
A0
Q
clk
6.7
First stage of register:
Select
S1
S0
0
1
2
3
0
Ii
4x1
Mux Y
D
Ai
Q
A'i
Q'
clk
6.8
A = 0010, 0001, 1000, 1100. Carry = 1, 1, 1, 0
6.9
(a) In Fig. 6.5, complement the serial output of shift register B (with an inverter), and set the initial
value of the carry to 1.
(b)
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
x
x
x
x
x
x
x
x
0
0
1
0
x
xy
Present
Next
FF
state Inputs state Output inputs
Q
x y
Q
D
JQ KQ
Q
00
0
Q
1
m0
m4
01
m1
m5
x
11
10
m3
1
m7
x
m2
m6
x
x
y
JQ = x'y
x
xy
Q
00
0
Q
1
m0
m4
x
01
m1
11
m3
x
m5
x
m7
10
m2
m6
x
1
x
KQ = xy'
D= Q x y
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6.10
174
See solution to Problem 5.7.
Note that y = x if Q = 0, and y = x' if Q = 1. Q is set on the first 1 from x.
Note that x ⊕ 0 = x, and x ⊕ 1 = x'.
Serial output
Shift Register
Serial input
D
From
shift
control
y
x
Q
Q
R
clk
Reset to 0
initially
6.11
(a) A count down counter.
(b) A count up counter.
6.12
Similar to diagram of Fig. 6.8.
(a) With the bubbles in C removed (positive-edge).
(b) With complemented flip-flops connected to C.
6.13
A1
4-Bit
Ripple Counter
Clear
Asynchronous, active-low)
6.14
A2
0
1
0
A3
1
A4
(a) 10_0110_0111 -> 10_011_1000 4;
(b) 11_1100_0111 -> 11_1100_1000 4;
(c) 00_0000_1111 -> 00_0001_0000 5
6.15
The worst case is when all 10 flip-flops are complemented. The maximum delay is 10 x 3ns = 30 ns.
The maximum frequency is 109/30 = 33.3 MHz
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6.16
6.17
6.18
175
Q8 Q4 Q2 Q1 :
Next state:
Next state:
1010
1011
0100
1100
1101
0100
1110 Self correcting
1111
0000
1010 → 1011 → 0100
1100 → 1101 → 0100
1110 → 1111 → 0000
With E denoting the count enable in Fig. 6.12 and D-flip-flops replacing the J-K flip-flops, the toggling
action of the bits of the counter is determined by: T0 = E, T1 = A0E, T2 = A0A1E, T3 = A0A1A2E. Since DA =
A ⊕ TA the inputs of the flip-flops of the counter are determined by: DA0 = A0⊕E; DA1 = A1⊕(A0E); DA2 =
A2⊕(A0A1E); DA3 = A3⊕(A0A1A2E).
When up = down = 1 the circuit counts up.
up
x
Combinational Circuit
down
y
up
down
x
y
Operation
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
No change
Count down
Count up
No change
Add this to Fig. 6.13
up
down
6.19
x
x = up (down)'
y = (up)'down
y
(b) From the state table in Table 6.5:
DQ1 = Q'1
DQ2 = ∑ (1, 2, 5, 6)
DQ4 = ∑ (3, 4, 5, 6)
DQ8 = ∑ (7, 8)
Don't care: d = ∑ (10, 11, 12, 13, 14, 15)
Simplifying with maps:
DQ2 = Q2Q'1 + Q'8Q'2Q1
DQ4 = Q4Q'1 + Q4Q'2 + Q'4Q2Q1
DQ8 = Q8Q'1 + Q4Q2Q1
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176
(a)
Present
state
Next
state
Flip-flop inputs
A8 A4 A2 A1 A8 A4 A2 A1
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
0001
0010
0011
0100
0101
0110
0111
1000
1001
0000
JA8 KA8
JA4 KA4
JA2 KA2
JA1 KA1
0
0
0
0
0
0
0
1
x
x
0
0
0
1
x
x
x
x
0
0
0
1
x
x
0
1
x
x
0
0
1
x
1
x
1
x
1
x
1
x
x
x
x
x
x
x
x
x
0
1
x
x
x
x
0
0
0
1
x
x
x
x
0
1
x
x
0
1
x
x
x
1
x
1
x
1
x
1
x
1
JA1 = 1
KA1 = 1
JA2 = A1A'8
KA2 = A1
JA4 = A1A2
KA4 = A1A2
JA8 = A1A2A4
KA8 = A1
d(A8, A4, A2, A1) = Σ (10, 11, 12, 13, 14, 15)
(b)
A_count[1]
A_count[0]
Count
Load
CLK
Clear
Data_in[0]
Data_in[3]
Fig. 6.14
Data_in[1]
C_out
16-bit counter needs 4 circuits
with output carry connected to
the count input of the next
stage.
Data_in[2]
Block diagram of 4-bit circuit:
A_count[2]
(a)
A_count[3]
6.20
Need 2 units to count to 127. Counter is re-loaded with 0s when count reaches 128.
An alternative version would AND output bits 0 through 6 and assert Load while the count is
127.
A_count[0]
A_count[1]
A_count[2]
A_count[3]
A_count[4]
A_count[5]
A_count[6]
A_count[7]
27 = 128
Count
Fig. 6.14
C_out
Count = 1
Fig. 6.14
C_out
0
Load
Load
Data_in[0]
Data_in[1]
Data_in[2]
CLK
Clear
Data_in[3]
Data_in[4]
Data_in[5]
Data_in[6]
Data_in[7]
CLK
Clear
Load
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6.21
177
(a)
JA0 = LI0 + L'C
KA0 = LI'0 + L'C
(b)
J = [L(LI)']'(L + C) = (L' + LI)(L + C)
LI + L'C + LIC = LI + L'C (use a map)
K = (LI)' (L + C) = (L' + I')(L + C) = LI' + L'C
6.22
C_out
Fig. 6.14
Count = 1
C_out
Load
CLK
Clear = 1
Fig. 6.14
0
0
Count sequence: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Count sequence: 6, 7, 8, 9, 10, 11, 12 13, 14, 15
Count = 1
Load
CLK
Clear = 1
1
C_out
Fig. 6.14
Count = 1
Load = 0
CLK
Clear
0
Count sequence: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
6.23
Use a 4-bit counter and a flip-flop (initially at 0). A start signal sets the flip-flop, which in turn enables
the counter. On the count of 11 (binary 1011) reset the flip-flop to 0 to disable the count (with the value
of 0000 ).
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178
6.24
Present Next
state state Flip-flop inputs
ABC ABC TA TB TC
0
1
000
001
0
1
0
001
011
0
x
x
010
xxx
x
1
0
011
111
1
1
0
100
000
1
x
x
101
xxx
x
1
0
110
100
0
0
1
111
110
0
A
00
0
A
B
BC
1
01
11
m0
m1
m3
m4
m5
m7
1
x
A
10
m2
1
00
x
0
m6
B
BC
A
1
01
m0
m1
m4
m5
1
x
C
0
A
B
1
m0
01
1
m4
11
m3
m2
m5
m7
m6
1
A
10
m1
x
x
m6
x
1
B
00
0
A
1
m0
1
m4
01
11
10
m1
m3
m2
m5
m7
m6
x
1
x
C
TC = AC + A'B'C'
101
101
No self-correcting
6.25
m7
BC
C
TC = A C
010
m2
TB = B C
BC
00
10
m3
C
TA = A B
A
11
010
100
Self-correcting
(a) Use a 6-bit ring counter.
(b)
Counter of
Fig. 6.16
6.26
C
B
A
20
21
22
3x8
Decoder
0
1
2
4
5
6
T0
T1
T2
T4
T5
T6
The clock generator has a period of 12.5 ns. Use a 2-bit counter to count four pulses.
80/4 = 20 MHz; cycle time = 1000 x 10-9 /20 = 50 ns.
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179
6.27
Present Next
state state Flip-flop inputs
ABC ABC JA KA JB KB JC KC
000
001
010
011
100
101
110
111
001
010
011
100
100
110
000
xxx
0
0
0
1
x
x
x
x
x
x
x
x
x
x
x
x
0
1
x
x
0
1
x
x
x
x
0
1
0
x
1
x
1
x
1
x
1
x
0
x
A
00
0
A
B
BC
1
01
11
m0
m1
m3
m4
m5
m7
x
x
A
10
m2
1
m6
x
A
B
BC
00
0
x
x
1
x
1
x
1
x
x
1
m0
x
m4
01
m1
x
m5
0
A
1
01
m1
m4
m5
1
1
11
m3
m7
A
10
m2
x
m6
x
x
00
0
x
A
1
0
A
1
m4
1
1
01
m5
x
x
m0
m4
x
x
01
m1
m5
x
x
11
m3
m7
10
m2
1
m6
x
1
C
B
m1
1
KB = A + C
BC
00
x
B
C
m0
m6
x
BC
JB = C
A
x
C
B
00
10
m2
KA = B
BC
m0
m3
m7
C
JA = BC
A
11
11
m3
m7
x
x
A
10
m2
1
m6
A
C
1
m0
m4
x
x
01
m1
m5
1
1
11
m3
m7
1
x
10
m2
m6
x
x
C
JC = A' + B'
111
00
0
B
BC
KC = 1
001
Self-correcting
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180
6.28
Present Next
state state
ABC ABC
000
001
010
011
100
101
110
111
A
001
010
100
xxx
110
xxx
000
xxx
A
00
1
m0
m4
1
1
01
m1
m5
11
m3
x
m7
x
x
m3
m4
m5
m7
1
x
A
1
A
x
10
m2
x
1
m6
x
C
DA = A B
BC
B
00
0
m6
11
m1
10
m2
01
m0
B
00
1
B
BC
0
BC
0
A
A
1
m0
m4
1
01
11
m1
m3
m5
m7
C
x
10
m2
x
m6
x
C
DB = AB' + C
DC = A'B'C'
Self-correcting
111
001
110
111
010
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reserved.
6.29
181
(a) The 8 valid states are listed in Fig. 8.18(b), with the sequence: 0, 8, 12, 14, 15, 7, 3, 1, 0, ....
The 8 unused states and their next states are shown below:
Next
state
State
All
invalid
states
ABCE ABCE
0000
0100
0101
0110
1001
1010
1011
1101
1001
1010
0010
1011
0100
1101
0101
0110
9
10
2
11
4
13
5
6
(b) Modification: DC = (A + C)B.
D
Q
A
D
Q
B
D
Q
C
D
Q
Q'
E
E'
clk
The valid states are the same as in (a). The unused states have the following sequences:
10→ 13→ 6→11→ 5→ 0. The final states, 0 and 8, are valid.
2→ 9→ 4→ 8 and
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182
6.30
D
Q
A
D
Q
B
D
C
Q
D
Q
D
D
Q
Q'
clk
E
E'
The 5-bit Johnson counter has the following state sequence:
ABCDE
decoded
output:
00000
A'E'
10000
AB'
11000
BC'
11100
CD'
11110
DE'
11111
A'E'
01111
AB'
00111
BC'
00011
CD'
00001
DE'
6.31
module Reg_4_bit_beh (output reg A3, A2, A1, A0, input I3, I2, I1, I0, Clock, Clear);
always @ (posedge Clock, negedge Clear)
if (Clear == 0) {A3, A2, A1, A0} <= 4'b0;
else {A3, A2, A1, A0} <= {I3, I2, I1, I0};
endmodule
module Reg_4_bit_Str (output A3, A2, A1, A0, input I3, I2, I1, I0, Clock, Clear);
DFF M3DFF (A3, I3, Clock, Clear);
DFF M2DFF (A2, I2, Clock, Clear);
DFF M1DFF (A1, I1, Clock, Clear);
DFF M0DFF (A0, I0, Clock, Clear);
endmodule
module DFF(output reg Q, input D, clk, clear);
always @ (posedge clk, posedge clear)
if (clear == 0) Q <= 0; else Q <= D;
endmodule
module t_Reg_4_bit ();
wire A3_beh, A2_beh, A1_beh, A0_beh;
wire A3_str, A2_str, A1_str, A0_str;
reg I3, I2, I1, I0, Clock, Clear;
wire [3: 0] I_data = {I3, I2, I1, I0};
wire [3: 0] A_beh = {A3_beh, A2_beh, A1_beh, A0_beh};
wire [3: 0] A_str = {A3_str, A2_str, A1_str, A0_str};
Reg_4_bit_beh M_beh (A3_beh, A2_beh, A1_beh, A0_beh, I3, I2, I1, I0, Clock, Clear);
Reg_4_bit_Str M_str (A3_str, A2_str, A1_str, A0_str, I3, I2, I1, I0, Clock, Clear);
initial #100 $finish;
initial begin Clock = 0; forever #5 Clock = ~Clock; end
initial begin Clear = 0; #2 Clear = 1; end
integer K;
initial begin
for (K = 0; K < 16; K = K + 1) begin {I3, I2, I1, I0} = K; #10 ; end
end
endmodule
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183
Name
0
50
100
Clock
Clear
I_data[3:0]
0
1
2
3
4
5
6
7
8
9
I3
I2
I1
I0
A_beh[3:0]
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
A3_beh
A2_beh
A1_beh
A0_beh
A_str[3:0]
A3_str
A2_str
A1_str
A0_str
6.32
(a)
module Reg_4_bit_Load (output reg A3, A2, A1, A0, input I3, I2, I1, I0, Load, Clock, Clear);
always @ (posedge Clock, negedge Clear)
if (Clear == 0) {A3, A2, A1, A0} <= 4'b0;
else if (Load) {A3, A2, A1, A0} <= {I3, I2, I1, I0};
endmodule
module t_Reg_4_Load ();
wire A3_beh, A2_beh, A1_beh, A0_beh;
reg I3, I2, I1, I0, Load, Clock, Clear;
wire [3: 0] I_data = {I3, I2, I1, I0};
wire [3: 0] A_beh = {A3_beh, A2_beh, A1_beh, A0_beh};
Reg_4_bit_Load M0 (A3_beh, A2_beh, A1_beh, A0_beh, I3, I2, I1, I0, Load, Clock, Clear);
initial #100 $finish;
initial begin Clock = 0; forever #5 Clock = ~Clock; end
initial begin Clear = 0; #2 Clear = 1; end
integer K;
initial fork
#20 Load = 1;
#30 Load = 0;
#50 Load = 1;
join
initial begin
for (K = 0; K < 16; K = K + 1) begin {I3, I2, I1, I0} = K; #10 ; end
end
endmodule
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184
Name
0
50
100
Clock
Clear
Load
I_data[3:0]
0
1
2
3
4
5
6
7
8
9
I_data[3]
I_data[2]
I_data[1]
I_data[0]
A_beh[3:0]
0
2
5
6
7
8
9
A_beh[3]
A_beh[2]
A_beh[1]
A_beh[0]
(b)
module Reg_4_bit_Load_str (output A3, A2, A1, A0, input I3, I2, I1, I0, Load, Clock, Clear);
wire y3, y2, y1, y0;
mux_2 M3 (y3, A3, I3, Load);
mux_2 M2 (y2, A2, I2, Load);
mux_2 M1 (y1, A1, I1, Load);
mux_2 M0 (y0, A0, I0, Load);
DFF M3DFF (A3, y3, Clock, Clear);
DFF M2DFF (A2, y2, Clock, Clear);
DFF M1DFF (A1, y1, Clock, Clear);
DFF M0DFF (A0, y0, Clock, Clear);
endmodule
module DFF(output reg Q, input D, clk, clear);
always @ (posedge clk, posedge clear)
if (clear == 0) Q <= 0; else Q <= D;
endmodule
module mux_2 (output y, input a, b, sel);
assign y = sel ? a: b;
endmodule
module t_Reg_4_Load_str ();
wire A3, A2, A1, A0;
reg I3, I2, I1, I0, Load, Clock, Clear;
wire [3: 0] I_data = {I3, I2, I1, I0};
wire [3: 0] A = {A3, A2, A1, A0};
Reg_4_bit_Load_str M0 (A3, A2, A1, A0, I3, I2, I1, I0, Load, Clock, Clear);
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185
initial #100 $finish;
initial begin Clock = 0; forever #5 Clock = ~Clock; end
initial begin Clear = 0; #2 Clear = 1; end
integer K;
initial fork
#20 Load = 1;
#30 Load = 0;
#50 Load = 1;
#80 Load = 0;
join
initial begin
for (K = 0; K < 16; K = K + 1) begin {I3, I2, I1, I0} = K; #10 ; end
end
endmodule
Name
0
60
Clock
Clear
Load
I_data[3:0]
A[3:0]
0
1
2
x
3
4
3
5
6
4
7
8
9
8
(c)
module Reg_4_bit_Load_beh (output reg A3, A2, A1, A0, input I3, I2, I1, I0, Load, Clock, Clear);
always @ (posedge Clock, negedge Clear)
if (Clear == 0) {A3, A2, A1, A0} <= 4'b0;
else if (Load) {A3, A2, A1, A0} <= {I3, I2, I1, I0};
endmodule
module Reg_4_bit_Load_str (output A3, A2, A1, A0, input I3, I2, I1, I0, Load, Clock, Clear);
wire y3, y2, y1, y0;
mux_2 M3 (y3, A3, I3, Load);
mux_2 M2 (y2, A2, I2, Load);
mux_2 M1 (y1, A1, I1, Load);
mux_2 M0 (y0, A0, I0, Load);
DFF M3DFF (A3, y3, Clock, Clear);
DFF M2DFF (A2, y2, Clock, Clear);
DFF M1DFF (A1, y1, Clock, Clear);
DFF M0DFF (A0, y0, Clock, Clear);
endmodule
module DFF(output reg Q, input D, clk, clear);
always @ (posedge clk, posedge clear)
if (clear == 0) Q <= 0; else Q <= D;
endmodule
module mux_2 (output y, input a, b, sel);
assign y = sel ? a: b;
endmodule
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186
module t_Reg_4_Load_str ();
wire A3_beh, A2_beh, A1_beh, A0_beh;
wire A3_str, A2_str, A1_str, A0_str;
reg I3, I2, I1, I0, Load, Clock, Clear;
wire [3: 0] I_data, A_beh, A_str;
assign I_data = {I3, I2, I1, I0};
assign A_beh = {A3_beh, A2_beh, A1_beh, A0_beh};
assign A_str = {A3_str, A2_str, A1_str, A0_str};
Reg_4_bit_Load_str M0 (A3_beh, A2_beh, A1_beh, A0_beh, I3, I2, I1, I0, Load, Clock, Clear);
Reg_4_bit_Load_str M1 (A3_str, A2_str, A1_str, A0_str, I3, I2, I1, I0, Load, Clock, Clear);
initial #100 $finish;
initial begin Clock = 0; forever #5 Clock = ~Clock; end
initial begin Clear = 0; #2 Clear = 1; end
integer K;
initial fork
#20 Load = 1;
#30 Load = 0;
#50 Load = 1;
#80 Load = 0;
join
initial begin
for (K = 0; K < 16; K = K + 1) begin {I3, I2, I1, I0} = K; #10 ; end
end
endmodule
Name
0
60
Clock
Clear
Load
I_data[3:0]
0
1
2
3
4
5
6
7
8
9
A_beh[3:0]
x
3
4
8
A_str[3:0]
x
3
4
8
6.33
// Stimulus for testing the binary counter of Example 6-3
module testcounter;
reg Count, Load, CLK, Clr;
reg [3: 0] IN;
wire C0;
wire [3: 0] A;
Binary_Counter_4_Par_Load M0 (
A,
// Data output
C0,
// Output carry
IN,
// Data input
Count,
// Active high to count
Load,
// Active high to load
CLK,
// Positive edge sensitive
Clr
// Active low
);
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187
always
#5 CLK = ~CLK;
initial
begin
Clr = 0;
// Clear de-asserted
CLK = 1;
// Clock initialized high
Load = 0; Count = 1;
// Enable count
#5 Clr = 1;
// Clears count, then counts for five cycles
#50 Load = 1; IN = 4'b1100;
// Count is set to 4'b1100 (12`0)
#10 Load = 0;
#70 Count = 0;
// Count is deasserted at t = 135
#20 $finish;
// Terminate simulation
end
endmodule
// Four-bit binary counter with parallel load
// See Figure 6-14 and Table 6-6
module Binary_Counter_4_Par_Load (
output reg [3:0] A_count, // Data output
output
C_out, // Output carry
input [3:0]
Data_in, // Data input
input
Count,
// Active high to count
Load, // Active high to load
CLK, // Positive edge sensitive
Clear // Active low
);
assign C_out = Count & (~Load) & (A_count == 4'b1111);
always @ (posedge CLK, negedge Clear)
if (~Clear)
A_count <= 4'b0000;
else if (Load) A_count <= Data_in;
else if (Count) A_count <= A_count + 1'b1;
else
A_count <= A_count; // redundant statement
endmodule
// Note: a preferred description if the clock is given by:
// initial begin CLK = 0; forever #5 CLK = ~CLK; end
Name
0
60
120
CLK
Clr
Load
x
IN[3:0]
c
Count
A[3:0]
0
1
2
3
4
5
c
d
e
f
0
1
2
3
C0
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188
6.34
module Shiftreg (SI, SO, CLK);
input
SI, CLK;
output SO;
reg [3: 0] Q;
assign SO = Q[0];
always @ (posedge CLK)
Q = {SI, Q[3: 1]};
endmodule
// Test plan
//
// Verify that data shift through the register
// Set SI =1 for 4 clock cycles
// Hold SI =1 for 4 clock cycles
// Set SI = 0 for 4 clock cycles
// Verify that data shifts out of the register correctly
module t_Shiftreg;
reg SI, CLK;
wire SO;
Shiftreg M0 (SI, SO, CLK);
initial #130 $finish;
initial begin CLK = 0; forever #5 CLK = ~CLK; end
initial fork
SI = 1'b1;
#80 SI = 0;
join
endmodule
Name 0
60
120
CLK
SI
SO
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6.35
189
(a) Note that Load has priority over Clear.
module Prob_6_35a (output [3: 0] A, input [3:0] I, input Load, Clock, Clear);
Register_Cell R0 (A[0], I[0], Load, Clock, Clear);
Register_Cell R1 (A[1], I[1], Load,
Clock, Clear);
Register_Cell R2 (A[2], I[2], Load, Clock, Clear);
Register_Cell R3 (A[3], I[3], Load, Clock, Clear);
endmodule
module Register_Cell (output A, input I, Load, Clock, Clear);
DFF M0 (A, D, Clock);
not (Load_b, Load);
not (w1, Load_b);
not (Clear_b, Clear);
and (w2, I, w1);
and (w3, A, Load_b, Clear_b);
or (D, w2, w3);
endmodule
module DFF (output reg Q, input D, clk);
always @ (posedge clk) Q <= D;
endmodule
module t_Prob_6_35a ( );
wire [3: 0] A;
reg [3: 0] I;
reg Clock, Clear, Load;
Prob_6_35a M0 ( A, I, Load, Clock, Clear);
initial #150 $finish;
initial begin Clock = 0; forever #5 Clock = ~Clock; end
initial fork
I = 4'b1010;Clear = 1;
#40 Clear = 0;
Load = 0;
#20 Load = 1;
#40 Load = 0;
join
endmodule
Name
0
60
120
Clock
Clear
Load
a
I[3:0]
A[3:0]
0
a
0
(b) Note: The solution below replaces the solution given on the preliminary CD.
module Prob_6_35b (output reg [3: 0] A, input [3:0] I, input Load, Clock, Clear);
always @ (posedge Clock)
if (Load) A <= I;
else if (Clear) A <= 4'b0;
//else A <= A;
// redundant statement
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190
endmodule
module t_Prob_6_35b ( );
wire [3: 0] A;
reg [3: 0] I;
reg Clock, Clear, Load;
Prob_6_35b M0 ( A, I, Load, Clock, Clear);
initial #150 $finish;
initial begin Clock = 0; forever #5 Clock = ~Clock; end
initial fork
I = 4'b1010; Clear = 1;
#60 Clear = 0;
Load = 0;
#20 Load = 1;
#40 Load = 0;
join
endmodule
Name
0
60
120
Clock
Clear
Load
a
I[3:0]
A[3:0]
0
a
0
(c)
module Prob_6_35c (output [3: 0] A, input [3:0] I, input Shift, Load, Clock);
Register_Cell R0 (A[0], I[0], A[1], Shift, Load, Clock);
Register_Cell R1 (A[1], I[1], A[2], Shift, Load, Clock);
Register_Cell R2 (A[2], I[2], A[3], Shift, Load, Clock);
Register_Cell R3 (A[3], I[3], A[0], Shift, Load, Clock);
endmodule
module Register_Cell (output A, input I, Serial_in, Shift, Load, Clock);
DFF M0 (A, D, Clock);
not (Shift_b, Shift);
not (Load_b, Load);
and (w1, Shift, Serial_in);
and (w2, Shift_b, Load, I);
and (w3, A, Shift_b, Load_b);
or (D, w1, w2, w3);
endmodule
module DFF (output reg Q, input D, clk);
always @ (posedge clk) Q <= D;
endmodule
module t_Prob_6_35c ( );
wire [3: 0] A;
reg [3: 0] I;
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191
reg Clock, Shift, Load;
Prob_6_35c M0 (A, I, Shift, Load, Clock);
initial #150 $finish;
initial begin Clock = 0; forever #5 Clock = ~Clock; end
initial fork
I = 4'b1010;
Load = 0; Shift = 0;
#20 Load = 1;
#40 Load = 0;
#50 Shift = 1;
join
endmodule
Name
0
60
120
Clock
Shift
Load
a
I[3:0]
A[3:0]
x
a
5
a
5
a
5
a
5
a
5
(d)
module Prob_6_35d (output reg [3: 0] A, input [3:0] I, input Shift,
Load, Clock, Clear);
always @ (posedge Clock)
if
(Shift)
A
<=
{A[0],
A[3:1]};
else
if (Load) A <= I;
else if (Clear) A <= 4'b0;
//else A <= A;
// redundant statement
endmodule
module t_Prob_6_35d ( );
wire [3: 0] A;
reg [3: 0] I;
reg Clock, Clear, Shift, Load;
Prob_6_35d M0 ( A, I, Shift, Load, Clock, Clear);
initial #150 $finish;
initial begin Clock = 0; forever #5 Clock = ~Clock; end
initial fork
I = 4'b1010; Clear = 1;
#100 Clear = 0;
Load = 0;
#20 Load = 1;
#40 Load = 0;
#30 Shift = 1;
#90 Shift = 0;
join
endmodule
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192
Name
0
60
120
Clock
Clear
Shift
Load
a
I[3:0]
A[3:0]
0
a
5
a
5
a
5
a
0
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193
(e)
module Shift_Register
(output [3: 0] A_par, input [3: 0] I_par, input MSB_in, LSB_in, s1, s0, CLK, Clear);
wire y3, y2, y1, y0;
DFF D3 (A_par[3], y3, CLK, Clear);
DFF D2 (A_par[2], y2, CLK, Clear);
DFF D1 (A_par[1], y1, CLK, Clear);
DFF D0 (A_par[0], y0, CLK, Clear);
MUX_4x1 M3 (y3, I_par[3], A_par[2], MSB_in, A_par[3], s1, s0);
MUX_4x1 M2 (y2, I_par[2], A_par[1], A_par[3], A_par[2], s1, s0);
MUX_4x1 M1 (y1, I_par[1], A_par[0], A_par[2], A_par[1], s1, s0);
MUX_4x1 M0 (y0, I_par[0], LSB_in, A_par[1], A_par[0], s1, s0);
endmodule
module MUX_4x1 (output reg y, input I3, I2, I1, I0, s1, s0);
always @ (I3, I2, I1, I0, s1, s0)
case ({s1, s0})
2'b11: y = I3;
2'b10: y = I2;
2'b01: y = I1;
2'b00: y = I0;
endcase
endmodule
module DFF (output reg Q, input D, clk, reset_b);
always @ (posedge clk, negedge reset_b) if (reset_b == 0) Q <= 0; else Q <= D;
endmodule
module t_Shift_Register ( );
wire [3: 0] A_par;
reg [3: 0] I_par;
reg MSB_in, LSB_in, s1, s0, CLK, Clear;
Shift_Register
M_SR(
A_par,
I_par,
MSB_in,
LSB_in,
s1,
s0,
CLK,
Clear);
initial
#300
$finish;
initial
begin
CLK
=
0;
forever
#5
CLK
=
~CLK;
end
initial fork
MSB_in = 0; LSB_in = 0;
Clear = 0;
// Active-low reset
s1 = 0; s0 = 0;
// No change
#10 Clear = 1;
#10 I_par = 4'hA;
#30 begin s1 = 1; s0 = 1; end // 00: load I_par into A_par
#50 s1 = 0;
// 01: shift right (1010 to 0101 to 0010 to 0001 to 0000)
#90 begin s1 = 1; s0 = 1; end // 11: reload A with 1010
#100 s0 = 0;
// 10: shift left (1010 to 0100 to 1000 to 000)
#140 begin s1 = 1; s0 = 1; MSB_in = 1; LSB_in = 1; end // Repeat with MSB and LSB
#150 s1 = 0;
#190 begin s1 = 1; s0 = 1; end // reload with A = 1010
#200 s0 = 0;
// Shift left
#220 s1 = 0;
// Pause
#240 s1 = 1;
// Shift left
join
endmodule
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
194
No
change
Name
Shift
right Load
Load
0
Shift
left
90
180
270
CLK
Clear
s1
s0
I_par[3:0]
x
a
MSB_in
LSB_in
A_par[3:0]
0
a
5
2
1
0
a
4
8
0
a
d
e
f
a
5
b
7
(f)
module Shift_Register_BEH
(output [3: 0] A_par, input [3: 0] I_par, input MSB_in, LSB_in, s1, s0, CLK, Clear);
always @ (posedge CLK, negedge Clear) if (Clear == 0) A_par <= 4'b0;
else case ({s1, s0})
2'b11: A_par <= I_par;
2'b01: A_par <= {MSB_in, A_par[3: 1]};
2'b10: A_par <= {A_par[2: 0], LSB_in};
2'b00: A_par <=A_par;
endcase
endmodule
module t_Shift_Register ( );
wire [3: 0] A_par;
reg [3: 0] I_par;
reg MSB_in, LSB_in, s1, s0, CLK, Clear;
Shift_Register_BEH
M_SR(
A_par,
I_par,
MSB_in,
LSB_in,
s1,
s0,
CLK,
Clear);
initial
#300
$finish;
initial
begin
CLK
=
0;
forever
#5
CLK
=
~CLK;
end
initial fork
MSB_in = 0; LSB_in = 0;
Clear = 0;
// Active-low reset
s1 = 0; s0 = 0;
// No change
#10 Clear = 1;
#10 I_par = 4'hA;
#30 begin s1 = 1; s0 = 1; end // 00: load I_par into A_par
#50 s1 = 0;
// 01: shift right (1010 to 0101 to 0010 to 0001 to 0000)
#90 begin s1 = 1; s0 = 1; end // 11: reload A with 1010
#100 s0 = 0;
// 10: shift left (1010 to 0100 to 1000 to 000)
#140 begin s1 = 1; s0 = 1; MSB_in = 1; LSB_in = 1; end // Repeat with MSB and LSB
#150 s1 = 0;
#190 begin s1 = 1; s0 = 1; end // reload with A = 1010
#200 s0 = 0;
// Shift left
#220 s1 = 0;
// Pause
#240 s1 = 1;
// Shift left
join
endmodule
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
f
195
Name
0
90
180
270
CLK
Clear
s1
s0
I_par[3:0]
x
a
MSB_in
LSB_in
A_par[3:0]
0
a
5
2
1
0
a
4
8
0
a
d
e
f
a
5
b
7
(g)
module Ripple_Counter_4bit_a (output [3: 0] A, input Count, reset_b);
reg A0, A1, A2, A3;
assign A = {A3, A2, A1, A0};
always @ (negedge Count, negedge reset_b)
if (reset_b == 0) A0 <= 0; else if (T) A0 <= ~A0;
always @ (negedge A0, negedge reset_b)
if (reset_b == 0) A1 <= 0; else if (T) A1 <= ~A1;
always @ (negedge A1, negedge reset_b)
if (reset_b == 0) A2 <= 0; else if (T) A2 <= ~A2;
always @ (negedge A2, negedge reset_b)
if (reset_b == 0) A3 <= 0; else if (T) A3 <= ~A3;
endmodule
module t_Ripple_Counter_4bit ();
wire [3: 0] A;
reg Count, reset_b;
Ripple_Counter_4bit_a M0 (A, Count, reset_b);
initial #300 $finish;
initial fork
reset_b = 0;
#60 reset_b = 1;
// Active-low reset
Count = 1;
#15 Count = 0;
#30 Count = 1;
#85 begin Count = 0; forever #10 Count = ~Count; end
join
endmodule
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
f
196
module Ripple_Counter_4bit_b (output [3: 0] A, input Count, reset_b);
reg A0, A1, A2, A3;
assign A = {A3, A2, A1, A0};
always @ (negedge Count, negedge reset_b)
if (reset_b == 0) A0 <= 0; else A0 <= ~A0;
always @ (negedge A0, negedge reset_b)
if (reset_b == 0) A1 <= 0; else A1 <= ~A1;
always @ (negedge A1, negedge reset_b)
if (reset_b == 0) A2 <= 0; else A2 <= ~A2;
always @ (negedge A2, negedge reset_b)
if (reset_b == 0) A3 <= 0; else A3 <= ~A3;
endmodule
module t_Ripple_Counter_4bit ();
wire [3: 0] A;
reg Count, reset_b;
Ripple_Counter_4bit_b M0 (A, Count, reset_b);
initial #300 $finish;
initial fork
reset_b = 0;
#60 reset_b = 1;
// Active-low reset
Count = 1;
#15 Count = 0;
#30 Count = 1;
#85 begin Count = 0; forever #10 Count = ~Count; end
join
endmodule
Name
0
90
180
270
Count
reset_b
A[3:0]
(h)
0
1
2
3
4
5
6
7
8
9
Note: This version of the solution situates the data shift registers in the test bench.
module Serial_Subtractor (output SO, input SI_A, SI_B, shift_control, clock, reset_b);
// See Fig. 6.5 and Problem 6.9a (2s complement serial subtractor)
reg [1: 0] sum;
wire mem = sum[1];
assign SO = sum[0];
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) begin
sum <= 2'b10;
end
else if (shift_control) begin
sum <= SI_A + (!SI_B) + sum[1];
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
a
b
197
end
endmodule
module t_Serial_Subtractor ();
wire SI_A, SI_B;
reg shift_control, clock, reset_b;
Serial_Subtractor M0 (SO, SI_A, SI_B, shift_control, clock, reset_b);
initial #250 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial fork
shift_control = 0;
#10 reset_b = 0;
#20 reset_b = 1;
#22 shift_control = 1;
#105 shift_control = 0;
#112 reset_b = 0;
#114 reset_b = 1;
#122 shift_control = 1;
#205 shift_control = 0;
join
reg [7: 0] A, B, SO_reg;
wire s7;
assign s7 = SO_reg[7];
assign SI_A = A[0];
assign SI_B = B[0];
wire SI_B_bar = ~SI_B;
initial fork
A = 8'h5A;
B = 8'h0A;
#122 A = 8'h0A;
#122 B = 8'h5A;
join
always @ (negedge clock, negedge reset_b)
if (reset_b == 0) SO_reg <= 0;
else if (shift_control == 1) begin
SO_reg <= {SO, SO_reg[7: 1]};
A <= A >> 1;
B <= B >> 1;
end
wire negative = !M0.sum[1];
wire [7: 0] magnitude = (!negative)? SO_reg: 1'b1 + ~SO_reg;
endmodule
Simulation results are shown for 5Ah – 0Ah = 50h = 80 d and 0Ah – 5Ah = -80. The magnitude of the
result is also shown.
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
05
5
0a
10
B[7:0]
B[7:0]
magnitude[7:0]
0
x
SO_reg[7:0]
x
0
xx
SO_reg[7:0]
negative
00
x
2
02
22
16
40
sum[1:0]
mem
SO
SI_B_bar
SI_A
2
45
90
SI_B
2d
5a
A[7:0]
0
A[7:0]
shift_control
reset_b
clock
Default
Name
1
01
11
0b
5
05
3
128
128
80
2
02
2
64
64
40
1
01
80
3
a0
160
160
0
00
80
80
50
0
00
90
5a
10
0a
120
2
45
2d
5
05
0
0
00
22
16
2
02
11
0b
1
01
5
05
160
128
128
80
1
2
02
64
192
c0
1
01
0
00
0
160
96
60
0
00
b0
80
176
1
200
198
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
199
(i) See Prob. 6.35h.
(j)
module Serial_Twos_Comp (output y, input [7: 0] data, input load, shift_control, Clock, reset_b);
reg [7: 0] SReg;
reg Q;
wire SO = SReg [0];
assign y = SO ^ Q;
always @ (posedge Clock, negedge reset_b)
if (reset_b == 0) begin
SReg <= 0;
Q <= 0;
end
else begin
if (load) SReg = data;
else if (shift_control) begin
Q <= Q | SO;
SReg <= {y, SReg[7: 1]};
end
end
endmodule
module t_Serial_Twos_Comp ();
wire y;
reg [7: 0] data;
reg load, shift_control, Clock, reset_b;
Serial_Twos_Comp M0 (y, data, load, shift_control, Clock, reset_b);
reg [7: 0] twos_comp;
always @ (posedge Clock, negedge reset_b)
if (reset_b == 0) twos_comp <= 0;
else if (shift_control && !load) twos_comp <= {y, twos_comp[7: 1]};
initial #200 $finish;
initial begin Clock = 0; forever #5 Clock = ~Clock; end
initial begin #2 reset_b = 0; #4 reset_b = 1; end
initial fork
data = 8'h5A;
#20 load = 1;
#30 load = 0;
#50 shift_control = 1;
#50 begin repeat (9) @ (posedge Clock) ;
shift_control = 0;
end
join
endmodule
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
200
Name
0
50
100
Clock
reset_b
5a
data[7:0]
load
shift_control
SReg[7:0]
00
5a
2d
96
cb
65
32
99
4c
80
c0
60
30
98
4c
a6
y
twos_comp[7:0]
(k)
00
From the solution to Problem 6.13:
A1
4-Bit
Ripple Counter
Clear
Asynchronous, active-low)
A2
0
1
0
A3
1
A4
module Prob_6_35k_BCD_Counter (output A1, A2, A3, A4, input clk, reset_b);
wire {A1, A2, A3, A4} = A;
nand (Clear, A2, A4);
Ripple_Counter_4bit M0 (A, Clear, reset_b);
endmodule
module Ripple_Counter_4bit (output [3: 0] A, input Count, reset_b);
reg A0, A1, A2, A3;
assign A = {A3, A2, A1, A0};
always @ (negedge Count, negedge reset_b)
if (reset_b == 0) A0 <= 0; else A0 <= ~A0;
always @ (negedge A0, negedge reset_b)
if (reset_b == 0) A1 <= 0; else A1 <= ~A1;
always @ (negedge A1, negedge reset_b)
if (reset_b == 0) A2 <= 0; else A2 <= ~A2;
always @ (negedge A2, negedge reset_b)
if (reset_b == 0) A3 <= 0; else A3 <= ~A3;
endmodule
module t_ Prob_6_35k_BCD_Counter ();
wire [3: 0] A;
reg Count, reset_b;
Prob_6_35k_BCD_Counter M0 (A1, A2, A3, A4, reset_b);
initial
#300
$finish;
initial fork
reset_b = 0;
#60 reset_b = 1;
// Active-low reset
/*
Count = 1;
#15 Count = 0;
#30 Count = 1;
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
a6
201
#85 begin Count = 0; forever #10 Count = ~Count; end*/
join
endmodule
(l)
module Prob_6_35l_Up_Dwn_Beh (output reg [3: 0] A, input CLK, Up, Down, reset_b);
always @ (posedge CLK, negedge reset_b)
if (reset_b ==0) A <= 4'b0000;
else case ({Up, Down})
2'b10: A <= A + 4'b0001; // Up
2'b01: A <= A - 4'b0001;
// Down
default: A <= A; // Suspend (Redundant statement)
endcase
endmodule
module t_Prob_6_35l_Up_Dwn_Beh ();
wire [3: 0] A;
reg CLK, Up, Down, reset_b;
Prob_6_35l_Up_Dwn_Beh M0 (A, CLK, Up, Down, reset_b);
initial #300 $finish;
initial begin CLK = 0; forever #5 CLK = ~CLK; end
initial fork
Down = 0; Up= 0;
#10 reset_b = 0;
#20 reset_b = 1;
#40 Up = 1;
#150 Down = 1;
#220 Up = 0;
#280 Down = 0;
join
endmodule
Name
0
90
180
270
CLK
reset_b
Up
Down
A[3:0]
6.36
x
0
1
2
3
4
5
6
7
8
9
a
b
a
9
8
7
6
(a)
// See Fig. 6.13., 4-bit Up-Down Binary Counter
module Prob_6_36_Up_Dwn_Beh (output reg [3: 0] A, input CLK, Up, Down, reset_b);
always @ (posedge CLK, negedge reset_b)
if (reset_b ==0) A <= 4'b0000;
else if (Up) A <= A + 4'b0001;
else if (Down) A <= A - 4'b0001;
endmodule
module t_Prob_6_36_Up_Dwn_Beh ();
wire [3: 0] A;
reg CLK, Up, Down, reset_b;
Digital
Design
With
An
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HDL
–
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Manual.
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2012,
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rights
reserved.
5
202
Prob_6_36_Up_Dwn_Beh M0 (A, CLK, Up, Down, reset_b);
initial #300 $finish;
initial begin CLK = 0; forever #5 CLK = ~CLK; end
initial fork
Down = 0; Up= 0;
#10 reset_b = 0;
#20 reset_b = 1;
#40 Up = 1;
#150 Down = 1;
#220 Up = 0;
#280 Down = 0;
join
endmodule
Name
0
80
160
240
CLK
reset_b
Up
Down
A[3:0]
x
0
1
2
3
4
5
6
7
8
9
a
b
c
d
e
f
0
1
2
1
0
f
e
d
c
(b)
module Prob_6_36_Up_Dwn_Str (output [3: 0] A, input CLK, Up, Down, reset_b);
wire Down_3, Up_3, Down_2, Up_2, Down_1, Up_1;
wire A_0b, A_1b, A_2b, A_3b;
stage_register SR3 (A[3], A_3b, Down_3, Up_3, Down_2, Up_2, A[2], A_2b, CLK, reset_b);
stage_register SR2 (A[2], A_2b, Down_2, Up_2, Down_1, Up_1, A[1], A_1b, CLK, reset_b);
stage_register SR1 (A[1], A_1b, Down_1, Up_1, Down_not_Up, Up, A[0], A_0b, CLK, reset_b);
not (Up_b, Up);
and (Down_not_Up, Down, Up_b);
or (T, Up, Down_not_Up);
Toggle_flop TF0 (A[0], A_0b, T, CLK, reset_b);
endmodule
module stage_register (output A, A_b, Down_not_Up_out, Up_out, input Down_not_Up, Up, A_in,
A_in_b, CLK, reset_b);
Toggle_flop T0 (A, A_b, T, CLK, reset_b);
or (T, Down_not_Up_out, Up_out);
and (Down_not_Up_out, Down_not_Up, A_in_b);
and (Up_out, Up, A_in);
endmodule
module Toggle_flop (output reg Q, output Q_b, input T, CLK, reset_b);
always @ (posedge CLK, negedge reset_b) if (reset_b == 0) Q <= 0; else Q <= Q ^ T;
assign Q_b = ~Q;
endmodule
module t_Prob_6_36_Up_Dwn_Str ();
wire [3: 0] A;
reg CLK, Up, Down, reset_b;
wire T3 = M0.SR3.T;
wire T2 = M0.SR2.T;
Digital
Design
With
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HDL
–
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Manual.
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2012,
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rights
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203
wire T1 = M0.SR1.T;
wire T0 = M0.T;
Prob_6_36_Up_Dwn_Str M0 (A, CLK, Up, Down, reset_b);
initial #150 $finish;
initial begin CLK = 0; forever #5 CLK = ~CLK; end
initial fork
Down = 0; Up= 0;
#10 reset_b = 0;
#20 reset_b = 1;
#50 Up = 1;
#140 Down = 1;
#120 Up = 0;
#140 Down = 0;
join
endmodule
Name
0
70
140
210
280
CLK
reset_b
Up
Down
A[3:0]
x
0
1
2
3
4
5
6
7
8
9
a
b
c
d
e
f
0
1
2
1
0
f
e
T0
T1
T2
T3
6.37
module Counter_if (output reg [3: 0] Count, input clock, reset);
always @ (posedge clock , posedge reset)
if (reset)Count <= 0;
else if (Count == 0) Count <= 1;
else if (Count == 1) Count <= 3; // Default interpretation is decimal
else if (Count == 3) Count <= 7;
else if (Count == 4) Count <= 0;
else if (Count == 6) Count <= 4;
else if (Count == 7) Count <= 6;
else Count <= 0;
endmodule
module Counter_case (output reg [3: 0] Count, input clock, reset);
always @ (posedge clock , posedge reset)
if (reset)Count <= 0;
else begin
Count <= 0;
case (Count)
0:
Count <= 1;
1:
Count <= 3;
3:
Count <= 7;
4:
Count <= 0;
6:
Count <= 4;
7:
Count <= 6;
default: Count <= 0;
endcase
end
endmodule
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
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rights
reserved.
d
c
204
module Counter_FSM (output reg [3: 0] Count, input clock, reset);
reg [2: 0] state, next_state;
parameter s0 = 0, s1 = 1, s2 = 2, s3 = 3, s4 = 4, s5 = 5, s6 = 6, s7 = 7;
always @ (posedge clock , posedge reset)
if (reset) state <= s0; else state <= next_state;
always @ (state) begin
Count = 0;
case (state)
s0:
begin next_state = s1; Count = 0; end
s1:
begin next_state = s2; Count = 1; end
s2:
begin next_state = s3; Count = 3; end
s3:
begin next_state = s4; Count = 7; end
s4:
begin next_state = s5; Count = 6; end
s5:
begin next_state = s6; Count = 4; end
default: begin next_state = s0; Count = 0; end
endcase
end
endmodule
6.38
(a)
module Prob_6_38a_Updown (OUT, Up, Down, Load, IN, CLK); // Verilog 1995
output [3: 0] OUT;
input [3: 0] IN;
input
Up, Down, Load, CLK;
reg [3:0] OUT;
always @ (posedge CLK)
if (Load) OUT <= IN;
else if (Up)
OUT <= OUT + 4'b0001;
else if (Down) OUT <= OUT - 4'b0001;
else
OUT <= OUT;
endmodule
module updown (
// Verilog 2001, 2005
output reg [3: 0] OUT,
input
[3: 0] IN,
input
Up, Down, Load, CLK
);
Name
0
110
220
330
440
clock
reset_b
Load
Down
Up
c
data[3:0]
count[3:0]
0
c
d e f 0 1
3 4 5
7 8 9
b c
c b a
8 7 6
4 3
1 0 f
d c
b
0
c
(b)
module Prob_6_38b_Updown (output reg [3: 0] OUT, input [3: 0] IN, input s1, s0, CLK);
always @ (posedge CLK)
Digital
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HDL
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2012,
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205
case ({s1, s0})
2'b00: OUT <= OUT + 4'b0001;
2'b01: OUT <= OUT - 4'b0001;
2'b10: OUT <= IN;
2'b11: OUT <= OUT;
endcase
endmodule
module t_Prob_6_38b_Updown ();
wire [3: 0] OUT;
reg [3: 0] IN;
reg s1, s0, CLK;
Prob_6_38b_Updown M0 (OUT, IN, s1, s0, CLK);
initial #150 $finish;
initial begin CLK = 0; forever #5 CLK = ~CLK; end
initial fork
IN = 4'b1010;
#10 begin s1 = 1; s0 = 0; end
#20 begin s1 = 1; s0 = 1; end
#40 begin s1 = 0; s0 = 0; end
#80 begin s1 = 0; s0 = 1; end
#120 begin s1 = 1; s0 = 1; end
join
endmodule
Name
// Load IN
// no change
// UP;
// DOWN
0
60
120
CLK
s1
s0
a
IN[3:0]
OUT[3:0]
x
a
b
c
d
e
d
c
b
a
6.39
module Prob_6_39_Counter_BEH (output reg [2: 0] Count, input Clock, reset_b);
always @ (posedge Clock, negedge reset_b) if (reset_b == 0) Count <= 0;
else case (Count)
0: Count <= 1;
1: Count <= 2;
2: Count <= 4;
4: Count <= 5;
5: Count <= 6;
6: Count <= 0;
endcase
endmodule
module Prob_6_39_Counter_STR (output [2: 0] Count, input Clock, reset_b);
supply1 PWR;
wire Count_1_b = ~Count[1];
JK_FF M2 (Count[2],
JK_FF M1 (Count[1],
JK_FF M0 (Count[0],
endmodule
Count[1], Count[1], Clock, reset_b);
Count[0], PWR,
Clock, reset_b);
Count_1_b,
PWR,
Clock, reset_b);
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206
module JK_FF (output reg Q, input J, K, clk, reset_b);
always @ (posedge clk, negedge reset_b) if (reset_b == 0) Q <= 0; else
case ({J,K})
2'b00: Q <= Q;
2'b01: Q <= 0;
2'b10: Q <= 1;
2'b11: Q <= ~Q;
endcase
endmodule
module t_Prob_6_39_Counter ();
wire [2: 0] Count_BEH, Count_STR;
reg Clock, reset_b;
Prob_6_39_Counter_BEH M0_BEH (Count_STR, Clock, reset_b);
Prob_6_39_Counter_STR M0_STR (Count_BEH, Clock, reset_b);
initial #250 $finish;
initial fork #1 reset_b = 0; #7 reset_b = 1; join
initial begin Clock = 1; forever #5 Clock = ~Clock; end
endmodule
Name
0
60
120
Clock
reset_b
Count_BEH[2:0]
0
1
2
4
5
6
0
1
2
4
5
6
0
1
2
4
Count_STR[2:0]
0
1
2
4
5
6
0
1
2
4
5
6
0
1
2
4
6.40
module Prob_6_40 (output reg [0: 7] timer, input clk, reset_b);
always @ (negedge clk, negedge reset_b)
if (reset_b == 0) timer <= 8'b1000_0000; else
case (timer)
8'b1000_0000: timer <= 8'b0100_0000;
8'b0100_0000: timer <= 8'b0010_0000;
8'b0010_0000: timer <= 8'b0001_0000;
8'b0001_0000: timer <= 8'b0000_1000;
8'b0000_1000: timer <= 8'b0000_0100;
8'b0000_0100: timer <= 8'b0000_0010;
8'b0000_0010: timer <= 8'b0000_0001;
8'b0000_0001: timer <= 8'b1000_0000;
default:
timer <= 8'b1000_0000;
endcase
endmodule
module t_Prob_6_40 ();
wire [0: 7] timer;
reg clk, reset_b;
Prob_6_40 M0 (timer, clk, reset_b);
initial #250 $finish;
initial fork #1 reset_b = 0; #7 reset_b = 1; join
initial begin clk = 1; forever #5 clk = ~clk; end
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207
endmodule
Name
0
70
140
210
clk
reset_b
timer[0:7]
80
timer[0]
timer[1]
timer[2]
timer[3]
timer[4]
timer[5]
timer[6]
timer[7]
6.41
module Prob_6_41_Switched_Tail_Johnson_Counter (output [0: 3] Count, input CLK, reset_b);
wire Q_0b, Q_1b, Q_2b, Q_3b;
DFF M3 (Count[3], Q_3b, Count[2], CLK, reset_b);
DFF M2 (Count[2], Q_2b, Count[1], CLK, reset_b);
DFF M1 (Count[1], Q_1b, Count[0], CLK, reset_b);
DFF M0 (Count[0], Q_0b, Q_3b, CLK, reset_b);
endmodule
module DFF (output reg Q, output Q_b, input D, clk, reset_b);
assign Q_b = ~Q;
always @ (posedge clk, negedge reset_b) if (reset_b ==0) Q <= 0; else Q <= D;
endmodule
module t_Prob_6_41_Switched_Tail_Johnson_Counter ();
wire [3: 0] Count;
reg CLK, reset_b;
wire s0 = ~ M0.Count[0] && ~M0.Count[3];
wire s1 = M0.Count[0] && ~M0.Count[1];
wire s2 = M0.Count[1] && ~M0.Count[2];
wire s3 = M0.Count[2] && ~M0.Count[3];
wire s4 = M0.Count[0] && M0.Count[3];
wire s5 = ~ M0.Count[0] && M0.Count[1];
wire s6 = ~ M0.Count[1] && M0.Count[2];
wire s7 = ~ M0.Count[2] && M0.Count[3];
Prob_6_41_Switched_Tail_Johnson_Counter M0 (Count, CLK, reset_b);
initial
#150
$finish;
initial
fork
#1
reset_b
=
0;
#7
reset_b
=
1;
join
initial
begin
CLK
=
1;
forever
#5
CLK
=
~CLK;
end
endmodule
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208
Name
0
60
120
CLK
reset_b
Count[3:0]
0
8
c
e
f
7
3
1
0
8
c
e
f
7
3
s0
s1
s2
s3
s4
s5
s6
s7
6.42
Because A is a register variable, it retains whatever value has been assigned to it until a new
value is assigned. Therefore, the statement A <= A has the same effect as if the statement was
omitted.
6.43
data
D_in
Shift_control
load
Clock
Mux
Mux
D
Q
DFF
[
module Prob_6_43_Str (output SO, input [7: 0] data, input load, Shift_control, Clock, reset_b);
supply0 gnd;
wire SO_A;
Shift_with_Load M_A (SO_A, SO_A, data, load, Shift_control, Clock, reset_b);
Shift_with_Load M_B (SO, SO_A, data, gnd, Shift_control, Clock, reset_b);
endmodule
module Shift_with_Load (output SO, input D_in, input [7: 0] data, input load, select, Clock, reset_b);
wire [7: 0] Q;
assign SO = Q[0];
SR_cell M7 (Q[7], D_in, data[7], load, select, Clock, reset_b);
SR_cell M6 (Q[6], Q[7], data[6], load, select, Clock, reset_b);
SR_cell M5 (Q[5], Q[6], data[5], load, select, Clock, reset_b);
SR_cell M4 (Q[4], Q[5], data[4], load, select, Clock, reset_b);
SR_cell M3 (Q[3], Q[4], data[3], load, select, Clock, reset_b);
SR_cell M2 (Q[2], Q[3], data[2], load, select, Clock, reset_b);
SR_cell M1 (Q[1], Q[2], data[1], load, select, Clock, reset_b);
SR_cell M0 (Q[0], Q[1], data[0], load, select, Clock, reset_b);
endmodule
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209
module SR_cell (output Q, input D, data, load, select, Clock, reset_b);
wire y;
DFF_with_load M0 (Q, y, data, load, Clock, reset_b);
Mux_2 M1 (y, Q, D, select);
endmodule
module DFF_with_load (output reg Q, input D, data, load, Clock, reset_b);
always @ (posedge Clock, negedge reset_b)
if (reset_b == 0) Q <= 0; else if (load) Q <= data; else Q <= D;
endmodule
module Mux_2 (output reg y, input a, b, sel);
always @ (a, b, sel) if (sel ==1) y = b; else y = a;
endmodule
module t_Fig_6_4_Str ();
wire SO;
reg load, Shift_control, Clock, reset_b;
reg [7: 0] data, Serial_Data;
Prob_6_43_Str M0 (SO, data, load, Shift_control, Clock, reset_b);
always @ (posedge Clock, negedge reset_b)
if (reset_b == 0) Serial_Data <= 0;
else if (Shift_control ) Serial_Data <= {M0.SO_A, Serial_Data [7: 1]};
initial #200 $finish;
initial begin Clock = 0; forever #5 Clock = ~Clock; end
initial begin #2 reset_b = 0; #4 reset_b = 1; end
initial fork
data = 8'h5A;
#20 load = 1;
#30 load = 0;
#50 Shift_control = 1;
#50 begin repeat (9) @ (posedge Clock) ;
Shift_control = 0;
end
join
endmodule
0
Name
50
100
Clock
reset_b
load
Shift_control
5a
data[7:0]
SO_A
SO
96
4b
a5
d2
69
b4
5a
Q[7:0]
00
80
40
a0
d0
68
b4
5a
Serial_Data[7:0]
00
80
40
a0
d0
68
b4
Q[7:0]
00
5a
2d
2d
2d
5a
Alternative: a behavioral model for synthesis is given below. The behavioral description implies
the need for a mux at the input to a D-type flip-flop.
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210
module Fig_6_4_Beh (output SO, input [7: 0] data, input load, Shift_control, Clock, reset_b);
reg [7: 0] Shift_Reg_A, Shift_Reg_B;
assign SO = Shift_Reg_B[0];
always @ (posedge Clock, negedge reset_b)
if (reset_b == 0) begin
Shift_Reg_A <= 0;
Shift_Reg_B <= 0;
end
else if (load) Shift_Reg_A <= data;
else if (Shift_control) begin
Shift_Reg_A <= { Shift_Reg_A[0], Shift_Reg_A[7: 1]};
Shift_Reg_B <= {Shift_Reg_A[0], Shift_Reg_B[7: 1]};
end
endmodule
module t_Fig_6_4_Beh ();
wire SO;
reg load, Shift_control, Clock, reset_b;
reg [7: 0] data, Serial_Data;
Fig_6_4_Beh M0 (SO, data, load, Shift_control, Clock, reset_b);
always @ (posedge Clock, negedge reset_b)
if (reset_b == 0) Serial_Data <= 0;
else if (Shift_control ) Serial_Data <= {M0.Shift_Reg_A[0], Serial_Data [7: 1]};
initial #200 $finish;
initial begin Clock = 0; forever #5 Clock = ~Clock; end
initial begin #2 reset_b = 0; #4 reset_b = 1; end
initial fork
data = 8'h5A;
#20 load = 1;
#30 load = 0;
#50 Shift_control = 1;
#50 begin repeat (9) @ (posedge Clock) ;
Shift_control = 0;
end
join
endmodule
Name
0
50
100
150
Clock
reset_b
load
Shift_control
5a
data[7:0]
Shift_Reg_A[7:0]
Shift_Reg_B[7:0]
00
5a
2d
96
4b
a5
d2
69
b4
5a
2d
00
80
40
a0
d0
68
b4
5a
2d
00
80
40
a0
d0
68
b4
SO
Serial_Data[7:0]
5a
6.44
// See Figure 6.5
// Note: Sum is stored in shift register A; carry is stored in Q
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211
// Note: Clear is active-low.
module Prob_6_44_Str (output SO, input [7: 0] data_A, data_B, input S_in, load, Shift_control, CLK,
Clear);
supply0 gnd;
wire sum, carry;
assign SO = sum;
wire SO_A, SO_B;
Shift_Reg_gated_clock M_A (SO_A, sum, data_A, load, Shift_control, CLK, Clear);
Shift_Reg_gated_clock M_B (SO_B, S_in, data_B, load, Shift_control, CLK, Clear);
FA M_FA (carry, sum, SO_A, SO_B, Q);
DFF_gated M_FF (Q, carry, Shift_control, CLK, Clear);
endmodule
module Shift_Reg_gated_clock (output SO, input S_in, input [7: 0] data, input load, Shift_control,
Clock, reset_b);
reg [7: 0] SReg;
assign SO = SReg[0];
always @ (posedge Clock, negedge reset_b)
if (reset_b == 0) SReg <= 0;
else if (load) SReg <= data;
else if (Shift_control) SReg <= {S_in, SReg[7: 1]};
endmodule
module DFF_gated (output Q, input D, Shift_control, Clock, reset_b);
DFF M_DFF (Q, D_internal, Clock, reset_b);
Mux_2 M_Mux (D_internal, Q, D, Shift_control);
endmodule
module DFF (output reg Q, input D, Clock, reset_b);
always @ (posedge Clock, negedge reset_b)
if (reset_b == 0) Q <= 0; else Q <= D;
endmodule
module Mux_2 (output reg y, input a, b, sel);
always @ (a, b, sel) if (sel ==1) y = b; else y = a;
endmodule
module FA (output reg carry, sum, input a, b, C_in);
always @ (a, b, C_in) {carry, sum} = a + b + C_in;
endmodule
module t_Prob_6_44_Str ();
wire SO;
reg SI, load, Shift_control, Clock, Clear;
reg [7: 0] data_A, data_B;
Prob_6_44_Str M0 (SO, data_A, data_B, SI, load, Shift_control, Clock, Clear);
initial #200 $finish;
initial begin Clock = 0; forever #5 Clock = ~Clock; end
initial begin #2 Clear = 0; #4 Clear = 1; end
initial fork
data_A = 8'hAA;
data_B = 8'h55;
SI = 0;
#20 load = 1;
#30 load = 0;
//8'h ff;
//8'h01;
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#50 Shift_control = 1;
#50 begin repeat (8) @ (posedge Clock) ;
#5 Shift_control = 0;
end
join
endmodule
Name
0
60
120
Clock
Clear
load
Shift_control
aah + 55h = {carry, sum} = {0, ffh}
aa
data_A[7:0]
SReg[7:0]
00
aa
d5
ea
00
55
2a
15
f5
fa
fd
fe
ff
05
02
01
00
Q
55
data_B[7:0]
SReg[7:0]
0a
SO
Name
0
60
120
Clock
Clear
load
Shift_control
ffh + 01h = {carry, sum} = {1, 00h}
ff
data_A[7:0]
SReg[7:0]
00
ff
00
01
7f
3f
1f
0f
07
03
01
00
Q
01
data_B[7:0]
SReg[7:0]
00
SO
6.45
module Prob_6_45 (output reg y_out, input start, clock, reset_bar);
parameter
s0 = 4'b0000,
s1 = 4'b0001,
s2 = 4'b0010,
s3 = 4'b0011,
s4 = 4'b0100,
s5 = 4'b0101,
s6 = 4'b0110,
s7 = 4'b0111,
s8 = 4'b1000;
reg [3: 0] state, next_state;
always @ (posedge clock, negedge reset_bar)
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if (!reset_bar) state <= s0; else state <= next_state;
always @ (state, start) begin
y_out = 1'b0;
case (state)
s0: if (start) next_state = s1; else next_state = s0;
s1: begin next_state = s2; y_out = 1; end
s2: begin next_state = s3; y_out = 1; end
s3: begin next_state = s4; y_out = 1; end
s4: begin next_state = s5; y_out = 1; end
s5: begin next_state = s6; y_out = 1; end
s6: begin next_state = s7; y_out = 1; end
s7: begin next_state = s8; y_out = 1; end
s8: begin next_state = s0; y_out = 1; end
default: next_state = s0;
endcase
end
endmodule
// Test plan
// Verify the following:
// Power-up reset
// Response to start in initial state
// Reset on-the-fly
// Response to re-assertion of start after reset on-the-fly
// 8-cycle counting sequence
// Ignore start during counting sequence
// Return to initial state after 8 cycles and await start
// Remain in initial state for one clock if start is asserted when the state is entered
module t_Prob_6_45;
wire y_out;
reg start, clock, reset_bar;
Prob_6_45 M0 (y_out, start, clock, reset_bar);
initial #300 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial fork
reset_bar = 0;
#2 reset_bar = 1;
#10 start = 1;
#20 start = 0;
#30 reset_bar = 0;
#50 reset_bar = 1;
#80 start = 1;
#90 start = 0;
#130 start = 1;
#140 start = 0;
#180 start = 1;
join
endmodule
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0
Name
70
140
210
280
clock
reset_bar
start
y_out
6.46
module Prob_6_46 (output reg [0: 3] timer, input clk, reset_b);
always @ (negedge clk, negedge reset_b)
if (reset_b == 0) timer <= 4'b1000; else
case (timer)
4'b1000: timer <= 4'b0100;
4'b0100: timer <= 4'b0010;
4'b0010: timer <= 4'b0001;
4'b0001: timer <= 4'b1000;
default: timer <= 4'b1000;
endcase
endmodule
module t_Prob_6_46 ();
wire [0: 3] timer;
reg clk, reset_b;
Prob_6_46 M0 (timer, clk, reset_b);
initial #150 $finish;
initial fork #1 reset_b = 0; #7 reset_b = 1; join
initial begin clk = 1; forever #5 clk = ~clk; end
endmodule
Name
0
60
120
clk
reset_b
timer [0:3]
8
4
2
1
8
4
2
1
8
4
2
1
8
4
timer [0]
timer [1]
timer [2]
timer [3]
6.47
module Prob_6_47 (
output reg P_odd,
input D_in, CLK, reset
);
wire D;
assign D = D_in ^ P_odd;
always @ (posedge CLK, posedge reset)
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215
if (reset)
P_odd <= 0;
else
P_odd <= D;
endmodule
module t_Prob_6_47 ();
wire P_odd;
reg D_in, CLK, reset;
Prob_6_47 M0 (P_odd, D_in, CLK, reset);
initial #150 $finish;
initial fork #1 reset = 1; #7 reset = 0; join
initial begin CLK = 0; forever #5 CLK = ~CLK; end
initial begin D_in = 1; forever #20 D_in = ~D_in; end
endmodule
Name
0
60
120
CLK
reset
D_in
P_odd
6.48
(a)
module Prob_6_48a (output reg [7: 0] count, input clk, reset_b);
reg [3: 0] state;
always @ (posedge clk, negedge reset_b)
if (reset_b == 0) state <= 0; else state <= state + 1;
always @ (state)
case (state)
0, 2, 4, 6, 8, 10, 12: count = 8'b0000_0001;
1:
count = 8'b0000_0010;
3:
count = 8'b0000_0100;
5:
count = 8'b0000_1000;
7:
count = 8'b0001_0000;
9:
count = 8'b0010_0000;
11:
count = 8'b0100_0000;
13:
count = 8'b1000_0000;
default: count = 8'b0000_0000;
endcase
endmodule
module t_Prob_6_48a ();
wire [7: 0] count;
reg clk, reset_b;
Prob_6_48a M0 (count, clk, reset_b);
initial #200 $finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial begin reset_b = 0; #2 reset_b = 1; end
endmodule
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216
Name
0
60
120
180
clk
reset_b
state[3:0]
1
2
3
4
5
6
7
8
9
a
b
c
d
count[7:0]
02
01
04
01
08
01
10
01
20
01
40
01
80
e
f
00
0
1
2
3
01
02
01
04
count[7]
count[6]
count[5]
count[4]
count[3]
count[2]
count[1]
count[0]
(b)
module Prob_6_48b (output reg [7: 0] count, input clk, reset_b);
reg [3: 0] state;
always @ (posedge clk, negedge reset_b)
if (reset_b == 0) state <= 0; else state <= state + 1;
always @ (state)
case (state)
0, 2, 4, 6, 8, 10, 12: count = 8'b1000_0000;
1:
count = 8'b0100_0000;
3:
count = 8'b0010_0000;
5:
count = 8'b0001_0000;
7:
count = 8'b0000_1000;
9:
count = 8'b0000_0100;
11:
count = 8'b0000_0010;
13:
count = 8'b0000_0001;
default:
count = 8'b0000_0000;
endcase
endmodule
module t_Prob_6_48b ();
wire [7: 0] count;
reg clk, reset_b;
Prob_6_48b M0 (count, clk, reset_b);
initial #180 $finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial begin reset_b = 0; #2 reset_b = 1; end
endmodule
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217
Name
0
60
120
180
clk
reset_b
state[3:1]
count[7:0]
0
40
1
80
2
20
80
3
10
80
4
08
80
5
04
80
6
02
80
7
01
00
0
80
count[7]
count[6]
count[5]
count[4]
count[3]
count[2]
count[1]
count[0]
6.49
// Behavioral description of a 4-bit universal shift register
// Fig. 6.7 and Table 6.3
module Shift_Register_4_beh (
// V2001, 2005
output reg [3: 0] A_par,
// Register output
input
[3: 0] I_par,
// Parallel input
input
s1, s0,
// Select inputs
MSB_in, LSB_in, // Serial inputs
CLK, Clear
// Clock and Clear
);
always @ (posedge CLK, negedge Clear) // V2001, 2005
if (~Clear) A_par <= 4'b0000;
else
case ({s1, s0})
2'b00: A_par <= A_par;
// No change
2'b01: A_par <= {MSB_in, A_par[3: 1]};
// Shift right
2'b10: A_par <= {A_par[2: 0], LSB_in};
// Shift left
2'b11: A_par <= I_par;
// Parallel load of input
endcase
endmodule
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40
218
// Test plan:
// test reset action load
// test parallel load
// test shift right
// test shift left
// test circulation of data
// test reset on the fly
module t_Shift_Register_4_beh ();
reg s1, s0,
// Select inputs
MSB_in, LSB_in,
// Serial inputs
clk, reset_b;
// Clock and Clear
reg [3: 0] I_par;
// Parallel input
wire [3: 0] A_par;
// Register output
Shift_Register_4_beh M0 (A_par, I_par,s1, s0, MSB_in, LSB_in, clk, reset_b);
initial #200 $finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
// test reset action load
#3 reset_b = 1;
#4 reset_b = 0;
#9 reset_b = 1;
// test parallel load
#10 I_par = 4'hA;
#10 {s1, s0} = 2'b11;
// test shift right
#30 MSB_in = 1'b0;
#30 {s1, s0} = 2'b01;
// test shift left
#80 LSB_in = 1'b1;
#80 {s1, s0} = 2'b10;
// test circulation of data
#130 {s1, s0} = 2'b11;
#140 {s1, s0} = 2'b00;
// test reset on the fly
#150 reset_b = 1'b0;
#160 reset_b = 1'b1;
#160 {s1, s0} = 2'b11;
join
endmodule
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219
0
Name
60
120
180
clk
reset_b
x
I_par[3:0]
a
MSB_in
LSB_in
A_par[3:0]
0
a
5
2
1
0
1
3
7
f
a
0
a
s1
s0
Reset A_par
Load_A_par
Shift right
6.50
Shift left
Load A_par
No change
Reset
Load A_par
(a) See problem 6.27.
module Prob_8_50a (output reg [2: 0] count, input clk, reset_b);
always @ (posedge clk, negedge reset_b)
if (!reset_b) count <= 0;
else case (count)
3'd0: count <= 3'd1;
3'd1: count <= 3'd2;
3'd2: count <= 3'd3;
3'd3: count <= 3'd4;
3'd4: count <= 3'd5;
3'd5: count <= 3'd6;
3'd4: count <= 3'd6;
3'd6: count <= 3'd0;
default: count <= 3'd0;
endcase
endmodule
module t_Prob_8_50a;
wire [2: 0] count;
reg clock, reset_b ;
Prob_8_50a M0 (count, clock, reset_b);
initial #130 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial fork
reset_b = 0;
#2 reset_b = 1;
#40 reset_b = 0;
#42 reset_b = 1;
join
endmodule
Name
0
40
80
120
clock
reset_b
count[2:0]
0
1
2
3
4
0
1
2
3
4
5
6
0
1
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2
220
(b) See problem 6.28.
module Prob_8_50b (output reg [2: 0] count, input clk, reset_b);
always @ (posedge clk, negedge reset_b)
if (!reset_b) count <= 0;
else case (count)
3'd0: count <= 3'd1;
3'd1: count <= 3'd2;
3'd2: count <= 3'd4;
3'd4: count <= 3'd6;
3'd6: count <= 3'd0;
default: count <= 3'd0;
endcase
endmodule
module t_Prob_8_50b;
wire [2: 0] count;
reg clock, reset_b ;
Prob_8_50b M0 (count, clock, reset_b);
initial #100 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial fork
reset_b = 0;
#2 reset_b = 1;
#40 reset_b = 0;
#42 reset_b = 1;
join
endmodule
0
30
60
90
reset_b
clock
count[2:0]
0
1
2
4
6
0
1
2
4
6
0
1
6.51
module Seq_Detector_Prob_5_51 (output detect, input bit_in, clk, reset_b);
reg [2: 0] sample_reg;
assign detect = (sample_reg == 3'b111);
always @ (posedge clk, negedge reset_b) if (reset_b ==0) sample_reg <= 0;
else sample_reg <= {bit_in, sample_reg [2: 1]};
endmodule
module Seq_Detector_Prob_5_45 (output detect, input bit_in, clk, reset_b);
parameter S0 = 0, S1 = 1, S2 = 2, S3 = 3;
reg [1: 0] state, next_state;
assign detect = (state == S3);
always @ (posedge clk, negedge reset_b)
if (reset_b == 0) state <= S0; else state <= next_state;
always @ (state, bit_in) begin
next_state = S0;
case (state)
0:
if (bit_in) next_state = S1; else state = S0;
1:
if (bit_in) next_state = S2; else next_state = S0;
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2:
if (bit_in) next_state = S3; else state = S0;
3:
if (bit_in) next_state = S3; else next_state = S0;
default: next_state = S0;
endcase
end
endmodule
module t_Seq_Detector_Prob_6_51 ();
wire detect_45, detect_51;
reg bit_in, clk, reset_b;
Seq_Detector_Prob_5_51 M0 (detect_51, bit_in, clk, reset_b);
Seq_Detector_Prob_5_45 M1 (detect_45, bit_in, clk, reset_b);
initial #350$finish;
initial begin clk = 0; forever #5 clk = ~clk; end
initial fork
reset_b = 0;
#4 reset_b = 1;
#10 bit_in = 1;
#20 bit_in = 0;
#30 bit_in = 1;
#50 bit_in = 0;
#60 bit_in = 1;
#100 bit_in = 0;
join
endmodule
Name
0
60
120
clk
reset_b
bit_in
detect_51
detect_45
The circuit using a shift register uses less hardware.
6.52
Universal Shift Register
module Prob_6_52 (
output [3:0] A_par,
input [3: 0] In_par,
input MSB_in, LSB_in,
input [1: 0] s1, s0,
input CLK, Clear_b
);
wire y0, y1, y2, y3;
Mux_4x1 M0 (y0, In_par[0], LSB_in, A_par[1], A_par[0], s1, s0);
Mux_4x1 M1 (y1, In_par[1], A_par[0], A_par[2], A_par[1], s1, s0);
Mux_4x1 M2 (y2, In_par[2], A_par[1], A_par[3], A_par[2], s1, s0);
Mux_4x1 M3 (y3, In_par[3], A_par[2], MSB_in, A_par[3], s1, s0);
DFF D0 (A_par[0], y0, CLK, Clear_b);
DFF D1 (A_par[1], y1, CLK, Clear_b);
DFF D2 (A_par[2], y2, CLK, Clear_b);
DFF D3 (A_par[3], y3, CLK, Clear_b);
endmodule
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module Mux_4x1 (output reg y, input in3, in2, in1, in0, s1, s0);
always @ (in3, in2, in1, in0, s1, s0)
case ({s1, s0})
2'b00: y = in0;
2'b01: y = in1;
2'b10: y = in2;
2'b11: y = in3;
endcase
endmodule
module DFF (output reg q, input d, clk, clr_b);
always @ (posedge clk, negedge clr_b)
if (clr_b == 1'b0) q <= 0; else q <= d;
endmodule
Features to be tested:
Action of Clear_b
Power-up initialization
On-the-fly
Action of mode controls
s1 s0
0 0 No change
0 1 Shift right
1 0 Shift left
1 1 Parallel load
module t_Problem_6_52 ();
wire [3:0]
A_par;
reg [3: 0]
In_par;
reg
MSB_in, LSB_in;
reg
s1, s0;
reg
CLK, Clear_b;
reg [3:0]
In_par;
Prob_6_52 M0 (A_par, In_par, MSB_in, LSB_in, s1, s0, CLK, Clear_b);
initial #300 $finish;
initial begin CLK = 0, forever #5 CLK = ~CLK; end
initial fork
Clear_b = 0;
// Power-up initialization
#20 Clear_b = 1;
// Running
In_par = 4'b1010;
MSB_in = 1'b1;
LSB_in = 1'b0;
s1 = 0; s0 = 0;
#40 begin s1 = 1; s0 = 1; end
#60 Clear_b = 1'b0;
#80 Clear_b = 1'b1;
#90 begin s1 = 0; s0 = 0; end
// Word for parallel load
// Bit for serial load
// Bit for serial load
// Initial action to no change
// parallel load
// Reset on-the-fly
// Resume action with parallel load at next clock edge
// No action – register holds 4'b1010
#120 Clear_b = 1'b0;
// Clear register
#130 Clear_b = 1'b1;
#140 begin s1 = 1'b0; s0 = 1'b1; end
// Shifting to right (from MSB)
#170 begin s1 = 1'b0; s0 = 1'b0; end
// Register should hold 4'b1111
#190 begin Clear_b = 1'b0; s1 = 1'b0; s0 = 1'b0; end
#200 begin Clear_b = 1'b1; s1 = 1'b1; s0 = 1'b0; end
#230 begin s1 = 1'b0; s0 = 1'b0; end
join
endmodule
// Resume action – shift left
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6.53
module Prob_6_53 (output reg [3:0] SR_A, input Shift_control, SI, CLK, Clear_b);
reg [3: 0] SR_B;
wire Sum, Carry;
wire SO_A = SR_A[3];
wire SO_B = SR_B[3];
wire SI_A = Sum;
wire SI_B = SI;
wire Q;
always @ (posedge CLK)
if (Clear_b == 1'b0) SR_A<= 4'b0; else if (Shift_control) SR_A <= {Sum, SR_A[3:1]};
always @ (posedge CLK)
if (Clear_b == 1'b0) SR_B <= 4'b0; else if (Shift_control) SR_B <= {SI, SR_B[3:1]};
FA M0 (Sum, Carry, SO_A, SO_B, Q);
and (clk_to_DFF, CLK, Shift_control);
// Caution: gated clock
DFF M1 (Q, Carry, clk_to_DFF, Clear_b);
endmodule
module FA (output S, C, input x, y, z);
assign {C, S} = x + y + z;
endmodule
module DFF (output reg Q, input D, C, Clear_b);
always @ (posedge C) if (Clear_b == 1'b0) Q <= 1'b0; else Q <= D;
endmodule
module t_Prob_6_53 ();
wire [3:0] SR_A;
reg Shift_control, SI, CLK, Clear_b;
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Prob_6_53 M0 (SR_A, Shift_control, SI, CLK, Clear_b);
initial #300 $finish;
initial begin CLK = 0; forever #5 CLK = ~CLK; end
initial fork
Clear_b = 0;
#20 Clear_b = 1;
#40 Shift_control = 1;
SI = 0;
// Sequence of 1s
/*
#60 SI = 1;
#70 SI = 0;
#100 SI = 1;
#110 SI = 0;
#140 SI = 1;
#150 SI = 0;
#180 SI = 1;
#190 SI = 0;
*/
// Sequence of threes
#60 SI = 1;
#80 SI = 0;
#100 SI = 1;
#120 SI = 0;
#140 SI = 1;
#160 SI = 0;
#180 SI = 1;
#200 SI = 0;
join
endmodule
Simulation results for accumulating a sequence of four 1s.
Sequence of four 1s
Accumulation of 1s
Simulation results for accumulating a sequence of four 3s.
Digital
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Sequence of four 3s
Accumulation of 3s
Additional test patterns are left to the student.
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226
6.54
module Prob_6_54 (output reg [3:0] SR_A, input Shift_control, SI, CLK, Clear_b);
reg [3:0] SR_B;
wire S;
wire Q;
wire SI_A = S;
wire SO_A = SR_A[0];
wire SO_B = SR_B[0];
wire SI_B = SI;
and (J_in, SO_A, SO_B);
nor (K_in, SO_A, SO_B);
xor (S, SO_A, SO_B, Q);
and (clk_to_JKFF, Shift_control, CLK);
always @ (posedge CLK)
if (Clear_b == 1'b0) SR_A<= 4'b0; else if (Shift_control) SR_A <= {SI_A, SR_A[3:1]};
always @ (posedge CLK)
if (Clear_b == 1'b0) SR_B <= 4'b0; else if (Shift_control) SR_B <= {SI_B, SR_B[3:1]};
and (clk_to_JKFF, CLK, Shift_control);
// Caution: gated clock
JKFF M1 (Q, J_in, K_in, clk_to_JKFF, Clear_b);
endmodule
module FA (output S, C, input x, y, z);
assign {C, S} = x + y + z;
endmodule
module JKFF (output reg Q, input J_in, K_in, C, Clear_b);
always @ (posedge C) if (Clear_b == 1'b0) Q <= 1'b0; else
case ({J_in, K_in})
2'b00:
Q <= Q;
2'b01:
Q <= 1'b0;
2'b10:
Q <= 1'b1;
2'b11:
Q <= ~Q;
endcase
endmodule
module t_Prob_6_54 ();
wire [3:0] SR_A;
reg Shift_control, SI, CLK, Clear_b;
Prob_6_54 M0 (SR_A, Shift_control, SI, CLK, Clear_b);
//initial #200 $finish;
// sequence of 1s
initial #400 $finish;
// sequence of 3s
initial begin CLK = 0; forever #5 CLK = ~CLK; end
initial fork
Clear_b = 0;
#20 Clear_b = 1;
#40 Shift_control = 1;
SI = 0;
// Sequence of 1s
/*
#60 SI = 1;
#70 SI = 0;
#100 SI = 1;
#110 SI = 0;
#140 SI = 1;
#150 SI = 0;
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#180 SI = 1;
#190 SI = 0;
*/
// Sequence of threes
#60 SI = 1;
#80 SI = 0;
#100 SI = 1;
#120 SI = 0;
#140 SI = 1;
#160 SI = 0;
#180 SI = 1;
#200 SI = 0;
join
endmodule
Simulation results: Accumulation of a sequence of four 1s.
Digital
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228
Sequence of four 1s
Accumulation of 1s
Digital
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229
Accumulation of a sequence of 3s:
Accumulation of 3s
Sequence of three 3s
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230
6.55
module Prob_6_55 (output Q8, Q4, Q2, Q1, input Count, Clear_b);
supply1 Pwr;
not (Q8_bar, Q8);
and (J_in_M8, Q2, Q4);
JKFF M1 (Q1, Pwr, Pwr, Count, Clear_b);
JKFF M2 (Q2, Q8_bar, Pwr, Q1, Clear_b);
JKFF M4 (Q4, Pwr, Pwr, Q2_ Clear_b);
JKFF M8 (Q8, J_in_M8, Pwr, Q1_ Clear_b);
endmodule
module JKFF (output reg Q, input J_in, K_in, C, Clear_b);
always @ (negedge C) if (Clear_b== 1'b0) Q <= 1'b0; else
case ({J_in, K_in})
2'b00:
Q <= Q;
2'b01:
Q <= 1'b0;
2'b10:
Q <= 1'b1;
2'b11:
Q <= ~Q;
endcase
endmodule
module t_Prob_6_55 ();
wire Q8, Q4, Q2, Q1;
reg Count , Clear_b;
wire [3:0] value = {Q8, Q4, Q2, Q1};
// Display counter
Prob_6_55 M0 (Q8, Q4, Q2, Q1, Count, Clear_b);
initial #200 $finish;
initial begin Count = 0; forever #5 Count = ~Count ; end
initial fork
Clear_b = 0;
#20 Clear_b = 1;
join
endmodule
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6.56
231
Clear_b
module Prob_6_56 (output A3, A2, A1, A0, Next_stage, input Count_enable, CLK, Clear_b);
assign Next_stage = A3 && A2 && A1 && A0;
and (JK_in_M1, Count_enable, A0);
and (JK_in_M2, JK_in_M1, A1);
and (JK_in_M3, JK_in_M2, A2);
and (Next_stage, JK_in_M3, A3);
JKFF M0 (A0, Count_enable, Count_enable, CLK, Clear_b);
JKFF M1 (A1, JK_in_M1, J_in_M1, CLK, Clear_b);
JKFF M2 (A2, JK_in_M2, JK_in_M2, CLK, Clear_b);
JKFF M3 (A3, JK_in_M3, JK_in_M3, A3, CLK, Clear_b);
endmodule
module JKFF (output reg Q, input J_in, K_in, C, Clear_b);
always @ (posedge C) if (Clear_b == 1'b0) Q <= 0; else
case ({J_in, K_in})
2'b00:
Q <= Q;
2'b01:
Q <= 1'b0;
2'b10:
Q <= 1'b1;
2'b11:
Q <= ~Q;
endcase
endmodule
module t_Prob_6_56 ();
wire A3, A2, A1, A0;
wire Next_stage;
reg Count_enable;
reg CLK, Clear_b
wire [3:0] value = {A3, A2, A1, A0};
Prob_6_56 M0 (A3, A2, A1, A0, Next_stage, Count_enable, CLK, Clear_b);
initial #400 $finish;
initial begin CLK = 0; forever #5 CLK = ~CLK; end
initial fork
Clear_b = 0;
#10 Clear_b = 1;
#100 Clear_b = 0;
// Reset on the fly
#120 Clear_b = 1;
Count_enable = 0;
#20 Count_enable = 1;
#50 Count_enable = 0;
#80 Count_enable = 1;
join
endmodule
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232
233
6.57
module Prob_6_57 (output A3, A2, A1, A0, input Up, Down, CLK, Clear_b);
not (Up_bar, Up);
not (A0_bar, A0);
not (A1_bar, A1);
not (A2_bar, A2);
and (w1, Up_bar, Down);
and (w2, w1, A0_bar);
and (w3, Up, A0);
and (w4, w2, A1_bar);
and (w5, w3, A1);
and (w6, w4, A2_bar);
and (w7, w5, A2);
or (T0, w1, Up);
or (T1, w2, w3);
or (T2, w4, w5);
or (T3, w6, w7);
TFF M0 (A0, A0_bar, T0, CLK, Clear_b);
TFF M1 (A1, A1_bar, T1, CLK, Clear_b);
TFF M2 (A2, A2_bar, T2, CLK, Clear_b);
TFF M3 (A3, A3_bar, T3, CLK, Clear_b);
endmodule
module TFF (output reg Q, output Q_bar, input T, Clear_b, C, Clear_b); // Active low reset is needed
assign Q_bar = ~Q;
always @ (posedge C) if (Clear_b == 1'b0) Q <= 0; else if (T) Q <= ~Q;
endmodule
module t_Prob_6_57 ();
wire A3, A2, A1, A0;
reg Up, Down, CLK, Clear_b;
wire [3:0] value = {A3, A2, A1, A0};
// Display count
Prob_6_57 M0(A3, A2, A1, A0, Up, Down, CLK, Clear_b);
initial #250 $finish;
initial begin CLK = 0; forever #5 CLK = ~CLK; end
initial fork
Clear_b = 1'b0;
#20 Clear_b = 1'b1;
#60 Clear_b = 0; // Reset on the fly
#80 Clear_b = 1;
Up = 1'b0;
Down = 1'b0;
#50 Up = 1'b1;
#80 Down = 1'b1;
#160 Up = 1'b0;
#200 Down = 1'b0;
join
endmodule
// Up has priority
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234
235
6.58
module Problem_6_58 (output A3, A2, A1, A0, C_out, input I3, I2, I1, I0, Count, Load, CLK, Clear_b);
not (Load_bar, Load);
not (I0_bar, I0);
not (I1_bar, I1);
not (I2_bar, I2);
not (I3_bar, I3);
and (w0, Count, Load_bar);
and (w1, Load, I0);
and (w2, Load, I0_bar);
and (w3, Load, I1);
and (w4, Load, I1_bar);
and (w5, Load, I2);
and (w6, Load, I2_bar);
and (w7, Load, I3);
and (w8, Load, I3_bar);
or ( w9, w1, w0);
or ( w10, w2, w0);
or ( w11, w3, w17);
or ( w12, w4, w17);
or ( w13, w5, w18);
or ( w14, w6, w18);
or ( w15, w7, w19);
or ( w16, w8, w19);
and (w17, w0, A0);
and (w18, w0, A0, A1);
and (w19, w0, A0, A1, A2);
and (C_out, w0, A0, A1, A2, A3);
JKFF M0 (A0, w9, w10, CLK, Clear_b);
JKFF M1 (A1, w11, w12, CLK, Clear_b);
JKFF M2 (A2, w13, w14, CLK, Clear_b);
JKFF M3 (A3, w15, w16, CLK, Clear_b);
endmodule
module JKFF (output reg Q, input J_in, K_in, C, Clear_b);
always @ (posedge C) if (Clear_b == 1'b0) Q <= 0; else
case ({J_in, K_in})
2'b00:
Q <= Q;
2'b01:
Q <= 1'b0;
2'b10:
Q <= 1'b1;
2'b11:
Q <= ~Q;
endcase
endmodule
module t_Problem_6_58 ();
wire A3, A2, A1, A0, C_out;
reg I3, I2, I1, I0, Count, Load, CLK, Clear_b;
wire [3:0] value = {A3, A2, A1, A0};
wire [3:0] Par_word = {I3, I2, I1, I0};
Problem_6_58 M0 (A3, A2, A1, A0, C_out, I3, I2, I1, I0, Count, Load, CLK, Clear_b);
initial #400 $finish;
initial begin CLK = 0; forever #5 CLK = ~CLK; end
initial fork
{I3, I2, I1, I0} = 4'b0101; // Data for parallel load
Clear_b = 0;
#20 Clear_b = 1;
Digital
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An
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HDL
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2012,
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Count = 0;
#50 Count = 1;
// Counting
#150 Count = 0; // Pause
#200 Count = 1; // Resume counting
Load = 0;
#250 Load = 1; // Parallel load
#260 Load = 0;
join
endmodule
Digital
Design
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An
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HDL
–
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2012,
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236
237
6.59
module Problem_6_59 (output reg A3, A2, A1, A0, output C_out, input I3, I2, I1, I0, Count, Load, CLK, Clear_b);
always @ (posedge CLK) if (Clear_b == 1'b0) {A3, A2, A1, A0} <= 4'b0; else
if (Load) {A3, A2, A1, A0} <= {I3, I2, I1, I0};
else if (Count) {A3, A2, A1, A0} <= {A3, A2, A1, A0} + 4'b0001;
assign C_out = A3 && A2 && A1 && A0 && Count && (!Load);
endmodule
module t_Problem_6_59 ();
wire A3, A2, A1, A0, C_out;
reg I3, I2, I1, I0, Count, Load, CLK, Clear_b;
wire [3:0] value = {A3, A2, A1, A0};
wire [3:0] Par_word = {I3, I2, I1, I0};
Problem_6_59 M0 (A3, A2, A1, A0, C_out, I3, I2, I1, I0, Count, Load, CLK, Clear_b);
initial #400 $finish;
initial begin CLK = 0; forever #5 CLK = ~CLK; end
initial fork
{I3, I2, I1, I0} = 4'b0101; // Data for parallel load
Clear_b = 0;
#20 Clear_b = 1;
Count = 0;
#50 Count = 1;
// Counting
#150 Count = 0; // Pause
#200 Count = 1; // Resume counting
Load = 0;
#250 Load = 1; // Parallel load
#260 Load = 0;
join
endmodule
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
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rights
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238
239
Chapter 7
7.1
mdc 1/19/07 11:02 AM
(a) 8 K x 32 = 213 x 16
A = 13
D = 16
(b) 2 G x 8 = 231 x 8
A = 31
D=8
(c) 16 M x 32 = 224 x 32
A = 24
D = 32
(d) 256 K x 64 = 218 x 64
A = 18
Comment [1]: Spell
check
D = 64
(e)
7.2
(a) 213
(b) 231
(c) 226
(d) 221
7.3
Address: 56310 = 10_0011_00112
Data word: 1,21210 = 0000_0100_1011_11002
7.4
f CPU = 150 MHz, TCPU = 1/fCPU = 6.67-9 Hz-1
15 ns
6.67 ns
CPU clock
Address
T1
6.67 ns
T2
6.67 ns
T3
Address
valid
Memory select
Data from CPU
Data valid for write
Data from memory
Data valid for read
7.5
Pending
Digital
Design
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HDL
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240
7.6
8 Data input lines
8
4
4
R/W
3
A0
A1
3
4 x 4 RAM
A'2
A2
4 x 4 RAM
A'2
E
E
4
4
4
4
3
3
4 x 4 RAM
A2
4 x 4 RAM
A2
E
4
E
4
8
8 Data output lines
Digital
Design
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HDL
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7.7
241
(a) 16 K = 214 = 27 x 27 = 128 x 128
Each decoder is 7 × 128
Decoders require 256 AND gates, each with 7 inputs
(b) 6,000 = 0101110_1110000
x = 46
y = 112
7.8
(a) 256 K / 32 K = 8 chips
(b) 256 K = 218 (18 address lines for memory); 32 K = 215 (15 address pins / chip)
(c) 18 – 15 = 3 lines ; must decode with 3 × 8 decoder
7.9
13 + 12 = 25 address lines. Memory capacity = 225 words.
7.10
01011011 = 1 2 3 4 5 6 7 8 9 10 11 12 13
P1 P2 0 P4 1 0 1 P8 1 0 1 1 P13
P1 = Xor of bits (3, 5, 7, 9, 11) = 0, 1, 1, 1, 1 = 0
P2 = Xor of bits (3, 6, 7, 10, 11) = 0, 0, 1, 0, 1 = 0
P4 = Xor of bits (5, 6, 7, 12) = 1, 0, 1, 1 = 1
P8= Xor of bits (9, 10, 11, 12) = 1, 0, 1, 1, = 1
(Note: even # of 0s)
(Note: odd # of 0s)
Composite 13-bit code word: 0001 1011 1011 1
7.11
11001001010 = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
P1 P2 1 P4 1 0 0 P8 1 0 0 1 0 1 0
P1 = Xor of bits (3, 5, 7, 9, 11, 13, 15) = 1, 1, 0, 1, 0, 0, 0 = 1
P2 = Xor of bits (3, 6, 7, 10, 11, 14, 15) = 1, 0, 0, 0, 0, 1, 0 = 0
P4 = Xor of bits (5, 6, 7, 12, 13, 14, 15) = 1, 0, 0, 1, 0, 1, 0 = 1
P8= Xor of bits (9, 10, 11, 12, 13, 14, 15) = 1, 0, 0, 1, 0, 1, 0 = 1
(Note: odd # of 0s)
(Note: even # of 0s)
Composite 15-bit code word: 101 110 011 001 010
7.12
(a) 1 2 3 4 5 6 7 8 9 10 11 12
0 0 0 0 1 1 1 0 1 0 1 0
C1 (1, 3, 5, 7, 9, 11) = 0, 0, 1, 1, 1, 1 = 0
C2 (2, 3, 6, 7, 10, 11) = 0, 0, 1, 1, 0, 1 = 1
C4 (4, 5, 6, 7, 12) = 0, 1, 1, 1, 0 = 1
C8 (8, 9, 10, 11, 12) = 0, 1, 0, 1, 0 = 0
C = 0110
Error in bit 6.
Correct data: 0101 1010
(b) 1 2 3 4 5 6 7 8 9 10 11 12
1 0 1 1 1 0 0 0 0 1 1 0
C1 (1, 3, 5, 7, 9, 11) = 1, 1, 1, 0, 0, 1 = 0
C2 (2, 3, 6, 7, 10, 11) = 0, 1, 0, 0, 1, 1 = 1
C4 (4, 5, 6, 7, 12) = 1, 1, 0, 0, 0 = 0
C8 (8, 9, 10, 11, 12) = 0, 0, 1, 1, 0 = 0
C = 0010
Digital
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An
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HDL
–
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rights
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242
Error in bit 2 = Parity bit P2.
Correct 8-bit data:
3 5 6 7 9 10 11 12
1 1 0 0 0 1 1 0
(c) 1 2 3 4 5 6 7 8 9 10 11 12
1 0 1 1 1 1 1 1 0 1 0 0
C = 0000 )No errors)
C1 (1, 3, 5, 7, 9, 11) = 1, 1, 1, 0, 0, 1 = 0
C2 (2, 3, 6, 7, 10, 11) = 0, 1, 0, 0, 1, 1 = 1
C4 (4, 5, 6, 7, 12) = 1, 1, 0, 0, 0 = 0
C8 (8, 9, 10, 11, 12) = 0, 0, 1, 1, 0 = 0
Correct 8-bit data:
7.13
7.14
3 5 6 7 9 10 11 12
1 1 1 1 0 1 0 0
(a) 16-bit data (From Table 7.2):
5 Check bits
1 bit
---------------6 parity bits
(b) 32-bit data (From Table 7.2):
6 Check bits
1 bit
---------------7 parity bits
(6) 16-bit data (From Table 7.2):
5 Check bits
1 bit
---------------6 parity bits
(a) 1 2 3 4 5 6 7
P1 P2 0 P4 0 1 0
P1 = Xor (3, 5, 7) = 0, 0, 0 = 1
P2 = Xor (3, 6, 7) = 0, 1, 0 = 0
P4 = Xor (5, 6, 7) = 0, 1, 0 = 1
7-bit word: 0101010
(b) No error:
C1 = Xor (1, 3, 5, 7) = 0, 0, 0, 0 = 0
C2 = Xor (2, 3, 6, 7) = 1, 0, 1, 0 = 0
C4 = Xor (4, 5, 6, 7) = 1, 0, 1, 0 = 0
(c) Error in bit 5:
1 2 3 4 5 6 7
0 1 0 1 1 1 0
C1 = Xor (0, 0, 1, 0) = 1
C2 = Xor (1, 0, 1, 0) = 0
C4 = Xor (1, 1, 1, 0) = 1
Error in bit 5: C = 101
Digital
Design
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HDL
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243
(d) 8-bit word
1 2 3 4 5 6 7 8
0 1 0 1 0 1 0 1
Error in bits 2 and 5: 0 0 0 1 1 1 0 1
C1 = Xor (0, 0, 1, 0) = 1
C2 = Xor (0, 0, 1, 0) = 1
C4 = Xor (1, 1, 1, 0) = 1
P=0
C =(1, 1, 1) ≠ 0 and P = 0 indicates double error.
7.15
6
Address
(9 bits)
6
6
6
6
64 x 8 ROM
64 x 8 ROM
64 x 8 ROM
64 x 8 ROM
3 x8
Decoder
En
Note: Outputs must be wired-OR or three-state outputs.
Data
(8 bits)
En
8
En
8
En
64 x 8 ROM
En
8
En
8
En
64 x 8 ROM
8
8
En
64 x 8 ROM
64 x 8 ROM
8
Note: Outputs must be wired-OR or three-state outputs.
7.16
Note: 4096 = 212
Pwr
Gnd
Inputs
12
4096 x 8
ROM
8
Outputs
CS
7.18
(a) 256 × 8
6
16 inputs + 8 outputs requires a 24-pin IC.
(b) 512 × 5 (c) 1024 × 4 (d) 32 × 7
7.17
Digital
Design
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HDL
–
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8
244
Input Address
7.18
Output of ROM
I5 I4 I3 I 2 I 1
D6D5D4
D3D2D1
00000
00001
…
…
01000
01001
…
…
11110
11111
000
000
…
…
001
001
…
…
110
110
000
001
…
…
011
100
…
…
000
001
(a) 8 inputs
8 outputs
28 x 8
256 x 8 ROM
(b) 9 inputs
5 outputs
29 x 5
512 x 5 ROM
(c) 10 inputs 4 outputs
210 x 4 1024 x 4 ROM
(d) 5 inputs
25 x 7
7 outputs
D0 (20) Decimal
0, 1
0, 1
…
…
0, 1
0, 1
…
…
0, 1
0, 1
0, 1
2, 3
…
…
16, 17
18, 19
…
…
60, 61
62, 63
32 x 7 ROM
Digital
Design
With
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HDL
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245
7.19
x
y
yz
00
m0
0
m4
x
01
1
11
m1
0
1
00
0
m6
0
01
m0
0
m7
y
yz
m2
1
m5
0
10
m3
1
x
x
1
0
m0
0
0
m4
x
1
m1
0
11
m3
0
m5
x
10
0
0
m6
0
Product Inputs
term x y z
1
2
3
4
5
6
7
8
9
10
11
00
-01
0-1
110
1100011
101
101–1
-01
010
01
m0
m1
0
0
x
1
11
m3
1
m4
z
C = x'yz + xy'z
C' = z' + x'y' + xy
y'z
x'z
xyz'
xy
x'y'
x'yz
xy'z
xy'
Xz
y'z
x'yz'
1
y
yz
m2
1
m7
1
1
B = xy + x'y'
B' = xy' + x'y
y
01
m6
z
yz
00
0
m7
z
A = y'z + x'z + xyz'
A' =y'z' + x'z' + xyz
x
m2
0
m5
0
10
m3
1
m4
1
11
m1
1
m5
1
0
m7
1
10
m2
1
m6
1
0
z
D = xy' + xz + y'z + x'yz'
D' = x'y'z' + x'yz + xyz'
Outputs
A B C D
1
1
1
-
1
1
-
1
1
-
1
1
1
1
1
7.20
Inputs
xyz
000
001
010
011
100
101
110
111
Outputs
A, B, C, D
1101
0111
0000
1001
1100
0011
1000
0101
M[001] = 0111
M[100] = 1100
Digital
Design
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HDL
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246
7.21 Note: See truth table in Fig. 7.12(b).
A2
00
0
A2
A1
A1A0
1
m0
m4
01
m1
0
m5
0
11
m3
0
m7
0
A2
10
m2
0
m6
1
0
00
0
1
A2
A1
A1A0
1
m0
m4
0
01
m1
m5
1
0
1
A0
0
A2
1
m0
m4
01
m1
0
m5
0
11
m3
0
m7
1
m6
1
0
0
F2 = A2A'1 + A2A0
F2' = A'2 + A1A'0
A1
A1A0
00
m7
10
m2
0
A0
F1 = A2A1
F'1 = A'2 + A'1
A2
11
m3
A2
10
m2
1
m6
0
0
00
0
0
A2
A1
A1A0
1
m0
m4
A0
0
0
01
m1
m5
0
0
11
m3
m7
0
0
10
m2
m6
1
1
A0
F3 = A'2A1A0 + A2A'1A0
F3' = A'0 + A'2A'1 +A2A1
F4 = A1A'0
F'4 = A'1 + A0
Product Inputs
Outputs
term A2A1A0 F1 F2 F3 F4
A2A1
A'2
A1A'0
A'2A1A0
A2A'1
1
2
3
4
5
1
0
1
1
1
1
0
0
1
1
1
T
1
1
C
1
1
T
1
T
Alternative: F'1, F'2, F3, F4
(5 terms)
7.22
Decimal
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
w x y z
b7 b6 b5 b4 b3 b2 b1 b0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
Note: b0 = z, and b1 = 0.
ROM would have 4 inputs
and 6 outputs. A 4 x 8
ROM would waste two
outputs.
Digital
Design
With
An
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Verilog
HDL
–
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2012,
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rights
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247
wx
00
00
01
11
w
10
wx
01
m3
m2
m4
m5
m7
m6
m12
m13
m15
m14
m8
m9
m11
m10
11
w
10
yz
m0
m4
1
01
11
w
10
m5
1
m3
m7
w
10
1
m9
m11
m10
x
11
w
10
z
b4 = w'xz + xy'z' + wx' z
y
m0
01
m1
11
m3
m2
m4
m5
m7
m12
m13
m15
m14
m8
m9
m11
m10
1
1
wx
10
1
1
z
b6 = wy + wx'
1
m5
m12
m8
x
11
w
10
11
m3
1
10
m2
m7
m6
m13
m15
m14
m9
m11
m10
1
1
1
x
z
b3 = xy'z + x' yz
y
01
11
10
m0
m1
m3
m4
m5
m7
m12
m13
m15
m14
m8
m9
m11
m10
1
1
1
1
m2
m6
1
x
1
z
b5 = w'xy + wxz + wx'y
y
00
01
1
m1
m4
yz
00
m6
m0
00
01
m8
01
yz
00
m6
m14
1
wx
m2
m15
1
11
10
m13
1
x
y
11
00
01
1
y
yz
00
1
m12
00
00
m1
1
1
z
b2 = yx'
01
wx
10
m1
00
01
11
m0
yz
00
wx
y
yz
m0
m4
01
m1
m5
11
m3
m7
10
m2
m6
m12
m13
m15
m14
m8
m9
m11
m10
1
1
1
x
1
z
b7 = wx
Digital
Design
With
An
Introduction
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Verilog
HDL
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rights
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248
7.23
Product Inputs
term A B C D
From Fig. 4-3:
w = A + BC + BD
w' = A'B' + A'C'D'
x = B'C + B'D + BC'D'
x' = B'C'D' + BC BD
y = CD + C'D'
y' = C'D + CD'
z = D'
z' = D
Use w, x', y, z (7 terms)
A
BC
BD
B'C'D'
CD
C'D'
D'
1
2
3
4
5
6
7
1
-
1
1
0
-
1
0
1
0
-
Outputs
F1 F2 F3 F4
1
0
1
0
0
1
1
1
-
1
1
1
-
1
1
-
1
T C T T
7.24
AND
Product Inputs
term A B C D
1
2
3
4
5
6
7
8
9
10
11
12
1
-
1
1
0
0
1
-
1
1
0
1
0
-
1
1
0
1
0
0
-
Outputs
w = A + BC + BD
x = B'C + B'D + BC'D'
y = CD + C'D'
z = D'
Digital
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249
7.25
x
y
yz
00
01
m0
0
m1
0
1
x
x
1
m7
0
m6
1
0
z
01
11
m1
0
m3
1
m4
1
m7
0
1
0
0
m4
1
x
1
m1
m3
1
m5
0
11
1
m7
1
10
m2
1
m6
1
0
z
D = z + x'y
Outputs
A = yz' + xz' + x'y'z
B = y'z' + x'y' + yz
C = A + xyz
1
-
m0
01
0
0
1
0
1
1
1
-
00
m2
z
C = A + xyz
1
0
0
0
1
1
1
-
y
yz
m6
1
AND
Product Inputs
term x y z A
x
10
0
m5
1
0
0
0
0
1
0
0
0
-
0
B = y'z' + x'y' + yz
y
1
2
3
4
5
6
7
8
9
10
11
12
m2
1
m5
1
10
m3
1
z
00
1
11
m1
1
m4
1
01
A = yz' + xz' + x'y'z
m0
x
0
m6
0
yz
0
00
m0
1
m7
0
y
yz
m2
0
m5
1
x
10
m3
1
m4
x
11
D = z + x'y
A = yzʹ′ + xzʹ′ + xʹ′yʹ′z
B = y'z' + x'y' + yz
C = A + xyz
D = z + xʹ′y
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250
x
x'
y
y'
z
z'
A
B
C
D
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251
7.26
x
x'
y
A
y'
A' CLK OE = 1
D
SET
CLR
A
Q
Q
x
y
7.27
The results of Prob. 6.17 can be used to develop the equations for a three-bit binary counter with D-type
flip-flops.
DA0 = A'0
DA1 = A'1A0 + A1A'0
DA2 = A'2 A1A0 + A2A'1 + A2A'0
Cout = A2A1A0
Cout
0
1
2
3
4
5
6
7
8
9
A0
A1
A2
10 11 12 13 14 15
D
SET
CLR
Q
A0
Q
clock
D
SET
CLR
Q
A1
Q
clock
D
SET
CLR
clock
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Q
Q
A2
252
7.28
A
B
C
A'B
AC
A'BC'
AC
AB
BC
F'2
F1
7.29
Product
term
x'y'A
1
x'yA'
2
xy'A'
3
xyA
4
Inputs
xyA
001
010
100
111
Output
DA
1
1
1
1
Digital
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253
CHAPTER 8
8.1
8.2
(a) The transfer and increment occur concurrently, i.e., at the same clock edge. After the transfer, R2
holds the contents that were in R1 before the clock edge, and R2 holds its previous value incremented
by 1.
(b) Decrement the content of R3 by one.
(c) If (S1 = 1), transfer content of R1 to R0. If (S1 = 0 and S2 = 1), transfer content of R2 to R0.
S1
clr_R
reset_b
x
y
x
y
0
...
incr_R
R
1
clr_R
reset_b
clock
1
y
R <= 0
1
Controller
Datapath
R <= R + 1
incr_R
S3
S2
8.3
reset_b
reset_b
S1
S1
x
S1
1
x
1
1
add_by_2
reset_b
S2
x
S3
y
S2
1
S2
R <= R + 2
S3
(a)
(c)
(b)
8.4
1
1
z
011
010
y
1
0
z
x
1
y
1
z
z
1
1
111
110
001
110
000
100
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254
8.5
The operations specified in a flowchart are executed sequentially, one at a time. The operations specified
in an ASM chart are executed concurrently for each ASM block. Thus, the operations listed within a state
box, the operations specified by a conditional box, and the transfer to the next state in each ASM block
are executed at the same clock edge. For example, in Fig. 8.5 with Start = 1 and Flag = 1, signal Flush_R
is asserted. At the clock edge the state moves to S_2, and register R is flushed.
An ASM chart describes the state transitions and output signals generated by a finite state machine in
response to its input signals. An ASMD chart is an ASM chart that has been annotated to indicate the
register operations that are executed by the machine in response to the control signals (outpus) generated
by the state machine.
8.6
Note: In practice, the asynchronous inputs x
and y should be synchronized to the clock to
avoid metastable conditons in the flip-flops..
count <= 0
reset_b
count <= count - 1
decr
count <= count + 1
S_idle
incr
11
01
10
{y, x}
00
S_out
01
S_in
00
{y, x}
11
10
00
01
S_in_out
00
10
decr
{y, x}
decr
incr
incr
S_in
11
incr
01
11
10
{y, x}
x
y
Controller
decr
Datapath
count
...
reset_b
clock
S_out
S_idle
Note: To avoid counting a person more than
once, the machine waits until x or y is deasserted before incrementing or
decrementing the counter. The machine also
accounts for persons entering and leaving
simultaneously.
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255
8.7
RTL notation:
S0: Initial state: if (start = 1) then (RA ← data_A, RB ← data_B, go to S1).
S1: {Carry, RA} ← RA + (2’s complement of RB), go to S2.
S2: If (borrow = 0) go to S0. If (borrow = 1) then RA ← (2’s complement of RA), go to S0.
Block diagram and ASMD chart:
reset_b
data_A data_B
borrow
8
Load_A_B
start
done
Controller
Subtract
Convert
carry
reset_b
clock
S0
done
8
Datapath
Reg_A
...
Reg_B
...
result
...
8
result
start
1
Reg_A <= data_A
Reg_B <= data_B
Load_A_B
S1
Subtract
Reg_A <= Reg_A + ~ Reg_B + 1
S2
borrow
Reg_A <= ~Reg_A + 1
1
Convert
module Subtractor_P8_7
(output done, output [7:0] result, input [7: 0] data_A, data_B, input start, clock, reset_b);
Controller_P8_7 M0 (Load_A_B, Subtract, Convert, done, start, borrow, clock, reset_b);
Datapath_P8_7 M1 (result, borrow, data_A, data_B, Load_A_B, Subtract, Convert, clock, reset_b);
endmodule
module Controller_P8_7 (output reg Load_A_B, Subtract, output reg Convert, output done,
input start, borrow, clock, reset_b);
parameter S0 = 2'b00, S1 = 2'b01, S2 = 2'b10;
reg [1: 0] state, next_state;
assign done = (state == S0);
always @ (posedge clock, negedge reset_b)
if (!reset_b) state <= S0; else state <= next_state;
always @ (state, start, borrow) begin
Load_A_B = 0;
Subtract = 0;
Convert = 0;
case (state)
S0:
if (start) begin Load_A_B = 1; next_state = S1; end
S1:
begin Subtract = 1; next_state = S2; end
S2:
begin next_state = S0; if (borrow) Convert = 1; end
default: next_state = S0;
endcase
end
endmodule
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256
module Datapath_P8_7 (output [7: 0] result, output borrow, input [7: 0] data_A, data_B,
input Load_A_B, Subtract, Convert, clock, reset_b);
reg
carry;
reg [8:0] diff;
reg [7: 0] RA, RB;
assign
borrow = carry;
assign result = RA;
always @ (posedge clock, negedge reset_b)
if (!reset_b) begin carry <= 1'b0; RA <= 8'b0000_0000; RB <= 8'b0000_0000; end
else begin
if (Load_A_B) begin RA <= data_A; RB <= data_B; end
else if (Subtract) {carry, RA} <= RA + ~RB + 1;
// In the statement above, the math of the LHS is done to the wordlength of the LHS
// The statement below is more explicit about how the math for subtraction is done:
// else if (Subtract) {carry, RA} <= {1'b0, RA} + {1'b1, ~RB } + 9'b0000_0001;
// If the 9-th bit is not considered, the 2s complement operation will generate a carry bit,
// and borrow must be formed as borrow = ~carry.
else if (Convert) RA <= ~RA + 8'b0000_0001;
end
endmodule
// Test plan – Verify;
// Power-up reset
// Subtraction with data_A > data_B
// Subtraction with data_A < data_B
// Subtraction with data_A = data_B
// Reset on-the-fly: left as an exercise
module t_Subtractor_P8_7;
wire
done;
wire [7:0] result;
reg [7: 0] data_A, data_B;
reg
start, clock, reset_b;
Subtractor_P8_7 M0 (done, result, data_A, data_B, start, clock, reset_b);
initial #200 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial fork
reset_b = 0;
#2 reset_b = 1;
#90 reset_b = 1;
#92 reset_b = 1;
join
initial fork
#20 start = 1;
#30 start = 0;
#70 start = 1;
#110 start = 1;
join
initial fork
data_A = 8'd50;
data_B = 8'd20;
#50 data_A = 8'd20;
#50 data_B = 8'd50;
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257
#100 data_A = 8'd50;
#100 data_B = 8'd50;
join
endmodule
Name
0
40
80
120
clock
reset_b
state[1:0]
0
x
0
1
2
0
1
2
0
1
14
e2
1e
50
32
2
0
1
2
start
Load_A_B
Subtract
carry
borrow
Convert
data_A[7:0]
RA[7:0]
data_B[7:0]
RB[7:0]
done
borrow
result[7:0]
50
00
20
32
1e
20
00
0
14
50
50
00
32
0
50
32
30
20
226
30
50
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8.8
258
RTL notation:
S0: if (start = 1) AR ← input data, BR ← input data, go to S1.
S1: if (AR [15]) = 1 (sign bit negative) then CR ← AR(shifted right, sign extension).
else if (positive non-zero) then (Overflow ← BR([15] ⊕ [14]), CR ← BR(shifted left)
else if (AR = 0) then (CR ← 0).
data_AR data_BR
AR_eq_0
AR_gt_0
16
AR_lt_0
16
Datapath
Ld_AR_BR
Controller
Div_AR_x2_CR
start
Mul_BR_x2_CR
done
Clr_CR
AR
...
...
...
BR
CR
reset_b
clock
reset_b
S0
done
AR <= data_A
BR<= data_B
start
1
Ld_AR_BR
S1
CR <= {AR[15], AR[15:1]}
1
AR < 0
Div_AR_x2_CR
CR <= BR << 1
AR > 0
1
Mul_BR_x2_CR
Note: Division by 2 of a
negative number
represented in 16-bit 2s
complement format
Note: Multiplication by
2 of a positive number
represented in 16-bit 2s
complement format
CR <= 0
Clr_CR
module Prob_8_8 (output done, input [15: 0] data_AR, data_BR, input start, clock, reset_b);
Controller_P8_8 M0 (
Ld_AR_BR, Div_AR_x2_CR, Mul_BR_x2_CR, Clr_CR, done,
start, AR_lt_0, AR_gt_0, AR_eq_0, clock, reset_b
);
Datapath_P8_8 M1 (
Overflow, AR_lt_0, AR_gt_0, AR_eq_0, data_AR, data_BR,
Ld_AR_BR, Div_AR_x2_CR, Mul_BR_x2_CR, Clr_CR, clock, reset_b
);
endmodule
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259
module Controller_P8_8 (
output reg Ld_AR_BR, Div_AR_x2_CR, Mul_BR_x2_CR, Clr_CR,
output done, input start, AR_lt_0, AR_gt_0, AR_eq_0, clock, reset_b
);
parameter S0 = 1'b0, S1 = 1'b1;
reg state, next_state;
assign done = (state == S0);
always @ (posedge clock, negedge reset_b)
if (!reset_b) state <= S0; else state <= next_state;
always @ (state, start, AR_lt_0, AR_gt_0, AR_eq_0) begin
Ld_AR_BR = 0;
Div_AR_x2_CR = 0;
Mul_BR_x2_CR = 0;
Clr_CR = 0;
case (state)
S0:
if (start) begin Ld_AR_BR = 1; next_state = S1; end
S1:
begin
next_state = S0;
if (AR_lt_0) Div_AR_x2_CR = 1;
else if (AR_gt_0) Mul_BR_x2_CR = 1;
else if (AR_eq_0) Clr_CR = 1;
end
default: next_state = S0;
endcase
end
endmodule
module Datapath_P8_8 (
output reg Overflow, output AR_lt_0, AR_gt_0, AR_eq_0, input [15: 0] data_AR, data_BR,
input Ld_AR_BR, Div_AR_x2_CR, Mul_BR_x2_CR, Clr_CR, clock, reset_b
);
reg [15: 0] AR, BR, CR;
assign
AR_lt_0 = AR[15];
assign
AR_gt_0 = (!AR[15]) && (| AR[14:0]);
// Reduction-OR
assign
AR_eq_0 = (AR == 16'b0);
always @ (posedge clock, negedge reset_b)
if (!reset_b) begin AR <= 8'b0; BR <= 8'b0; CR <= 16'b0; end
else begin
if (Ld_AR_BR) begin AR <= data_AR; BR <= data_BR; end
else if (Div_AR_x2_CR) CR <= {AR[15], AR[15:1]}; // For compiler without arithmetic right shift
else if (Mul_BR_x2_CR) {Overflow, CR} <= (BR << 1);
else if (Clr_CR) CR <= 16'b0;
end
endmodule
// Test plan – Verify;
// Power-up reset
// If AR < 0 divide AR by 2 and transfer to CR
// If AR > 0 multiply AR by 2 and transfer to CR
// If AR = 0 clear CR
// Reset on-the-fly
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260
module t_Prob_P8_8;
wire
done;
reg [15: 0] data_AR, data_BR;
reg
start, clock, reset_b;
reg [15: 0] AR_mag, BR_mag, CR_mag;
// To illustrate 2s complement math
// Probes for displaying magnitude of numbers
always @ (M0.M1.AR)
// Hierarchical dereferencing
if (M0.M1.AR[15]) AR_mag = ~M0.M1.AR+ 16'd1; else AR_mag = M0.M1.AR;
always @ (M0.M1.BR )
if (M0.M1.BR[15]) BR_mag = ~M0.M1.BR+ 16'd1; else BR_mag = M0.M1.BR;
always @ (M0.M1.CR)
if (M0.M1.CR[15]) CR_mag = ~M0.M1.CR + 16'd1; else CR_mag = M0.M1.CR;
Prob_8_8 M0 (done, data_AR, data_BR, start, clock, reset_b);
initial #250 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial fork
reset_b = 0;
// Power-up reset
#2 reset_b = 1;
#50 reset_b = 0; // Reset on-the-fly
#52 reset_b = 1;
#90 reset_b = 1;
#92 reset_b = 1;
join
initial fork
#20 start = 1;
#30 start = 0;
#70 start = 1;
#110 start = 1;
join
initial fork
data_AR = 16'd50;
data_BR = 16'd20;
// AR > 0
// Result should be 40
#50 data_AR = 16'd20;
#50 data_BR = 16'd50; // Result should be 100
#100 data_AR = 16'd50;
#100 data_BR = 16'd50;
#130 data_AR = 16'd0; // AR = 0, result should clear CR
#160 data_AR = -16'd20; // AR < 0, Verilog stores 16-bit 2s complement
#160 data_BR = 16'd50; // Result should have magnitude10
#190 data_AR = 16'd20; // AR < 0, Verilog stores 16-bit 2s complement
#190 data_BR = 16'hffff; // Result should have overflow
join
endmodule
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261
Reset on-the-fly
Name
0
60
120
180
240
reset_b
clock
start
Divide by 2 and xfer to CR
Multiply by 2 and xfer to CR
AR_lt_0
AR_gt_0
AR_eq_0
state
Ld_AR_BR
Div_AR_x2_CR
Mul_BR_x2_CR
Clr_CR
done
data_AR[15:0]
AR[15:0]
AR[15:0]
AR_mag[15:0]
50
BR[15:0]
BR_mag[15:0]
CR[15:0]
CR[15:0]
CR_mag[15:0]
50
0
65516
20
50
0
20
50
0
65516
20
0000
0032
0000
0014
0032
0000
ffec
0014
0
50
0
20
50
0
0
20
0
50
0000
0014
0000
0032
0
20
0
50
data_BR[15:0]
BR[15:0]
20
0
20
0
50
40
0000
0
20
40
65535
65535
ffff
1
0
100
0
65526
65534
0000
0064
0
100
0000
fff6
fffe
0
10
2
Overflow
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262
8.9
Design equations:
DS_idle = S_2 + S_idle Start'
DS_1 = S_idle Start + S_1 (A2 A3)'
DS_2 = A2 A3 S_1
HDL description:
module Prob_8_9 (output E, F, output [3: 0] A, output A2, A3, input Start, clock, reset_b);
Controller_Prob_8_9 M0 (set_E, clr_E, set_F, clr_A_F, incr_A, Start, A2, A3, clock, reset_b);
Datapath_Prob_8_9 M1 (E, F, A, A2, A3, set_E, clr_E, set_F, clr_A_F, incr_A, clock, reset_b);
endmodule
// Structural version of the controller (one-hot)
// Note that the flip-flop for S_idle must have a set input and reset_b is wire to the set
// Simulation results match Fig. 8-13
module Controller_Prob_8_9 (
output set_E, clr_E, set_F, clr_A_F, incr_A,
input
Start, A2, A3, clock, reset_b
);
wire
D_S_idle, D_S_1, D_S_2;
wire
q_S_idle, q_S_1, q_S_2;
wire
w0, w1, w2, w3;
wire [2:0]
state = {q_S_2, q_S_1, q_S_idle};
// Next-State Logic
or (D_S_idle, q_S_2, w0);
and (w0, q_S_idle, Start_b);
not (Start_b, Start);
or (D_S_1, w1, w2, w3);
and (w1, q_S_idle, Start);
and (w2, q_S_1, A2_b);
not (A2_b, A2);
and (w3, q_S_1, A2, A3_b);
not (A3_b, A3);
and (D_S_2, A2, A3, q_S_1);
// input to D-type flip-flop for q_S_idle
// input to D-type flip-flop for q_S_1
// input to D-type flip-flop for q_S_2
D_flop_S M0 (q_S_idle, D_S_idle, clock, reset_b);
D_flop M1 (q_S_1, D_S_1, clock, reset_b);
D_flop M2 (q_S_2, D_S_2, clock, reset_b);
// Output Logic
and (set_E, q_S_1, A2);
and (clr_E, q_S_1, A2_b);
buf (set_F, q_S_2);
and (clr_A_F, q_S_idle, Start);
buf (incr_A, q_S_1);
endmodule
module D_flop (output reg q, input data, clock, reset_b);
always @ (posedge clock, negedge reset_b)
if (!reset_b) q <= 1'b0; else q <= data;
endmodule
module D_flop_S (output reg q, input data, clock, set_b);
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always @ (posedge clock, negedge set_b)
if (!set_b) q <= 1'b1; else q <= data;
endmodule
/*
// RTL Version of the controller
// Simulation results match Fig. 8-13
module Controller_Prob_8_9 (
output reg set_E, clr_E, set_F, clr_A_F, incr_A,
input
Start, A2, A3, clock, reset_b
);
parameter S_idle = 3'b001, S_1 = 3'b010, S_2 = 3'b100;
reg [2: 0] state, next_state;
// One-hot
always @ (posedge clock, negedge reset_b)
if (!reset_b) state <= S_idle; else state <= next_state;
always @ (state, Start, A2, A3) begin
set_E = 1'b0;
clr_E = 1'b0;
set_F = 1'b0;
clr_A_F
= 1'b0;
incr_A = 1'b0;
case (state)
S_idle:
if (Start) begin next_state = S_1; clr_A_F = 1; end
else next_state = S_idle;
S_1:
begin
incr_A = 1;
if (!A2) begin next_state = S_1; clr_E = 1; end
else begin
set_E = 1;
if (A3) next_state = S_2; else next_state = S_1;
end
end
S_2: begin next_state = S_idle; set_F = 1; end
default: next_state = S_idle;
endcase
end
endmodule
*/
module Datapath_Prob_8_9 (
output reg E, F, output reg [3: 0] A, output A2, A3,
input set_E, clr_E, set_F, clr_A_F, incr_A, clock, reset_b
);
assign A2 = A[2];
assign A3 = A[3];
always @ (posedge clock, negedge reset_b) begin
if (!reset_b) begin E <= 0; F <= 0; A <= 0; end
else begin
if (set_E) E <= 1;
if (clr_E) E <= 0;
if (set_F) F <= 1;
if (clr_A_F) begin A <= 0; F <= 0; end
if (incr_A) A <= A + 1;
end
end
endmodule
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// Test Plan - Verify: (1) Power-up reset, (2) match ASMD chart in Fig. 8-9 (d),
// (3) recover from reset on-the-fly
module t_Prob_8_9;
wire E, F;
wire [3: 0] A;
wire A2, A3;
reg Start, clock, reset_b;
Prob_8_9 M0 (E, F, A, A2, A3, Start, clock, reset_b);
initial #500 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial begin reset_b = 0; #2 reset_b = 1; end
initial fork
#20 Start = 1;
#40 reset_b = 0;
#62 reset_b = 1;
join
endmodule
8.10
reset_b
s0
x
1
s1
1
y
0
s3
0
s2
x
1
y
0
x
1
0
1
y
1
module Prob_8_10 (input x, y, clock, reset_b);
reg [ 1: 0]
state, next_state;
parameter s0 = 2'b00, s1 = 2'b01, s2 = 2'b10, s3 = 2'b11;
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) state <= s0; else state <= next_state;
always @ (state, x, y) begin
next_state = s0;
case (state)
s0: if (x == 0) next_state = s0; else next_state = s1;
s1: if (y == 0) next_state = s2; else next_state = s3;
s2: if (x == 0) next_state = s0; else if (y == 0) next_state = s2; else next_state = s3;
s3: if (x == 0) next_state = s0; else if (y == 0) next_state = s2; else next_state = s3;
endcase
end
endmodule
module t_Prob_8_10 ();
reg x, y, clock, reset_b;
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Prob_8_10 M0 (x, y, clock, reset_b);
initial #150 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial fork
reset_b = 0;
#12 reset_b = 1;
x = 0; y = 0;
// Remain in s0
#10 y = 1;
// Remain in s0
#20 x = 1;
// Go to s1 to s3
#40 reset_b = 0; // Go to s0
#42 reset_b = 1; // Go to s2 to s3
#60 y = 0;
// Go to s2
#80 y = 1;
// Go to s3
#90 x = 0;
// Go to s0
#100 x = 1;
// Go to s1
#110 y = 0;
// Go to s2
#130 x = 0;
// Go to s0
join
endmodule
Name
0
50
100
150
clock
reset_b
x
y
state[1:0]
0
1
3 0
1
3
2
3
0
1
2
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0
8.11
266
DA = Aʹ′B + Ax
DB = Aʹ′Bʹ′x + Aʹ′By + xy
state inputs
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
next
state
0
0
0
0
AB
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
xy
x
00
00
01
11
A
10
m0
m4
1
01
m1
m5
1
11
10
m3
m7
m2
m6
1
1
m12
m13
m15
m14
m8
m9
m11
m10
1
B
1
1
1
y
DA = A'B + Ax
AB
xy
x
00
00
01
11
A
10
01
11
10
m0
m1
m3
m4
m5
m7
m12
m13
m15
m14
m8
m9
m11
m10
1
1
1
1
1
m2
1
m6
B
y
DB = A'B' x + A'By + xy
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8.12
267
For the 4-bit synchronous counter, modify the counter in Fig. 6.12 to add a signal, Clear, to clear the
counter synchronously, as shown in the circuit diagram below.
Count enable
Clear
J
Q
K
QB
J
Q
K
QB
J
Q
K
QB
J
Q
K
QB
A0
A1
A2
A3
To next stage
CLK
module Counter_4bit_Synch_Clr (output [3: 0] A, output next_stage, input Count_enable, Clear, CLK);
wire A0, A1, A2, A3;
assign A[3: 0] = {A3, A2, A1, A0};
JK_FF M0 (A0, J0, K0, CLK);
JK_FF M1 (A1, J1, K1, CLK);
JK_FF M2 (A2, J2, K2, CLK);
JK_FF M3 (A3, J3, K3, CLK);
not (Clear_b, Clear);
and (J0, Count_enable, Clear_b);
and (J1, J0, A0);
and (J2, J1, A1);
and (J3, J2, A2);
or (K0, Clear, J0);
or (K1, Clear, J1);
or (K2, Clear, J2);
or (K3, Clear, J3);
and (next_stage, A3, J3);
endmodule
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module JK_FF (output reg Q, input J, K, clock);
always @ (posedge clock)
case ({J,K})
2'b00: Q <= Q;
2'b01: Q <= 0;
2'b10: Q <= 1;
2'b11: Q <= ~Q;
endcase
endmodule
module t_Counter_4bit_Synch_Clr ();
wire [3: 0] A;
wire next_stage;
reg Count_enable, Clear, clock;
Counter_4bit_Synch_Clr M0 (A, next_stage, Count_enable, Clear, clock);
initial #300 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial fork
Clear = 1;
Count_enable = 0;
#12 Clear = 0;
#20 Count_enable = 1;
#180 Clear = 1;
#190 Clear = 0;
#230 Count_enable = 0;
join
endmodule
Simulation
results:
synchronous
clear.
Name
0
50
100
150
200
250
clock
Clear
Count_enable
J0
K0
A0
J1
K1
A1
J2
K2
A2
J3
K3
A3
A[3:0]
x
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0
1
2
3
next_stage
(b)
module Counter_4bit_Asynch_Clr_b (
output [3: 0] A, output next_stage, input Count_enable, Clk, Clear_b
);
wire A0, A1, A2, A3;
assign A[3: 0] = {A3, A2, A1, A0};
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269
wire J0, K0, J1, K1, J2, K2, J3, K3;
assign K0 = J0;
assign K1 = J1;
assign K2 = J2;
assign K3 = J3;
JK_FF M0 (A0, J0, K0, Clk, Clear_b);
JK_FF M1 (A1, J1, K1, Clk, Clear_b);
JK_FF M2 (A2, J2, K2, Clk, Clear_b);
JK_FF M3 (A3, J3, K3, Clk, Clear_b);
and (J0, Count_enable);
and (J1, J0, A0);
and (J2, J1, A1);
and (J3, J2, A2);
and (next_stage, A3, J3);
endmodule
module JK_FF (output reg Q, input J, K, clock, Clear_b);
always @ (posedge clock, negedge Clear_b)
if (Clear_b == 1'b0) Q <= 0;
else
case ({J,K})
2'b00: Q <= Q;
2'b01: Q <= 0;
2'b10: Q <= 1;
2'b11: Q <= ~Q;
endcase
endmodule
module t_Counter_4bit_Asynch_Clr_b ();
wire [3: 0] A;
wire next_stage;
reg Count_enable, Clk, Clear_b;
Counter_4bit_Asynch_Clr_b M0 (A, next_stage, Count_enable, Clk, Clear_b);
initial #200 $finish;
initial begin Clk = 0; forever #5 Clk = ~Clk; end
initial fork
Count_enable = 0;
Clear_b = 0;
#30 Count_enable = 1;
#50 Clear_b = 1;
#90 Count_enable = 0;
#110 Count_enable= 1;
#150 Clear_b = 0;
#170 Clear_b = 1;
join
endmodule
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Count_enable
J
Q
A0
Q
A1
Q
A2
Q
A3
Clk
K
CLR
Clear_b
J
K
CLR
J
K
CLR
J
K
CLR
next_stage
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8.13
// Structural description of design example (Fig. 8-10, 8-12)
module Design_Example_STR
( output [3:0]
output
input
);
A,
E, F,
Start, clock, reset_b
Controller_STR M0 (clr_A_F, set_E, clr_E, set_F, incr_A, Start, A[2], A[3], clock, reset_b );
Datapath_STR M1 (A, E, F, clr_A_F, set_E, clr_E, set_F, incr_A, clock);
endmodule
module Controller_STR
( output clr_A_F, set_E, clr_E, set_F, incr_A,
input Start, A2, A3, clock, reset_b
);
wire
G0, G1;
parameter S_idle = 2'b00, S_1 = 2'b01, S_2 = 2'b11;
wire
w1, w2, w3;
not (G0_b, G0);
not (G1_b, G1);
buf (incr_A, w2);
buf (set_F, G1);
not (A2_b, A2);
or (D_G0, w1, w2);
and (w1, Start, G0_b);
and (clr_A_F, G0_b, Start);
and (w2, G0, G1_b);
and (set_E, w2, A2);
and (clr_E, w2, A2_b);
and (D_G1, w3, w2);
and (w3, A2, A3);
D_flip_flop_AR M0 (G0, D_G0, clock, reset_b);
D_flip_flop_AR M1 (G1, D_G1, clock, reset_b);
endmodule
// datapath unit
module Datapath_STR
( output [3: 0] A,
output E, F,
input
clr_A_F, set_E, clr_E, set_F, incr_A, clock
);
JK_flip_flop_2 M0 (E, E_b, set_E, clr_E, clock);
JK_flip_flop_2 M1 (F, F_b, set_F, clr_A_F, clock);
Counter_4 M2 (A, incr_A, clr_A_F, clock);
endmodule
module Counter_4 (output reg [3: 0] A, input incr, clear, clock);
always @ (posedge clock)
if (clear)
A <= 0; else if (incr) A <= A + 1;
endmodule
module D_flip_flop_AR (Q, D, CLK, RST);
output Q;
input D, CLK, RST;
reg Q;
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always @ (posedge CLK, negedge RST)
if (RST == 0) Q <= 1'b0;
else Q <= D;
endmodule
module JK_flip_flop_2 (Q, Q_not, J, K, CLK);
output Q, Q_not;
input J, K, CLK;
reg Q;
assign
Q_not = ~Q
;
always @ (posedge CLK)
case ({J, K})
2'b00: Q <= Q;
2'b01: Q <= 1'b0;
2'b10: Q <= 1'b1;
2'b11: Q <= ~Q;
endcase
endmodule
module t_Design_Example_STR;
reg
Start, clock, reset_b;
wire [3: 0] A;
wire
E, F;
wire [1:0] state_STR = {M0.M0.G1, M0.M0.G0};
Design_Example_STR M0 (A, E, F, Start, clock, reset_b);
initial #500 $finish;
initial
begin
reset_b = 0;
Start = 0;
clock = 0;
#5 reset_b = 1; Start = 1;
repeat (32)
begin
#5 clock = ~ clock;
end
end
initial
$monitor ("A = %b E = %b F = %b time = %0d", A, E, F, $time);
endmodule
The simulation results shown below match Fig. 8.13.
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Name
0
50
100
150
200
clock
reset_b
Start
A2
A3
state_STR[1:0]
0
1
3
0
1
clr_A_F
set_E
clr_E
set_F
incr_A
A[3:0]
x
0
1
2
3
4
5
6
7
8
9
a
b
c
d
0
E
F
8.14
8.15
The state code 2'b10 is unused. If the machine enters an unused state, the controller is written with default
assignment to next_state. The default assignment forces the state to S_idle, so the machine recovers from
the condition.
Modify the test bench to insert a reset event and extend the clock.
// RTL description of design example (see Fig.8-11)
module Design_Example_RTL (A, E, F, Start, clock, reset_b);
// Specify ports of the top-level module of the design
// See block diagram Fig. 8-10
output [3: 0] A;
output
E, F;
input
Start, clock, reset_b;
// Instantiate controller and datapath units
Controller_RTL M0 (set_E, clr_E, set_F, clr_A_F, incr_A, A[2], A[3], Start, clock, reset_b );
Datapath_RTL M1 (A, E, F, set_E, clr_E, set_F, clr_A_F, incr_A, clock);
endmodule
module Controller_RTL (set_E, clr_E, set_F, clr_A_F, incr_A, A2, A3, Start, clock, reset_b);
output reg set_E, clr_E, set_F, clr_A_F, incr_A;
input
Start, A2, A3, clock, reset_b;
reg [1:0] state, next_state;
parameter S_idle = 2'b00, S_1 = 2'b01, S_2 = 2'b11; // State codes
always @ (posedge clock or negedge reset_b)
if (reset_b == 0) state <= S_idle;
else state <= next_state;
// State transitions (edge-sensitive)
// Code next state logic directly from ASMD chart (Fig. 8-9d)
always @ (state, Start, A2, A3 ) begin
next_state = S_idle;
case (state)
// Next state logic (level-sensitive)
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S_idle:
S_1:
S_2:
default:
endcase
end
if (Start) next_state = S_1; else next_state = S_idle;
if (A2 & A3) next_state = S_2; else next_state = S_1;
next_state = S_idle;
next_state = S_idle;
// Code output logic directly from ASMD chart (Fig. 8-9d)
always @ (state, Start, A2) begin
set_E = 0;
// default assignments; assign by exception
clr_E = 0;
set_F = 0;
clr_A_F = 0;
incr_A = 0;
case (state)
S_idle:
if (Start) clr_A_F = 1;
S_1:
begin incr_A = 1; if (A2) set_E = 1; else clr_E = 1; end
S_2:
set_F = 1;
endcase
end
endmodule
module Datapath_RTL (A, E, F, set_E, clr_E, set_F, clr_A_F, incr_A, clock);
output reg [3: 0]
A;
// register for counter
output reg
E, F;
// flags
input
set_E, clr_E, set_F, clr_A_F, incr_A, clock;
// Code register transfer operations directly from ASMD chart (Fig. 8-9d)
always @ (posedge clock) begin
if (set_E)
E <= 1;
if (clr_E)
E <= 0;
if (set_F)
F <= 1;
if (clr_A_F)
begin A <= 0; F <= 0; end
if (incr_A)
A <= A + 1;
end
endmodule
module t_Design_Example_RTL;
reg
Start, clock, reset_b;
wire [3: 0] A;
wire
E, F;
// Instantiate design example
Design_Example_RTL M0 (A, E, F, Start, clock, reset_b);
// Describe stimulus waveforms
initial #500 $finish;
// Stopwatch
initial fork
#25 reset_b = 0;
// Test for recovery from reset on-the-fly.
#27 reset_b = 1;
join
initial
begin
reset_b = 0;
Start = 0;
clock = 0;
#5 reset_b = 1; Start = 1;
//repeat (32)
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repeat (38)
// Modify for test of reset_b on-the-fly
begin
#5 clock = ~ clock;
// Clock generator
end
end
initial
$monitor ("A = %b E = %b F = %b time = %0d", A, E, F, $time);
endmodule
Name
0
40
80
120
160
200
Default
clock
reset_b
Start
A2
A3
state[1:0]
0
1
0
1
3
0
1
clr_A_F
set_E
clr_E
set_F
incr_A
A[3:0]
x
0
1
0
1
2
3
4
5
6
7
8
9
a
b
c
d
0
1
E
F
8.16
RTL notation:
s0: (initial state) If start = 0 go back to state s0, If (start = 1) then BR ← multiplicand, AR ← multiplier,
PR ← 0, go to s1.
s1: (check AR for Zero) Zero = 1 if AR = 0, if (Zero = 1) then go back to s0 (done) If (Zero = 0) then go
to s1, PR ← PR + BR, AR ← AR – 1.
The internal architecture of the datapath consists of a double-width register to hold the product (PR), a
register to hold the multiplier (AR), a register to hold the multiplicand (BR), a double-width parallel adder,
and single-width parallel adder. The single-width adder is used to implement the operation of decrementing
the multiplier unit. Adding a word consisting entirely of 1s to the multiplier accomplishes the 2's
complement subtraction of 1 from the multiplier. Figure 8.16 (a) below shows the ASMD chart, block
diagram, and controller of the circuit. Figure 8.16 (b) shows the internal architecture of the datapath. Figure
8.16 (c) shows the results of simulating the circuit.
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276
reset_b
s0
done
data_AR data_BR
AR <= data_A
BR <= data_B
PR <= 0
start
16
zero
1
Ld_regs
PR <= PR + BR
AR <= AR -1
Controller
Add_decr
Datapath
AR
...
BR
...
PR
...
Ld_regs
s1
Zero
1
16
Add_decr
start
done
reset_b
clock
16
PR
Note: Form Zero as the output of an OR gate whose inputs
are the bits of the register AR.
Add_decr
Controller
s0 = s1'
Zero
done
D
Start
clock
reset_b
Ld_regs
(a) ASMD chart, block diagram, and controller
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277
data_BR
16
1
Ld_regs
mux
0
16
...
All 0's
BR
1
Add_decr
32
0
+
16
data_AR
16
32
mux
16
Note: all registers have active-low
asynchronous reset
1
Ld_regs
mux
32
0
16
...
...
PR
...
...
32
AR
16
16
0
mux
Ld_regs
1
+
32
1
mux
0
Add_decr
0
16
A// 1s
(b) Datapath
Name
0
40
80
120
160
200
reset_b
clock
start
Ld_regs
Add_decr
zero
state
data_AR[7:0]
5
data_BR[7:0]
20
AR[7:0]
BR[7:0]
0
3
4
9
5
4
3
2
0
1
0
4
3
2
20
1
0
4
36
0
9
done
PR[15:0]
0
20
40
60
80
100
0
9
18
27
(c) Simulation results
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module Prob_8_16_STR (
output [15: 0] PR, output done,
input [7: 0] data_AR, data_BR, input start, clock, reset_b
);
Controller_P8_16 M0 (done, Ld_regs, Add_decr, start, zero, clock, reset_b);
Datapath_P8_16 M1 (PR, zero, data_AR, data_BR, Ld_regs, Add_decr, clock, reset_b);
endmodule
module Controller_P8_16 (output done, output reg Ld_regs, Add_decr, input start, zero, clock, reset_b);
parameter s0 = 1'b0, s1 = 1'b1;
reg state, next_state;
assign done = (state == s0);
always @ (posedge clock, negedge reset_b)
if (!reset_b) state <= s0; else state <= next_state;
always @ (state, start, zero) begin
Ld_regs = 0;
Add_decr = 0;
case (state)
s0:
if (start) begin Ld_regs = 1; next_state = s1; end
s1:
if (zero) next_state = s0; else begin next_state = s1; Add_decr = 1; end
default: next_state = s0;
endcase
end
endmodule
module Register_32 (output [31: 0] data_out, input [31: 0] data_in, input clock, reset_b);
Register_8 M3 (data_out [31: 24] , data_in [31: 24], clock, reset_b);
Register_8 M2 (data_out [23: 16] , data_in [23: 16], clock, reset_b);
Register_8 M1 (data_out [15: 8] , data_in [15: 8], clock, reset_b);
Register_8 M0 (data_out [7: 0] , data_in [7: 0], clock, reset_b);
endmodule
module Register_16 (output [15: 0] data_out, input [15: 0] data_in, input clock, reset_b);
Register_8 M1 (data_out [15: 8] , data_in [15: 8], clock, reset_b);
Register_8 M0 (data_out [7: 0] , data_in [7: 0], clock, reset_b);
endmodule
module Register_8 (output [7: 0] data_out, input [7: 0] data_in, input clock, reset_b);
D_flop M7 (data_out[7] data_in[7], clock, reset_b);
D_flop M6 (data_out[6] data_in[6], clock, reset_b);
D_flop M5 (data_out[5] data_in[5], clock, reset_b);
D_flop M4 (data_out[4] data_in[4], clock, reset_b);
D_flop M3 (data_out[3] data_in[3], clock, reset_b);
D_flop M2 (data_out[2] data_in[2], clock, reset_b);
D_flop M1 (data_out[1] data_in[1], clock, reset_b);
D_flop M0 (data_out[0] data_in[0], clock, reset_b);
endmodule
module Adder_32 (output c_out, output [31: 0] sum, input [31: 0] a, b);
assign {c_out, sum} = a + b;
endmodule
module Adder_16 (output c_out, output [15: 0] sum, input [15: 0] a, b);
assign {c_out, sum} = a + b;
endmodule
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module D_flop (output q, input data, clock, reset_b);
always @ (posedge clock, negedge reset_b)
if (!reset_b) q <= 0; else q <= data;
endmodule
module Datapath_P8_16 (
output reg [15: 0] PR, output zero,
input [7: 0] data_AR, data_BR, input Ld_regs, Add_decr, clock, reset_b
);
reg [7: 0] AR, BR;
assign
zero = ~( | AR);
always @ (posedge clock, negedge reset_b)
if (!reset_b) begin AR <= 8'b0; BR <= 8'b0; PR <= 16'b0; end
else begin
if (Ld_regs) begin AR <= data_AR; BR <= data_BR; PR <= 0; end
else if (Add_decr) begin PR <= PR + BR; AR <= AR -1; end
end
endmodule
// Test plan – Verify;
// Power-up reset
// Data is loaded correctly
// Control signals assert correctly
// Status signals assert correctly
// start is ignored while multiplying
// Multiplication is correct
// Recovery from reset on-the-fly
module t_Prob_P8_16;
wire
done;
wire [15: 0] PR;
reg [7: 0] data_AR, data_BR;
reg
start, clock, reset_b;
Prob_8_16_STR M0 (PR, done, data_AR, data_BR, start, clock, reset_b);
initial #500 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial fork
reset_b = 0;
#12 reset_b = 1;
#40 reset_b = 0;
#42 reset_b = 1;
#90 reset_b = 1;
#92 reset_b = 1;
join
initial fork
#20 start = 1;
#30 start = 0;
#40 start = 1;
#50 start = 0;
#120 start = 1;
#120 start = 0;
join
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initial fork
data_AR = 8'd5;
data_BR = 8'd20;
// AR > 0
#80 data_AR = 8'd3;
#80 data_BR = 8'd9;
#100 data_AR = 8'd4;
#100 data_BR = 8'd9;
join
endmodule
8.17
8.18
(2n – 1) (2n – 1) < (22n – 1) for n ≥ 1
(a) The maximum product size is 32 bits available in registers A and Q.
(b) P counter must have 5 bits to load 16 (binary 10000) initially.
(c) Z (zero) detection is generated with a 5-input NOR gate.
8.19
Multiplicand B = 110112 = 2710
Multiplier Q = 101112 = 2310
Product: CAQ = 62110
Multiplier in Q
Q0 = 1; add B
First partial product
Shift right CAQ
Q0 = 1; add B
Second partial product
Shift right CAQ
Q0 = 1; add B
Third partial product
Shift right CAQ
Shift right CAQ
Fourth partial product
Q0 = 1; add B
Fifth partial product
Shift right CAQ
Final product in AQ:
AQ = 10011_01101 = 62110
8.20
C
0
0
0
1
0
1
0
0
0
1
0
A
00000
11011
11011
01101
11011
01000
10100
11011
01111
10111
Q
10111
P
101
10111
11011
100
11011
01101
011
01101
10110
010
01011
01011
11011
00110
10011
11011
11011
11011
01101
001
000
S_idle = 1t ns
The loop between S_add and S_shift takes 2nt ns)
Total time to multiply: (2n + 1)t
8.21
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State codes:
S_idle
S_add
S_shift1
unused
0
0
1
1
Zero'
0
Mux_1
G1
0
0
0
0
G0
0
1
0
G1
D
Start
2
3
s1
Load_regs
C
s0
Q[0]
0
Add_regs
1
2 x 4 Decoder
2
Shift_regs
3
Start
0
0
1
0
2
0
3
s1
s0
Mux_2
G0
D
C
clock
reset_b
8.22
Note that the machine described by Fig. P8.22 requires four states, but the machine described byFig. 8.15
(b) requires only three. Also, observe that the sample simulation results show a case where the carry bit
regsiter, C, is needed to support the addition operation. The datapath is 8 bits wide.
module Prob_8_22 # (parameter m_size = 9)
(
output [2*m_size -1: 0] Product,
output Ready,
input [m_size -1: 0] Multiplicand, Multiplier,
input Start, clock, reset_b
);
wire [m_size -1: 0] A, Q;
assign Product = {A, Q};
wire Q0, Zero, Load_regs, Decr_P, Add_regs, Shift_regs;
Datapath_Unit M0 (A, Q, Q0, Zero, Multiplicand, Multiplier, Load_regs, Decr_P, Add_regs, Shift_regs,
clock, reset_b);
Control_Unit M1 (Ready, Decr_P, Load_regs, Add_regs, Shift_regs, Start, Q0, Zero, clock, reset_b);
endmodule
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module Datapath_Unit # (parameter m_size = 9, BC_size = 4)
(
output reg [m_size -1: 0] A, Q,
output Q0, Zero,
input [m_size -1: 0] Multiplicand, Multiplier,
input Load_regs, Decr_P, Add_regs, Shift_regs, clock, reset_b
);
reg C;
reg [BC_size -1: 0] P;
reg [m_size -1: 0] B;
assign Q0 = Q[0];
assign Zero = (P == 0);
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) begin
B <= 0;C <= 0;
A <= 0;
Q <= 0;
P <= m_size;
end
else begin
if (Load_regs) begin
A <= 0;
C <= 0;
Q <= Multiplier;
B <= Multiplicand;
P <= m_size;
end
if (Decr_P) P <= P -1;
if (Add_regs) {C, A} <= A + B;
if (Shift_regs) {C, A, Q} <= {C, A, Q} >> 1;
end
endmodule
module Control_Unit (
output Ready, Decr_P, output reg Load_regs, Add_regs, Shift_regs, input Start, Q0, Zero, clock,
reset_b
);
reg [ 1: 0]
state, next_state;
parameter S_idle = 2'b00, S_loaded = 2'b01, S_sum = 2'b10, S_shifted = 2'b11;
assign Ready = (state == S_idle);
assign Decr_P = (state == S_loaded);
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) state <= S_idle; else state <= next_state;
always @ (state, Start, Q0, Zero) begin
next_state = S_idle;
Load_regs = 0;
Add_regs = 0;
Shift_regs = 0;
case (state)
S_idle: if (Start == 0) next_state = S_idle; else begin next_state = S_loaded; Load_regs = 1; end
S_loaded: if (Q0) begin next_state = S_sum; Add_regs = 1; end
else begin next_state = S_shifted; Shift_regs = 1; end
S_sum: begin next_state = S_shifted; Shift_regs = 1; end
S_shifted: if (Zero) next_state = S_idle; else next_state = S_loaded;
endcase
end
endmodule
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module t_Prob_8_22 ();
parameter
m_size = 9;
// Width of datapath
wire [2 * m_size - 1: 0]
Product;
wire
Ready;
reg [m_size - 1: 0]
Multiplicand, Multiplier;
reg
Start, clock, reset_b;
integer
Exp_Value;
reg
Error;
Prob_8_22 M0 (Product, Ready, Multiplicand, Multiplier, Start, clock, reset_b);
initial #140000 $finish;
initial begin clock = 0; #5 forever #5 clock = ~clock; end
initial fork
reset_b = 1;
#2 reset_b = 0;
#3 reset_b = 1;
join
initial begin #5 Start = 1; end
always @ (posedge Ready) begin
Exp_Value = Multiplier * Multiplicand;
//Exp_Value = Multiplier * Multiplicand +1;
end
always @ (negedge Ready) begin
Error = (Exp_Value ^ Product) ;
end
// Inject error to confirm detection
initial begin
#5 Multiplicand = 0;
Multiplier = 0;
repeat (64) #10 begin Multiplier = Multiplier + 1;
repeat (64) @ (posedge M0.Ready) #5 Multiplicand = Multiplicand + 1;
end
end
endmodule
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Name
76811
76861
76911
76961
77011
clock
reset_b
Ready
Start
Load_regs
Add_regs
Shift_regs
Decr_P
Q0
Zero
state[1:0]
0
1
P[3:0]
0
9
3
1
8
2
3
1
7
2
3
1
6
3
1
3
5
1
4
3
1
3
3
1
2
3
1
1
3
0
0
1
3
8
177
B[8:0]
1
9
178
C
A[8:0]
000
0bb
Q[8:0]
003
Product[17:0]
3
101
119
08c
046
023
011
008
004
080
140
0a0
050
128
194
0ca
72000
36000
18000
9000
4500
2250
96001
003
3
375
Multiplicand[8:0]
376
6
Multiplier[8:0]
Product[17:0]
000
3
96001
72000
36000
18000
9000
4500
2250
3
Ready
Exp_Value
2244
2250
Error
8.23
As shown in Fig. P8.23 the machine asserts Load_regs in state S_load. This will cause the machine to
operate incorrectly. Once Load_regs is removed from S_load the machine operates correctly. The state
S_load is a wasted state. Its removal leads to the same machine as dhown in Fig. P8.15b.
module Prob_8_23 # (parameter m_size = 9)
(
output [2*m_size -1: 0] Product,
output Ready,
input [m_size -1: 0] Multiplicand, Multiplier,
input Start, clock, reset_b
);
wire [m_size -1: 0] A, Q;
assign Product = {A, Q};
wire Q0, Zero, Load_regs, Decr_P, Add_regs, Shift_regs;
Datapath_Unit M0 (A, Q, Q0, Zero, Multiplicand, Multiplier, Load_regs, Decr_P, Add_regs, Shift_regs,
clock, reset_b);
Control_Unit M1 (Ready, Decr_P, Shift_regs, Add_regs, Load_regs, Start, Q0, Zero, clock, reset_b);
endmodule
module Datapath_Unit # (parameter m_size = 9, BC_size = 4)
(
output reg [m_size -1: 0] A, Q,
output Q0, Zero,
input [m_size -1: 0] Multiplicand, Multiplier,
input Load_regs, Decr_P, Add_regs, Shift_regs, clock, reset_b
);
reg C;
reg [BC_size -1: 0] P;
reg [m_size -1: 0] B;
assign Q0 = Q[0];
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assign Zero = (P == 0);
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) begin
A <= 0;
C <= 0;
Q <= 0;
B <= 0;
P <= m_size;
end
else begin
if (Load_regs) begin
A <= 0;
C <= 0;
Q <= Multiplier;
B <= Multiplicand;
P <= m_size;
end
if (Decr_P) P <= P -1;
if (Add_regs) {C, A} <= A + B;
if (Shift_regs) {C, A, Q} <= {C, A, Q} >> 1;
end
endmodule
module Control_Unit (
output Ready, Decr_P, Shift_regs, output reg Add_regs, Load_regs, input Start, Q0, Zero, clock,
reset_b
);
reg [ 1: 0]
state, next_state;
parameter S_idle = 2'b00, S_load = 2'b01, S_decr = 2'b10, S_shift = 2'b11;
assign Ready = (state == S_idle);
assign Shift_regs = (state == S_shift);
assign Decr_P = (state == S_decr);
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) state <= S_idle; else state <= next_state;
always @ (state, Start, Q0, Zero) begin
next_state = S_idle;
Load_regs = 0;
Add_regs = 0;
case (state)
S_idle: if (Start == 0) next_state = S_idle; else begin next_state = S_load; Load_regs = 1; end
S_load: begin next_state = S_decr; end
S_decr: begin next_state = S_shift; if (Q0) Add_regs = 1; end
S_shift: if (Zero) next_state = S_idle; else next_state = S_load;
endcase
end
endmodule
module t_Prob_8_23 ();
parameter
m_size = 9;
// Width of datapath
wire [2 * m_size - 1: 0]
Product;
wire
Ready;
reg [m_size - 1: 0]
Multiplicand, Multiplier;
reg
Start, clock, reset_b;
integer
Exp_Value;
reg
Error;
Prob_8_23 M0 (Product, Ready, Multiplicand, Multiplier, Start, clock, reset_b);
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initial #140000 $finish;
initial begin clock = 0; #5 forever #5 clock = ~clock; end
initial fork
reset_b = 1;
#2 reset_b = 0;
#3 reset_b = 1;
join
initial begin #5 Start = 1; end
always @ (posedge Ready) begin
Exp_Value = Multiplier * Multiplicand;
//Exp_Value = Multiplier * Multiplicand +1;
end
always @ (negedge Ready) begin
Error = (Exp_Value ^ Product) ;
end
// Inject error to confirm detection
initial begin
#5 Multiplicand = 0;
Multiplier = 0;
repeat (64) #10 begin Multiplier = Multiplier + 1;
repeat (64) @ (posedge M0.Ready) #5 Multiplicand = Multiplicand + 1;
end
end
endmodule
Name
21403
21433
21463
21493
21523
21553
clock
reset_b
Ready
Start
Load_regs
Add_regs
Shift_regs
Decr_P
Q0
Zero
state[1:0]
3
1
2
5
P[3:0]
3
1
2
4
3
1
2
3
3
1
2
2
3
1
2
3
1
0
1
0
9
04c
B[8:0]
04d
C
A[8:0]
013
Q[8:0]
000
Product[17:0]
002
001
100
180
0c0
060
4864
009
2432
004
1216
000
130
304
098
002
152
2
76
Multiplicand[8:0]
77
2
Multiplier[8:0]
Product[17:0]
608
4864
2432
1216
608
304
152
2
Ready
Exp_Value
150
Error
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287
8.24
module Prob_8_24 # (parameter dp_width = 5)
(
output [2*dp_width - 1: 0]
Product,
output
Ready,
input
[dp_width - 1: 0]
Multiplicand, Multiplier,
input
Start, clock, reset_b
);
wire Load_regs, Decr_P, Add_regs, Shift_regs, Zero, Q0;
Controller M0 (
Ready, Load_regs, Decr_P, Add_regs, Shift_regs, Start, Zero, Q0,
clock, reset_b
);
Datapath M1(Product, Q0, Zero,Multiplicand, Multiplier,
Start, Load_regs, Decr_P, Add_regs, Shift_regs, clock, reset_b);
endmodule
module Controller (
output Ready,
output reg Load_regs, Decr_P, Add_regs, Shift_regs,
input Start, Zero, Q0, clock, reset_b
);
parameter
reg [2: 0]
assign
S_idle = 3'b001,
// one-hot code
S_add = 3'b010,
S_shift = 3'b100;
state, next_state;
// sized for one-hot
Ready = (state == S_idle);
always @ (posedge clock, negedge reset_b)
if (~reset_b) state <= S_idle; else state <= next_state;
always @ (state, Start, Q0, Zero) begin
next_state = S_idle;
Load_regs = 0;
Decr_P = 0;
Add_regs = 0;
Shift_regs = 0;
case (state)
S_idle: if (Start) begin next_state = S_add; Load_regs = 1; end
S_add: begin next_state = S_shift; Decr_P = 1; if (Q0) Add_regs = 1; end
S_shift: begin
Shift_regs = 1;
if (Zero) next_state = S_idle;
else next_state = S_add;
end
default: next_state = S_idle;
endcase
end
endmodule
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
288
module Datapath #(parameter dp_width = 5, BC_size = 3) (
output [2*dp_width - 1: 0] Product, output Q0, output Zero,
input [dp_width - 1: 0] Multiplicand, Multiplier,
input Start, Load_regs, Decr_P, Add_regs, Shift_regs, clock, reset_b
);
// Default configuration: 5-bit datapath
reg [dp_width - 1: 0]
A, B, Q;
// Sized for datapath
reg
C;
reg [BC_size - 1: 0]
P;
// Bit counter
assign Q0 = Q[0];
assign Zero = (P == 0);
// Counter is zero
assign Product = {C, A, Q};
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) begin
// Added to this solution, but
P <= dp_width;
// not really necessary since Load_regs
B <= 0;
// initializes the datapath
C <= 0;
A <= 0;
Q <= 0;
end
else begin
if (Load_regs) begin
P <= dp_width;
A <= 0;
C <= 0;
B <= Multiplicand;
Q <= Multiplier;
end
if (Add_regs) {C, A} <= A + B;
if (Shift_regs) {C, A, Q} <= {C, A, Q} >> 1;
if (Decr_P) P <= P -1;
end
endmodule
module t_Prob_8_24;
parameter
wire [2 * dp_width - 1: 0]
wire
reg [dp_width - 1: 0]
reg
integer
reg
dp_width = 5;
// Width of datapath
Product;
Ready;
Multiplicand, Multiplier;
Start, clock, reset_b;
Exp_Value;
Error;
Prob_8_24 M0(Product, Ready, Multiplicand, Multiplier, Start, clock, reset_b);
initial #115000 $finish;
initial begin clock = 0; #5 forever #5 clock = ~clock; end
initial fork
reset_b = 1;
#2 reset_b = 0;
#3 reset_b = 1;
join
always @ (negedge Start) begin
Exp_Value = Multiplier * Multiplicand;
//Exp_Value = Multiplier * Multiplicand +1; // Inject error to confirm detection
end
always @ (posedge Ready) begin
# 1 Error <= (Exp_Value ^ Product) ;
end
initial begin
Digital
Design
With
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HDL
–
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2012,
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rights
reserved.
289
#5 Multiplicand = 0;
Multiplier = 0;
repeat (32) #10 begin
Start = 1;
#10 Start = 0;
repeat (32) begin
Start = 1;
#10 Start = 0;
#100 Multiplicand = Multiplicand + 1;
end
Multiplier = Multiplier + 1;
end
end
endmodule
Name
45340
45380
45420
45460
45500
clock
reset_b
Start
Load_regs
Add_regs
Shift_regs
Decr_P
Q0
Zero
P[2:0]
1
0
5
4
3
2
19
B[4:0]
1
0
5
1a
4
1b
C
A[4:0]
18
Q[4:0]
18
Multiplicand[4:0]
9
0
0c
26
06
25
7
01
19
9
10
18
26
0
0c
27
12
Multiplier[4:0]
Product[9:0]
13
03
600
300
12
6
3
835
417
225
624
312
12
Ready
Exp_Value
300
312
Error
Digital
Design
With
An
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to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
324
290
8.25
(a)
Ready
Multiplicand
reset
Datapath
Empty
Load_regs
A
Shift_regs
Controller
Start
Multiplier
Add_regs
Decr_P
B
S_idle
Ready
Q
Start
1
P
C
A <= 0
C <= 0
B <= Multiplicand
Q <= Multiplier
P <= m_size
Load_regs
reset
clock
Product
Zero
Q[0]
Empty
1
Register B (Multiplicand)
1
1
0
7
1
0
1
1
Register P (Counter)
1
1
0
0
0
Q[0]
Clr_P
{C, A} <= A + B
1
0
8
P <= P-1
S_add
Decr_P
Add_regs
+
16
15
0
9
C
8
0
0
0
0
0
Register A (Sum)
0
8
7
0
0
0
0
0
1
0
1
1
S_shift
Shift_regs
1
Register Q (Multiplier)
{C, A, Q} <= {C, A, Q} >> 1
1
Empty
Zero
1
(b)
//
The
multiplier
of
Fig.
8.15
is
modified
to
detect
whether
the
multiplier
or
multiplicand
are
initially
zero,
//
and
to
detect
whether
the
multiplier
becomes
zero
before
the
entire
multiplier
has
been
applied
//
to
the
multiplicand.
Signal
empty
is
generated
by
the
datapath
unit
and
used
by
the
//
controller.
Note
that
the
bits
of
the
product
must
be
selected
according
to
the
stage
at
which
//
termination
occurs.
The
test
for
the
condition
of
an
empty
multiplier
is
hardwired
here
for
//
dp_width
=
5
because
the
range
bounds
of
a
vector
must
be
defined
by
integer
constants.
//
This
prevents
development
of
a
fully
parameterized
model.
//
Note:
the
test
bench
has
been
modified.
module Prob_8_25 #(parameter dp_width = 5)
(
output [2*dp_width - 1: 0]
Product,
output
Ready,
input
[dp_width - 1: 0]
Multiplicand, Multiplier,
input
Start, clock, reset_b
);
wire Load_regs, Decr_P, Add_regs, Shift_regs, Empty, Zero, Q0;
Controller M0 (
Ready, Load_regs, Decr_P, Add_regs, Shift_regs, Start, Empty, Zero, Q0,
clock, reset_b
);
Datapath M1(Product, Q0, Empty, Zero,Multiplicand, Multiplier,
Start, Load_regs, Decr_P, Add_regs, Shift_regs, clock, reset_b);
endmodule
Digital
Design
With
An
Introduction
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the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
291
module Controller (
output Ready,
output reg Load_regs, Decr_P, Add_regs, Shift_regs,
input Start, Empty, Zero, Q0, clock, reset_b
);
parameter
parameter
reg [2: 0]
assign
BC_size =
3;
// Size of bit counter
S_idle = 3'b001,
// one-hot code
S_add = 3'b010,
S_shift = 3'b100;
state, next_state;
// sized for one-hot
Ready = (state == S_idle);
always @ (posedge clock, negedge reset_b)
if (~reset_b) state <= S_idle; else state <= next_state;
always @ (state, Start, Q0, Empty, Zero) begin
next_state = S_idle;
Load_regs = 0;
Decr_P = 0;
Add_regs = 0;
Shift_regs = 0;
case (state)
S_idle:
if (Start) begin next_state = S_add; Load_regs = 1; end
S_add:
begin next_state = S_shift; Decr_P = 1; if (Q0) Add_regs = 1; end
S_shift: begin
Shift_regs = 1;
if (Zero) next_state = S_idle;
else if (Empty) next_state = S_idle;
else next_state = S_add;
end
default: next_state = S_idle;
endcase
end
endmodule
module Datapath #(parameter dp_width = 5, BC_size = 3) (
output reg [2*dp_width - 1: 0] Product, output Q0, output Empty, output Zero,
input [dp_width - 1: 0] Multiplicand, Multiplier,
input Start, Load_regs, Decr_P, Add_regs, Shift_regs, clock, reset_b
);
// Default configuration: 5-bit datapath
parameter
S_idle = 3'b001,
// one-hot code
S_add = 3'b010,
S_shift = 3'b100;
reg [dp_width - 1: 0]
A, B, Q;
// Sized for datapath
reg
C;
reg [BC_size - 1: 0]
P;
// Bit counter
wire [2*dp_width -1: 0]
Internal_Product = {C, A, Q};
assign
assign
Q0 = Q[0];
Zero = (P == 0);
// Bit counter is zero
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) begin
// Added to this solution, but
P <= dp_width;
// not really necessary since Load_regs
B <= 0;
// initializes the datapath
C <= 0;
A <= 0;
Q <= 0;
end
else begin
Digital
Design
With
An
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HDL
–
Solution
Manual.
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Mano.
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Copyright
2012,
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rights
reserved.
292
if (Load_regs) begin
P <= dp_width;
A <= 0;
C <= 0;
B <= Multiplicand;
Q <= Multiplier;
end
if (Add_regs) {C, A} <= A + B;
if (Shift_regs) {C, A, Q} <= {C, A, Q} >> 1;
if (Decr_P) P <= P -1;
end
// Status signals
reg Empty_multiplier;
wire Empty_multiplicand = (Multiplicand == 0);
assign Empty = Empty_multiplicand || Empty_multiplier;
always @ (P, Internal_Product) begin // Note: hardwired for dp_width 5
Product = 0;
case (P)
// Examine multiplier bits
0: Product = Internal_Product;
1: Product = Internal_Product [2*dp_width -1: 1];
2: Product = Internal_Product [2*dp_width -1: 2];
3: Product = Internal_Product [2*dp_width -1: 3];
4: Product = Internal_Product [2*dp_width -1: 4];
5: Product = 0;
endcase
end
always @ (P, Q) begin
// Note: hardwired for dp_width 5
Empty_multiplier = 0;
case (P)
0: Empty_multiplier = 1;
1: if (Q[1] == 0) Empty_multiplier = 1;
2: if (Q[2: 1] == 0) Empty_multiplier = 1;
3: if (Q[3: 1] == 0) Empty_multiplier = 1;
4: if (Q[4: 1] == 0) Empty_multiplier = 1;
5: if (Q[5: 1] == 0) Empty_multiplier = 1;
default: Empty_multiplier = 1'bx;
endcase
end
endmodule
module t_Prob_8_25;
parameter
dp_width = 5;
// Width of datapath
wire [2 * dp_width - 1: 0] Product;
wire
Ready;
reg [dp_width - 1: 0]
Multiplicand, Multiplier;
reg
Start, clock, reset_b;
integer
Exp_Value;
reg
Error;
Prob_8_25 M0(Product, Ready, Multiplicand, Multiplier, Start, clock, reset_b);
initial #115000 $finish;
initial begin clock = 0; #5 forever #5 clock = ~clock; end
initial fork
reset_b = 1;
#2 reset_b = 0;
#3 reset_b = 1;
join
always @ (negedge Start) begin
Exp_Value = Multiplier * Multiplicand;
Digital
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With
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HDL
–
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M.D.
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2012,
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reserved.
293
//Exp_Value = Multiplier * Multiplicand +1;
end
always @ (posedge Ready) begin
# 1 Error <= (Exp_Value ^ Product) ;
end
// Inject error to confirm detection
initial begin
#5 Multiplicand = 0;
Multiplier = 0;
repeat (32) #10 begin
Start = 1;
#10 Start = 0;
repeat (32) begin
Start = 1;
#10 Start = 0;
#100 Multiplicand = Multiplicand + 1;
end
Multiplier = Multiplier + 1;
end
end
endmodule
(c) Test plan: Exhaustively test all combinations of multiplier and multiplicand, using automatic error
checking. Verify that early termination is implemented. Sample of simulation results is shown below.
Name
6902
6992
7082
7172
reset_b
clock
Start
state[2:0]
1
2 4
1
2 4
1
2 4 2
Early termination
Empty_multiplicand
Empty_multiplier
Empty
Clr_CAQ
Load_regs
Decr_P
Add_regs
Shift_regs
Q0
P[4:0]
4
5
4
5
4
5
4
Zero
B[4:0]
30
A[4:0]
15
31
0
1
15
0
C
Q[4:0]
Multiplicand[4:0]
0
16
30
31
2
1
2
0
1
1
1
Multiplier[4:0]
Product[9:0]
1
2
30
31
0
Ready
Exp_Value
30
31
0
Error
8.26
Digital
Design
With
An
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HDL
–
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2012,
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rights
reserved.
2
294
reset
S_idle
/Ready
A <= 0
C <= 0
B <= Multiplicand
Q <= Multiplier
P <= m_size
Start
1
Load_regs
P <= P-1
S_add_shift
/ Decr_P
{C, A, Q} <= {A + B, Q} >> 1
Q[0]
1
Add_Shift
Zero
1
Zero
1
module Prob_8_26 (Product, Ready, Multiplicand, Multiplier, Start, clock, reset_b);
// Default configuration: 5-bit datapath
parameter
dp_width = 5;
// Set to width of datapath
output [2*dp_width - 1: 0]
Product;
output
Ready;
input
[dp_width - 1: 0] Multiplicand, Multiplier;
input
Start, clock, reset_b;
parameter
BC_size =
3;
// Size of bit counter
parameter
S_idle = 2'b01,
// one-hot code
S_add_shift =
2'b10;
reg [2: 0]
state, next_state;
reg [dp_width - 1: 0]
A, B, Q;
// Sized for datapath
reg
C;
reg [BC_size -1: 0]
P;
reg
Load_regs, Decr_P, Add_shift, Shift;
assign
Product = {C, A, Q};
wire
Zero = (P == 0);
// counter is zero
wire
Ready = (state == S_idle); // controller status
// control unit
always @ (posedge clock, negedge reset_b)
if (~reset_b) state <= S_idle; else state <= next_state;
always @ (state, Start, Q[0], Zero) begin
next_state = S_idle;
Load_regs = 0;
Decr_P = 0;
Add_shift = 0;
Shift = 0;
case (state)
S_idle:
begin if (Start) next_state = S_add_shift; Load_regs = 1; end
S_add_shift:
begin
Decr_P = 1;
if (Zero) next_state = S_idle;
Digital
Design
With
An
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HDL
–
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Manual.
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Mano.
M.D.
Ciletti,
Copyright
2012,
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rights
reserved.
295
default:
endcase
end
else begin
next_state = S_add_shift;
if (Q[0]) Add_shift = 1; else Shift = 1;
end
end
next_state = S_idle;
// datapath unit
always @ (posedge clock) begin
if (Load_regs) begin
P <= dp_width;
A <= 0;
C <= 0;
B <= Multiplicand;
Q <= Multiplier;
end
if (Decr_P) P <= P -1;
if (Add_shift) {C, A, Q} <= {C, A+B, Q} >> 1;
if (Shift) {C, A, Q} <= {C, A, Q} >> 1;
end
endmodule
module t_Prob_8_26;
parameter
dp_width = 5;
// Width of datapath
wire [2 * dp_width - 1: 0] Product;
wire
Ready;
reg [dp_width - 1: 0]
Multiplicand, Multiplier;
reg
Start, clock, reset_b;
integer
Exp_Value;
wire
Error;
Prob_8_26 M0 (Product, Ready, Multiplicand, Multiplier, Start, clock, reset_b);
initial #70000 $finish;
initial begin clock = 0; #5 forever #5 clock = ~clock; end
initial fork
reset_b = 1;
#2 reset_b = 0;
#3 reset_b = 1;
join
initial begin #5 Start = 1; end
always @ (posedge Ready) begin
Exp_Value = Multiplier * Multiplicand;
end
assign Error = Ready & (Exp_Value ^ Product);
initial begin
#5 Multiplicand = 0;
Multiplier = 0;
repeat (32) #10 begin Multiplier = Multiplier + 1;
repeat (32) @ (posedge M0.Ready) #5 Multiplicand = Multiplicand + 1;
end
end
endmodule
Digital
Design
With
An
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Verilog
HDL
–
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Ciletti,
Copyright
2012,
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rights
reserved.
296
Sample
of
simulation
results.
Name
23982
24042
24102
24162
clock
reset_b
Start
Load_regs
Shift
Add_shift
Decr_P
P[2:0]
2
1
0
7
5
4
3
2
22
B[4:0]
1
0
7
5
4
3
2
23
1
0
7
5
4
24
25
C
A[4:0]
0
11
5
Q[4:0]
9
4
18
Multiplicand[4:0]
22
11
1
11 21
0
10
0
5
0
12
2
1
12
6
0
12
29
11
5
2
1
16
8
11
21
23
24
25
11
Multiplier[4:0]
178
Product[9:0]
Exp_Value
11
21 26
231
189
242
200
253
264
Error
8.27
(a)
// Test bench for exhaustive simulation
module t_Sequential_Binary_Multiplier;
parameter
dp_width = 5;
// Width of datapath
wire [2 * dp_width - 1: 0] Product;
wire
Ready;
reg [dp_width - 1: 0]
Multiplicand, Multiplier;
reg
Start, clock, reset_b;
Sequential_Binary_Multiplier M0 (Product, Ready, Multiplicand, Multiplier, Start, clock, reset_b);
initial #109200 $finish;
initial begin clock = 0; #5 forever #5 clock = ~clock; end
initial fork
reset_b = 1;
#2 reset_b = 0;
#3 reset_b = 1;
join
initial begin #5 Start = 1; end
initial begin
#5 Multiplicand = 0;
Multiplier = 0;
repeat (31) #10 begin Multiplier = Multiplier + 1;
repeat (32) @ (posedge M0.Ready) #5 Multiplicand = Multiplicand + 1;
end
Start = 0;
end
// Error Checker
Digital
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HDL
–
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2012,
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rights
reserved.
297
reg Error;
reg [2*dp_width -1: 0] Exp_Value;
always @ (posedge Ready) begin
Exp_Value = Multiplier * Multiplicand;
//Exp_Value = Multiplier * Multiplicand + 1;
Error = (Exp_Value ^ Product);
end
endmodule
// Inject error to verify detection
module Sequential_Binary_Multiplier (Product, Ready, Multiplicand, Multiplier, Start, clock, reset_b);
// Default configuration: 5-bit datapath
parameter
dp_width = 5;
// Set to width of datapath
output [2*dp_width - 1: 0]
Product;
output
Ready;
input
[dp_width - 1: 0]
Multiplicand, Multiplier;
input
Start, clock, reset_b;
parameter
parameter
reg
reg
reg
reg
reg
BC_size =
S_idle =
S_add =
S_shift =
[2: 0]
[dp_width - 1: 0]
[BC_size - 1: 0]
3; // Size of bit counter
3'b001,
// one-hot code
3'b010,
3'b100;
state, next_state;
A, B, Q;
// Sized for datapath
C;
P;
Load_regs, Decr_P, Add_regs, Shift_regs;
// Miscellaneous combinational logic
assign
wire
wire
Product = {C, A, Q};
Zero = (P == 0);
// counter is zero
Ready = (state == S_idle);
// controller status
// control unit
always @ (posedge clock, negedge reset_b)
if (~reset_b) state <= S_idle; else state <= next_state;
always @ (state, Start, Q[0], Zero) begin
next_state = S_idle;
Load_regs = 0;
Decr_P = 0;
Add_regs = 0;
Shift_regs = 0;
case (state)
S_idle: begin if (Start) next_state = S_add; Load_regs = 1; end
S_add: begin next_state = S_shift; Decr_P = 1; if (Q[0]) Add_regs = 1; end
S_shift: begin Shift_regs = 1; if (Zero) next_state = S_idle;
else next_state = S_add; end
default: next_state = S_idle;
endcase
end
Digital
Design
With
An
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the
Verilog
HDL
–
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Manual.
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Mano.
M.D.
Ciletti,
Copyright
2012,
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rights
reserved.
298
// datapath unit
always @ (posedge clock) begin
if (Load_regs) begin
P <= dp_width;
A <= 0;
C <= 0;
B <= Multiplicand;
Q <= Multiplier;
end
if (Add_regs) {C, A} <= A + B;
if (Shift_regs) {C, A, Q} <= {C, A, Q} >> 1;
if (Decr_P) P <= P -1;
end
endmodule
Sample of simulation results:
Name
99539
99579
99619
99659
clock
reset_b
Start
state[2:0]
4
1
2
4
2
4
2
4
2
4
2
4
1
2
4
5
4
Load_regs
Decr_P
Add_regs
Shift_regs
Zero
0
P[2:0]
4
3
2
08
B[4:0]
A[4:0]
5
1
0
09
0e
07
11
08
00
09
04
02
0b
0a
05
0e
07
10
08
00
C
Q[4:0]
Multiplicand[4:0]
1d
1e
0f
8
0b
05
1d
9
10
29
Multiplier[4:0]
Product[9:0]
17
465
232
29
317
158
79
367
183
471
235
523
261
29
Ready
Exp_Value[9:0]
203
232
261
Error
Digital
Design
With
An
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the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
299
(b) In this part the controller is described by Fig. 8.18. The test bench includes probes to display the state
of the controller.
// Test bench for exhaustive simulation
module t_Sequential_Binary_Multiplier;
parameter
dp_width = 5;
// Width of datapath
wire [2 * dp_width - 1: 0] Product;
wire
Ready;
reg [dp_width - 1: 0]
Multiplicand, Multiplier;
reg
Start, clock, reset_b;
Sequential_Binary_Multiplier M0 (Product, Ready, Multiplicand, Multiplier, Start, clock, reset_b);
initial #109200 $finish;
initial begin clock = 0; #5 forever #5 clock = ~clock; end
initial fork
reset_b = 1;
#2 reset_b = 0;
#3 reset_b = 1;
join
initial begin #5 Start = 1; end
initial begin
#5 Multiplicand = 0;
Multiplier = 0;
repeat (31) #10 begin Multiplier = Multiplier + 1;
repeat (32) @ (posedge M0.Ready) #5 Multiplicand = Multiplicand + 1;
end
Start = 0;
end
// Error Checker
reg Error;
reg [2*dp_width -1: 0] Exp_Value;
always @ (posedge Ready) begin
Exp_Value = Multiplier * Multiplicand;
//Exp_Value = Multiplier * Multiplicand + 1;
Error = (Exp_Value ^ Product);
end
// Inject error to verify detection
wire [2: 0] state = {M0.G2, M0.G1, M0.G0};
endmodule
module Sequential_Binary_Multiplier (Product, Ready, Multiplicand, Multiplier, Start, clock, reset_b);
// Default configuration: 5-bit datapath
parameter
dp_width =
5;
// Set to width of datapath
output [2*dp_width - 1: 0]
Product;
output
Ready;
input
[dp_width - 1: 0]
Multiplicand, Multiplier;
input
Start, clock, reset_b;
parameter
reg [dp_width - 1: 0]
reg
reg [BC_size - 1: 0]
wire
BC_size =
3; // Size of bit counter
A, B, Q;
// Sized for datapath
C;
P;
Load_regs, Decr_P, Add_regs, Shift_regs;
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// Status signals
assign
wire
wire
Product = {C, A, Q};
Zero = (P == 0);
Q0 = Q[0];
// counter is zero
// One-Hot Control unit (See Fig. 8.18)
DFF_S M0 (G0, D0, clock, Set);
DFF M1 (G1, D1, clock, reset_b);
DFF M2 (G2, G1, clock, reset_b);
or (D0, w1, w2);
and (w1, G0, Start_b);
and (w2, Zero, G2);
not (Start_b, Start);
not (Zero_b, Zero);
or (D1, w3, w4);
and (w3, Start, G0);
and (w4, Zero_b, G2);
and (Load_regs, G0, Start);
and (Add_regs, Q0, G1);
assign Ready = G0;
assign Decr_P = G1;
assign Shift_regs = G2;
not (Set, reset_b);
// datapath unit
always @ (posedge clock) begin
if (Load_regs) begin
P <= dp_width;
A <= 0;
C <= 0;
B <= Multiplicand;
Q <= Multiplier;
end
if (Add_regs) {C, A} <= A + B;
if (Shift_regs) {C, A, Q} <= {C, A, Q} >> 1;
if (Decr_P) P <= P -1;
end
endmodule
module DFF_S (output reg Q, input data, clock, Set);
always @ ( posedge clock, posedge Set)
if (Set) Q <= 1'b1; else Q<= data;
endmodule
module DFF (output reg Q, input data, clock, reset_b);
always @ ( posedge clock, negedge reset_b)
if (reset_b == 0) Q <= 1'b0; else Q<= data;
endmodule
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Sample of simulation results:
ts:
Name
40699
40739
40779
40819
clock
reset_b
Start
state[2:0]
1
2
0
5
4
2
4
2
4
2
4
2
4
1
2
4
5
4
Load_regs
Decr_P
Add_regs
Shift_regs
P[2:0]
4
3
2
1
0
Zero
B[4:0]
11
A[4:0]
06
12
00
12
13
09
1b
0d
06
00
10
18
0c
C
0c
Q[4:0]
Multiplicand[4:0]
06
03
17
18
19
12
Multiplier[4:0]
Product[9:0]
01
204
12
6
3
579
289
865
432
216
12
Ready
Exp_Value[9:0]
204
216
Error
8.28
// Test bench for exhaustive simulation
module t_Sequential_Binary_Multiplier;
parameter
dp_width = 5;
// Width of datapath
wire [2 * dp_width - 1: 0] Product;
wire
Ready;
reg [dp_width - 1: 0]
Multiplicand, Multiplier;
reg
Start, clock, reset_b;
Sequential_Binary_Multiplier M0 (Product, Ready, Multiplicand, Multiplier, Start, clock, reset_b);
initial #109200 $finish;
initial begin clock = 0; #5 forever #5 clock = ~clock; end
initial fork
reset_b = 1;
#2 reset_b = 0;
#3 reset_b = 1;
join
initial begin #5 Start = 1; end
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302
initial begin
#5 Multiplicand = 0;
Multiplier = 0;
repeat (31) #10 begin Multiplier = Multiplier + 1;
repeat (32) @ (posedge M0.Ready) #5 Multiplicand = Multiplicand + 1;
end
Start = 0;
end
// Error Checker
reg Error;
reg [2*dp_width -1: 0] Exp_Value;
always @ (posedge Ready) begin
Exp_Value = Multiplier * Multiplicand;
//Exp_Value = Multiplier * Multiplicand + 1;
// Inject error to verify detection
Error = (Exp_Value ^ Product);
end
wire [2: 0] state = {M0.M0.G2, M0.M0.G1, M0.M0.G0}; // Watch state
endmodule
module Sequential_Binary_Multiplier
#(parameter dp_width = 5)
(
output [2*dp_width -1: 0] Product,
output
Ready,
input [dp_width -1: 0]
Multiplicand, Multiplier,
input
Start, clock, reset_b
);
wire Load_regs, Decr_P, Add_regs, Shift_regs, Zero, Q0;
Controller M0 (Ready, Load_regs, Decr_P, Add_regs, Shift_regs, Start, Zero, Q0, clock, reset_b);
Datapath M1(Product, Q0, Zero,Multiplicand, Multiplier, Start, Load_regs, Decr_P, Add_regs,
Shift_regs, clock, reset_b);
endmodule
module Controller (
output Ready,
output Load_regs, Decr_P, Add_regs, Shift_regs,
input Start, Zero, Q0, clock, reset_b
);
// One-Hot Control unit (See Fig. 8.18)
DFF_S M0 (G0, D0, clock, Set);
DFF M1 (G1, D1, clock, reset_b);
DFF M2 (G2, G1, clock, reset_b);
or (D0, w1, w2);
and (w1, G0, Start_b);
and (w2, Zero, G2);
not (Start_b, Start);
not (Zero_b, Zero);
or (D1, w3, w4);
and (w3, Start, G0);
and (w4, Zero_b, G2);
and (Load_regs, G0, Start);
and (Add_regs, Q0, G1);
assign Ready = G0;
assign Decr_P = G1;
assign Shift_regs = G2;
not (Set, reset_b);
endmodule
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module Datapath #(parameter dp_width = 5, BC_size = 3) (
output [2*dp_width - 1: 0] Product, output Q0, output Zero,
input [dp_width - 1: 0] Multiplicand, Multiplier,
input Start, Load_regs, Decr_P, Add_regs, Shift_regs, clock, reset_b
);
reg [dp_width - 1: 0]
A, B, Q;
// Sized for datapath
reg
C;
reg [BC_size - 1: 0]
P;
assign
Product = {C, A, Q};
// Status signals
assign
Zero = (P == 0);
// counter is zero
assign
Q0 = Q[0];
always @ (posedge clock) begin
if (Load_regs) begin
P <= dp_width;
A <= 0;
C <= 0;
B <= Multiplicand;
Q <= Multiplier;
end
if (Add_regs) {C, A} <= A + B;
if (Shift_regs) {C, A, Q} <= {C, A, Q} >> 1;
if (Decr_P) P <= P -1;
end
endmodule
module DFF_S (output reg Q, input data, clock, Set);
always @ ( posedge clock, posedge Set)
if (Set) Q <= 1'b1; else Q<= data;
endmodule
module DFF (output reg Q, input data, clock, reset_b);
always @ ( posedge clock, negedge reset_b)
if (reset_b == 0) Q <= 1'b0; else Q<= data;
endmodule
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304
Name
58738
58778
58818
58858
clock
reset_b
Start
state[2:0]
1
2
0
5
4
2
4
2
4
2
4
2
4
1
2
4
5
4
Load_regs
Decr_P
Add_regs
Shift_regs
P[2:0]
4
3
2
1
0
Q0
Zero
B[4:0]
15
16
17
C
A[4:0]
0b
Q[4:0]
05
Multiplicand[4:0]
00
16
11
0b
05
02
08
14
1a
21
17
0d
0b
00
16
11
22
23
17
Multiplier[4:0]
Product[9:0]
01
357
17
721
360
180
90
45
749
374
17
Ready
357
Exp_Value[9:0]
374
Error
8.29
(a)
Inputs: xyEF
00-S0
01-1---
S1
S2
---1
S3
S4
--0-
S7
S6
--1-
S5
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(b)
DS0 = x'y'S0 + S3 + S5 +S7
DS1 = xS0
DS2 = x'yS0 + S1
DS3 = FS2
DS4 = F'S2
DS5 = E'S5
DS6 = E'S4
DS7 = S6
(c)
Present
state
Output G G G
1 2 3
Inputs
x y E F
Next
state
G1 G2 G3
S0
S0
S0
0 0 0
0 0 0
0 0 0
0 0 x x
1 x x x
0 1 x x
0 0 0
0 0 1
0 1 0
S1
0 0 1
x x x x
0 1 0
S2
S2
0 1 0
0 1 0
x x 0 x
x x 1 x
1 0 0
0 1 1
S3
0 1 1
x x x x
0 0 0
S4
S4
1 0 0
1 0 0
x x x 0
x x x 1
1 1 0
1 0 1
S5
1 0 1
x x x x
0 0 0
S6
1 1 0
x x x x
1 1 0
S7
1 1 1
x x x x
0 0 0
(d)
DG1
D
Q
Q'
DG2
D
Q
Q'
DG3
D
Q
S0
S1
S2
S3
S4
S5
S6
S7
Q'
Clock
Reset
DG1 = F'S2 + S4 + S6
DG2 = x'yS0 + S1 + FS2 + E'S4 + S6
DG3 = xS0 + FS2 + ES4 + S6
(e)
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Present
state
G1 G2 G3
Next
state
G1 G2 G3
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 1 0
x’y’
x
x’y
0 0 1
0 1 0
0 1 0
0 1 0
Input
conditions
Mux1
Mux2
Mux3
0
x'y
x
None
0
1
0
1 0 0
0 1 1
F’
F’
F'
F
F
0 1 1
0 0 0
None
0
0
0
1 0 0
1 0 0
1 1 0
1 0 1
E’
E’
1
E'
E
1 0 1
0 0 0
None
0
0
0
1 1 0
1 1 0
None
1
1
1
1 1 1
0 0 0
None
0
0
0
(f)
F'
0
1
x'
y
F
E'
1
0
x
0
F
E
1
0 s2 s1 s0
1 8x1
2
3 Mux
4
5
6
7
D
Q
G3
Q'
0 s2 s1 s0
1
2 8x1
3
4 Mux
5
6
7
D
0 s2 s1 s0
1
2 8x1
3
4 Mux
5
6
7
D
S0
S1
Q
G2
Q'
Q
3 x 8 S2
S
Decoder S34
S5
S6
S7
G1
Q'
Clock
reset_b
(g)
module Controller_8_29g (input x, y, E, F, clock, reset_b);
supply0 GND;
supply1 VCC;
mux_8x1 M3 (m3, GND, GND, F_bar, GND, VCC, GND, VCC, GND, G3, G2, G1);
mux_8x1 M2 (m2, w1, VCC, F, GND, E_bar, GND, VCC, GND, G3, G2, G1);
mux_8x1 M1 (m1, x, GND, F, GND, E, GND, VCC, GND, G3, G2, G1);
DFF_8_28g DM3 (G3, m3, clock, reset_b);
DFF_8_28g DM2 (G2, m2, clock, reset_b);
DFF_8_28g DM1 (G1, m1, clock, reset_b);
decoder_3x8 M0_D (y0, y1, y2, y3, y4, y5, y6, y7, G3, G2, G1);
Digital
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and (w1, x_bar, y);
not (F_bar, F);
not (E_bar, E);
not (x_bar, x);
endmodule
// Test plan: Exercise all paths of the ASM chart
module t_Controller_8_29g ();
reg x, y, E, F, clock, reset_b;
Controller_8_29g M0 (x, y, E, F, clock, reset_b);
wire [2: 0] state = {M0.G3, M0.G2, M0.G1};
initial #500 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial begin end
initial fork
reset_b = 0; #2 reset_b = 1;
#0 begin x = 1; y = 1; E = 1; F = 1; end // Path: S_0, S_1, S_2, S_34
#80 reset_b = 0; #92 reset_b = 1;
#90 begin x = 1; y = 1; E = 1; F = 0; end
#150 reset_b = 0;
#152 reset_b = 1;
#150 begin x = 1; y = 1; E = 0; F = 0; end // Path: S_0, S_1, S_2, S_4, S_5
#200 reset_b = 0;
#202 reset_b = 1;
#190 begin x = 1; y = 1; E = 0; F = 0; end // Path: S_0, S_1, S_2, S_4, S_6, S_7
#250 reset_b = 0;
#252 reset_b = 1;
#240 begin x = 0; y = 0; E = 0; F = 0; end // Path: S_0
#290 reset_b = 0;
#292 reset_b = 1;
#280 begin x = 0; y = 1; E = 0; F = 0; end // Path: S_0, S_2, S_4, S_6, S_7
#360 reset_b = 0;
#362 reset_b = 1;
#350 begin x = 0; y = 1; E = 1; F = 0; end // Path: S_0, S_2, S_4, S_5
#420 reset_b = 0;
#422 reset_b = 1;
#410 begin x = 0; y = 1; E = 0; F = 1; end // Path: S_0, S_2, S_3
join
endmodule
module mux_8x1 (output reg y, input x0, x1, x2, x3, x4, x5, x6, x7, s2, s1, s0);
always @ (x0, x1, x2, x3, x4, x5, x6, x7, s0, s1, s2)
case ({s2, s1, s0})
3'b000: y = x0;
3'b001: y = x1;
3'b010: y = x2;
3'b011: y = x3;
3'b100: y = x4;
3'b101: y = x5;
3'b110: y = x6;
3'b111: y = x7;
endcase
endmodule
module DFF_8_28g (output reg q, input data, clock, reset_b);
always @ (posedge clock, negedge reset_b)
if (!reset_b) q <= 1'b0; else q <= data;
endmodule
module decoder_3x8 (output reg y0, y1, y2, y3, y4, y5, y6, y7, input x2, x1, x0);
Digital
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always @ (x0, x1, x2) begin
{y7, y6, y5, y4, y3, y2, y1, y0} = 8'b0;
case ({x2, x1, x0})
3'b000: y0= 1'b1;
3'b001: y1= 1'b1;
3'b010: y2= 1'b1;
3'b011: y3= 1'b1;
3'b100: y4= 1'b1;
3'b101: y5= 1'b1;
3'b110: y6= 1'b1;
3'b111: y7= 1'b1;
endcase
end
endmodule
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Path: S_0, S_1, S_2, S_3 and Path: S_0, S_1, S_2, S_4, S_5
Name
0
30
60
90
120
clock
reset_b
x
y
E
F
state[2:0]
0
1
2
3
0
1
2
3
0
1
2
4
5
0
Path: S_0, S_1, S_2, S_4, S_6, S_7
Name
120
150
180
210
240
clock
reset_b
x
y
E
F
state[2:0]
4
5
0
1
0
1
2
4
6
7
0
1
2
4
6
7
0
Path: S_0 and Path , S_0, S_2, S_4, S_6, S_7
Name
240
270
300
330
360
clock
reset_b
x
y
E
F
state[2:0]
6
7
0
2
0
2
4
6
7
0
2
4
0
2
4
Path: S_0, S_2, S_4, S_5 and path S_0, S_2, S_3
Name
324
354
384
414
444
clock
reset_b
x
y
E
F
state[2:0]
7
0
2
4
0
2
4
5
0
2
3
0
2
3
0
(h)
module Controller_8_29h (input x, y, E, F, clock, reset_b);
parameter S_0 = 3'b000, S_1 = 3'b001, S_2 = 3'b010,
S_3 = 3'b011, S_4 = 3'b100, S_5 = 3'b101, S_6 = 3'b110, S_7 = 3'b111;
reg [2: 0 ] state, next_state;
always @ (posedge clock, negedge reset_b)
if (!reset_b) state <= S_0; else state <= next_state;
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310
always @ (state, x, y, E, F) begin
case (state)
S_0:
if (x) next_state = S_1;
else next_state = y ? S_2: S_0;
S_1:
next_state = S_2;
S_2:
if (F) next_state = S_3; else next_state = S_4;
S_3, S_5, S_7: next_state = S_0;
S_4:
if (E) next_state = S_5; else next_state = S_6;
S_6:
next_state = S_7;
default:
next_state = S_0;
endcase
end
endmodule
// Test plan: Exercise all paths of the ASM chart
module t_Controller_8_29h ();
reg x, y, E, F, clock, reset_b;
Controller_8_29h M0 (x, y, E, F, clock, reset_b);
initial #500 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial begin end
initial fork
reset_b = 0; #2 reset_b = 1;
#20 begin x = 1; y = 1; E = 1; F = 1; end // Path: S_0, S_1, S_2, S_34
#80 reset_b = 0; #92 reset_b = 1;
#90 begin x = 1; y = 1; E = 1; F = 0; end
#150 reset_b = 0;
#152 reset_b = 1;
#150 begin x = 1; y = 1; E = 0; F = 0; end // Path: S_0, S_1, S_2, S_4, S_5
#200 reset_b = 0;
#202 reset_b = 1;
#190 begin x = 1; y = 1; E = 0; F = 0; end // Path: S_0, S_1, S_2, S_4, S_6, S_7
#250 reset_b = 0;
#252 reset_b = 1;
#240 begin x = 0; y = 0; E = 0; F = 0; end // Path: S_0
#290 reset_b = 0;
#292 reset_b = 1;
#280 begin x = 0; y = 1; E = 0; F = 0; end // Path: S_0, S_2, S_4, S_6, S_7
#360 reset_b = 0;
#362 reset_b = 1;
#350 begin x = 0; y = 1; E = 1; F = 0; end // Path: S_0, S_2, S_4, S_5
#420 reset_b = 0;
#422 reset_b = 1;
#410 begin x = 0; y = 1; E = 0; F = 1; end // Path: S_0, S_2, S_3
join
endmodule
Note: Simulation results match those for 8.39g.
8.30
8.31
(a) E = 1
(b) E = 0
A = 0110, B = 0010, C = 0000.
A * B = 1100
A | B = 0110
A + B = 1000
A ∧ B = 0100
A – B = 0100
&A = 0
~ C = 1111
~|C = 1
A & B = 0010
A || B = 1
A && C = 0
|A=1
AB=1
A != B = 1
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311
8.32
4
+
S1
4-bit
Counter
select
S2
4
R1
count
load
R2
4
Mux
select = S1
load = S1 + S'1S'2
count = S'1S2
clock
8.33
Assume that the states are encoded one-hot as T0, T1, T2,
T3. The select lines of the mux are generated as:
s1 = T2 + T3
s0 = T1 + T3
The signal to load R4 can be generated by the host
processor or by:
load = T0 + T1 + T2 + T3.
R1
R2
R3
T0
T1
T2
T3
8
8
8
8
0
1
8
Mux
Register
8
R4
2
3
s1 s0
load
R0
4x2
Encoder
load
clock
8.34
(a)
module Datapath_BEH
#(parameter dp_width = 8, R2_width = 4)
(
output [R2_width -1: 0] count, output reg E, output Zero, input [dp_width -1: 0] data,
input Load_regs, Shift_left, Incr_R2, clock, reset_b);
reg [dp_width -1: 0] R1;
reg [R2_width -1: 0] R2;
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312
assign count = R2;
assign Zero = ~(| R1);
always @ (posedge clock) begin
E <= R1[dp_width -1] & Shift_left;
if (Load_regs) begin R1 <= data; R2 <= {R2_width{1'b1}}; end
if (Shift_left) {E, R1} <= {E, R1} << 1;
if (Incr_R2) R2 <= R2 + 1;
end
endmodule
// Test Plan for Datapath Unit:
// Demonstrate action of Load_regs
//
R1 gets data, R2 gets all ones
// Demonstrate action of Incr_R2
// Demonstrate action of Shift_left and detect E
// Test bench for datapath
module t_Datapath_Unit
#(parameter dp_width = 8, R2_width = 4)
( );
wire [R2_width -1: 0] count;
wire
E, Zero;
reg [dp_width -1: 0] data;
reg
Load_regs, Shift_left, Incr_R2, clock, reset_b;
Datapath_BEH M0 (count, E, Zero, data, Load_regs, Shift_left, Incr_R2, clock, reset_b);
initial #250 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial begin reset_b = 0; #2 reset_b = 1; end
initial fork
data = 8'haa;
Load_regs = 0;
Incr_R2 = 0;
Shift_left = 0;
#10 Load_regs = 1;
#20 Load_regs = 0;
#50 Incr_R2 = 1;
#120 Incr_R2 = 0;
#90 Shift_left = 1;
#200 Shift_left = 0;
join
endmodule
Note: The simulation results show tests of the operations of the datapath independent of the control unit, so
count does not represent the number of ones in the data.
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313
R1gets data and R2 gets all ones
Name
0
60
120
180
clock
reset_b
R2 increments while
Incr_R2 is asserted
R1 shifts left
Zero asserts
Load_regs
Incr_R2
Shift_left
Note that E matches previous
value of R1[7]
Zero
E
aa
data[7:0]
R1[7:0]
xx
aa
54
a8
50
a0
40
80
00
R1[7]
R1[6]
R1[5]
R1[4]
R1[3]
R1[2]
R1[1]
R1[0]
R2[3:0]
x
f
0
1
2
3
4
5
6
count[3:0]
x
f
0
1
2
3
4
5
6
(b) // Control Unit
module Controller_BEH (
output
Ready,
output reg Load_regs,
output
Incr_R2, Shift_left,
input
Start, Zero, E, clock, reset_b
);
parameter S_idle = 0, S_1 = 1, S_2 = 2, S_3 = 3;
reg [1:0] state, next_state;
assign Ready = (state == S_idle);
assign Incr_R2 = (state == S_1);
assign Shift_left = (state == S_2);
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) state <= S_idle;
else state <= next_state;
always @ (state, Start, Zero, E) begin
Load_regs = 0;
case (state)
S_idle:
if (Start) begin Load_regs = 1; next_state = S_1; end
else next_state = S_idle;
S_1:
if (Zero) next_state = S_idle; else next_state = S_2;
S_2:
S_3:
endcase
end
endmodule
next_state = S_3;
if (E) next_state = S_1; else next_state = S_2;
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314
// Test plan for Control Unit
// Verify that state enters S_idle with reset_b asserted.
// With reset_b de-asserted, verify that state enters S_1 and asserts Load_Regs when
// Start is asserted.
// Verify that Incr_R2 is asserted in S_1.
// Verify that state returns to S_idle from S_1 if Zero is asserted.
// Verify that state goes to S_2 if Zero is not asserted.
// Verify that Shift_left is asserted in S_2.
// Verify that state goes to S_3 from S_2 unconditionally.
// Verify that state returns to S_2 from S_3 id E is not asserted.
// Verify that state goes to S_1 from S_3 if E is asserted.
// Test bench for Control Unit
module t_Control_Unit ();
wire Ready, Load_regs, Incr_R2, Shift_left;
reg Start, Zero, E, clock, reset_b;
Controller_BEH M0 (Ready, Load_regs, Incr_R2, Shift_left, Start, Zero, E, clock, reset_b);
initial #250 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial begin reset_b = 0; #2 reset_b = 1; end
initial fork
Zero = 1;
E = 0;
Start = 0;
#20 Start = 1; // Cycle from S_idle to S_1
#80 Start = 0;
#70 Zero = 0; // S_idle to S_1 to S_2 to S_3 and cycle to S_2.
#130 E = 1; // Cycle to S_3 to S_1 to S_2 to S_3
#150 Zero = 1; // Return to S_idle
join
endmodule
Go to S_1 and cyle to
S_idle while Zero = 1
Name
Go to S_2 and cyle
to S_3 while E = 0
0
Go to S_1 and cyle to
S_3 while Zero = 0
Return to S_idle
70
140
210
clock
reset_b
Start
Zero
E
state[1:0]
0
1
0
1
0
1
2
3
2
3
2
3
1
2
3
1
0
Ready
Load_regs
Incr_R2
Shift_left
Ready asserts while Load_regs asserts while Incr_R2 asserts while state = S_1
state = S_idle
state = S_idle and Start = 1
Shift_left asserts while state = S_2
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315
(c)
// Integrated system
module Count_Ones_BEH_BEH
# (parameter dp_width = 8, R2_width = 4)
(
output [R2_width -1: 0]
count,
input [dp_width -1: 0] data,
input
Start, clock, reset_b
);
wire Load_regs, Incr_R2, Shift_left, Zero, E;
Controller_BEH M0 (Ready, Load_regs, Incr_R2, Shift_left, Start, Zero, E, clock, reset_b);
Datapath_BEH M1 (count, E, Zero, data, Load_regs, Shift_left, Incr_R2, clock, reset_b);
endmodule
// Test plan for integrated system
// Test for data values of 8'haa, 8'h00, 8'hff.
// Test bench for integrated system
module t_count_Ones_BEH_BEH ();
parameter dp_width = 8, R2_width = 4;
wire [R2_width -1: 0] count;
reg [dp_width -1: 0] data;
reg Start, clock, reset_b;
Count_Ones_BEH_BEH M0 (count, data, Start, clock, reset_b);
initial #700 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial begin reset_b = 0; #2 reset_b = 1; end
initial fork
data = 8'haa;
// Expect count = 4
Start = 0;
#20 Start = 1;
#30 Start = 0;
#40 data = 8'b00; // Expect count = 0
#250 Start = 1;
#260 Start = 0;
#280 data = 8'hff;
#280 Start = 1;
#290 Start = 0;
join
endmodule
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316
Name
0
70
140
210
clock
reset_b
Ready
Start
Load_regs
Incr_R2
Shift_left
Zero
E
0
state[1:0]
1
3
1
2
3
2
3
1
2
3
2
3
aa
data[7:0]
R1[7:0]
xx
R2[3:0]
x
count[3:0]
x
Name
2
1
2
3
2
3
1
0
00
aa
f
54
a8
50
a0
40
80
00
0
1
2
3
4
0
1
2
3
4
188
248
308
368
clock
reset_b
Ready
Start
Load_regs
Incr_R2
Shift_left
Zero
E
state[1:0]
2
3
1
0
1
0
1
2
3
1
2
3
00
data[7:0]
2
3
1
2
3
ff
00
R1[7:0]
1
ff
fe
fc
f8
f0
R2[3:0]
3
4
f
0
f
0
1
2
3
count[3:0]
3
4
15
0
15
0
1
2
3
Digital
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317
Name
258
318
378
438
498
558
clock
reset_b
Ready
Start
Load_regs
Incr_R2
Shift_left
Zero
E
state[1:0]
1
2
3
1
2
3
1
2
3
1
2
3
1
f
2
3
1
2
3
1
2
3
1
2
3
1
0
ff
00
R1[7:0]
count[3:0]
1
00
data[7:0]
R2[3:0]
0
ff
fe
fc
f8
f0
e0
c0
80
00
0
f
0
1
2
3
4
5
6
7
8
0
15
0
1
2
3
4
5
6
7
8
(d)
// One-Hot Control unit
module Controller_BEH_1Hot
(
output
Ready,
output reg Load_regs,
output
Incr_R2, Shift_left,
input
Start, Zero, E, clock, reset_b
);
parameter S_idle = 4'b001, S_1 = 4'b0010, S_2 = 4'b0100, S_3 = 4'b1000;
reg [3:0] state, next_state;
assign Ready = (state == S_idle);
assign Incr_R2 = (state == S_1);
assign Shift_left = (state == S_2);
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) state <= S_idle;
else state <= next_state;
always @ (state, Start, Zero, E) begin
Load_regs = 0;
case (state)
S_idle: if (Start) begin Load_regs = 1; next_state = S_1; end
else next_state = S_idle;
S_1: if (Zero) next_state = S_idle; else next_state = S_2;
S_2: next_state = S_3;
S_3: if (E) next_state = S_1; else next_state = S_2;
endcase
end
endmodule
Note: Test plan, test bench and simulation results are same as (b), but with states numbered with one-hot
codes.
(e)
// Integrated system with one-hot controller
module Count_Ones_BEH_1Hot
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# (parameter dp_width = 8, R2_width = 4)
(
output [R2_width -1: 0]
count,
input [dp_width -1: 0]
data,
input
Start, clock, reset_b
);
wire Load_regs, Incr_R2, Shift_left, Zero, E;
Controller_BEH_1Hot M0 (Ready, Load_regs, Incr_R2, Shift_left, Start, Zero, E, clock, reset_b);
Datapath_BEH M1 (count, E, Zero, data, Load_regs, Shift_left, Incr_R2, clock, reset_b);
endmodule
Note: Test plan, test bench and simulation results are same as (c), but with states numbered with one-hot
codes.
8.35
Note: Signal Start is initialized to 0 when the simulation begins. Otherwise, the state of the structural model
will become X at the first clock after the reset condition is deasserted, with Start and Load_Regs having
unknown values. In this condition the structural model cannot operate correctly.
0
Name
30
60
clock
reset_b
Start
Load_regs
Shift_left
Incr_R2
Zero
Ready
x
state[1:0]
0
X
data[7:0]
ff
count[3:0]
x
module Count_Ones_STR_STR (count, Ready, data, Start, clock, reset_b);
// Mux – decoder implementation of control logic
// controller is structural
// datapath is structural
parameter
output
output
input
input
wire
R1_size = 8, R2_size = 4;
[R2_size -1: 0]
count;
Ready;
[R1_size -1: 0]
data;
Start, clock, reset_b;
Load_regs, Shift_left, Incr_R2, Zero, E;
Controller_STR M0 (Ready, Load_regs, Shift_left, Incr_R2, Start, E, Zero, clock, reset_b);
Datapath_STR M1 (count, E, Zero, data, Load_regs, Shift_left, Incr_R2, clock);
endmodule
module Controller_STR (Ready, Load_regs, Shift_left, Incr_R2, Start, E, Zero, clock, reset_b);
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output
output
input
input
input
supply0
supply1
parameter
wire
wire
wire
Ready;
Load_regs, Shift_left, Incr_R2;
Start;
E, Zero;
clock, reset_b;
GND;
PWR;
S0 = 2'b00, S1 = 2'b01, S2 = 2'b10, S3 = 2'b11; // Binary code
Load_regs, Shift_left, Incr_R2;
G0, G0_b, D_in0, D_in1, G1, G1_b;
Zero_b = ~Zero;
wire
E_b = ~E;
wire [1:0]select = {G1, G0};
wire [0:3]Decoder_out;
assign
Ready = ~Decoder_out[0];
assign
Incr_R2 = ~Decoder_out[1];
assign
Shift_left = ~Decoder_out[2];
and
(Load_regs, Ready, Start);
mux_4x1_beh
Mux_1 (D_in1, GND, Zero_b, PWR, E_b, select);
mux_4x1_beh
Mux_0
(D_in0, Start, GND, PWR, E, select);
D_flip_flop_AR_b M1
(G1, G1_b, D_in1, clock, reset_b);
D_flip_flop_AR_b M0
(G0, G0_b, D_in0, clock, reset_b);
decoder_2x4_df
M2
(Decoder_out, G1, G0, GND);
endmodule
module Datapath_STR (count, E, Zero, data, Load_regs, Shift_left, Incr_R2, clock);
parameter
R1_size = 8, R2_size = 4;
output [R2_size -1: 0] count;
output
E, Zero;
input [R1_size -1: 0] data;
input
Load_regs, Shift_left, Incr_R2, clock;
wire [R1_size -1: 0] R1;
supply0
Gnd;
supply1
Pwr;
assign
Zero = (R1 == 0);
Shift_Reg
Counter
D_flip_flop_AR
and
(
endmodule
M1
M2
M3
(R1, data, Gnd, Shift_left, Load_regs, clock, Pwr);
(count, Load_regs, Incr_R2, clock, Pwr);
(E, w1, clock, Pwr);
w1, R1[R1_size -1], Shift_left);
module Shift_Reg (R1, data, SI_0, Shift_left, Load_regs, clock, reset_b);
parameter
R1_size = 8;
output [R1_size -1: 0] R1;
input [R1_size -1: 0] data;
input
SI_0, Shift_left, Load_regs;
input
clock, reset_b;
reg [R1_size -1: 0]
R1;
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) R1 <= 0;
else begin
if (Load_regs) R1 <= data; else
if (Shift_left) R1 <= {R1[R1_size -2:0], SI_0}; end
endmodule
module Counter (R2, Load_regs, Incr_R2, clock, reset_b);
parameter
R2_size = 4;
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output [R2_size -1: 0]
input
input
reg [R2_size -1: 0]
R2;
Load_regs, Incr_R2;
clock, reset_b;
R2;
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) R2 <= 0;
else if (Load_regs) R2 <= {R2_size {1'b1}}; // Fill with 1
else if (Incr_R2 == 1) R2 <= R2 + 1;
endmodule
module D_flip_flop_AR (Q, D, CLK, RST);
output Q;
input
D, CLK, RST;
reg
Q;
always @ (posedge CLK, negedge RST)
if (RST == 0) Q <= 1'b0;
else Q <= D;
endmodule
module D_flip_flop_AR_b (Q, Q_b, D, CLK, RST);
output Q, Q_b;
input
D, CLK, RST;
reg
Q;
assign
Q_b = ~Q;
always @ (posedge CLK, negedge RST)
if (RST == 0) Q <= 1'b0;
else Q <= D;
endmodule
// Behavioral description of 4-to-1 line multiplexer
// Verilog 2005 port syntax
module mux_4x1_beh
( output reg m_out,
input
in_0, in_1, in_2, in_3,
input [1: 0] select
);
always @ (in_0, in_1, in_2, in_3, select) // Verilog 2005 syntax
case (select)
2'b00: m_out = in_0;
2'b01: m_out = in_1;
2'b10: m_out = in_2;
2'b11: m_out = in_3;
endcase
endmodule
// Dataflow description of 2-to-4-line decoder
// See Fig. 4.19. Note: The figure uses symbol E, but the
// Verilog model uses enable to clearly indicate functionality.
module decoder_2x4_df (D, A, B, enable);
output [0: 3] D;
input
input
A, B;
enable;
assign D[0] = ~(~A & ~B & ~enable),
D[1] = ~(~A & B & ~enable),
D[2] = ~(A & ~B & ~enable),
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D[3] = ~(A & B & ~enable);
endmodule
module t_Count_Ones;
parameter R1_size = 8, R2_size = 4;
wire [R2_size -1: 0]
R2;
wire [R2_size -1: 0]
count;
wire
Ready;
reg [R1_size -1: 0]
data;
reg
Start, clock, reset_b;
wire [1: 0] state;
// Use only for debug
assign state = {M0.M0.G1, M0.M0.G0};
Count_Ones_STR_STR M0 (count, Ready, data, Start, clock, reset_b);
initial #4000 $finish;
initial begin clock = 0; #5 forever #5 clock = ~clock; end
initial fork
Start = 0;
#1 reset_b = 1;
#3 reset_b = 0;
#4 reset_b = 1;
data = 8'Hff;
# 25 Start = 1;
# 35 Start = 0;
#310 data = 8'h0f;
#310 Start = 1;
#320 Start = 0;
#610 data = 8'hf0;
#610 Start = 1;
#620 Start = 0;
#910 data = 8'h00;
#910 Start = 1;
#920 Start = 0;
#1210 data = 8'haa;
#1210 Start = 1;
#1220 Start = 0;
#1510 data = 8'h0a;
#1510 Start = 1;
#1520 Start = 0;
#1810 data = 8'ha0;
#1810 Start = 1;
#1820 Start = 0;
#2110 data = 8'h55;
#2110 Start = 1;
#2120 Start = 0;
#2410 data = 8'h05;
#2410 Start = 1;
#2420 Start = 0;
#2710 data = 8'h50;
#2710 Start = 1;
#2720 Start = 0;
#3010 data = 8'ha5;
#3010 Start = 1;
#3020 Start = 0;
#3310 data = 8'h5a;
#3310 Start = 1;
#3320 Start = 0;
join
endmodule
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322
Name
2184
2324
2464
2604
2744
2884
clock
reset_b
Start
Load_regs
Shift_left
Incr_R2
Zero
Ready
0
state[1:0]
55
data[7:0]
count[3:0]
8.36
0
1
2
0
05
3
4
0
50
1
2
0
1
2
Note: See Prob. 8.35 for a behavioral model of the datapath unit, Prob. 8.36d for a one-hot control unit.
(a) T0, T1, T2, T3 be asserted when the state is in S_idle, S_1, S_2, and S_3, respectively. Let D0, D1, D2, and
D3 denote the inputs to the one-hot flip-flops.
D0 = T0 Start' + T1 Zero
D1 = T0 Start + T3 E
D2 = T1 Zero' + T3 E'
D3 = T2
(b) Gate-level one-hot controller
module Controller_Gates_1Hot
(
output
Ready,
output
Load_regs, Incr_R2, Shift_left,
input
Start, Zero, E, clock, reset_b
);
wire w1, w2, w3, w4, w5, w6;
wire T0, T1, T2, T3;
wire set;
assign Ready = T0;
assign Incr_R2 = T1;
assign Shift_left = T2;
and (Load_regs, T0, Start);
not (set, reset_b);
DFF_S M0 (T0, D0, clock, set);
// Note: reset action must initialize S_idle = 4'b0001
DFF M1 (T1, D1, clock, reset_b);
DFF M2 (T2, D2, clock, reset_b);
DFF M3 (T3, D3, clock, reset_b);
not (Start_b, Start);
and (w1, T0, Start_b);
and (w2, T1, Zero);
or (D0, w1, w2);
Digital
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323
and (w3, T0, Start);
and (w4, T3, E);
or (D1, w3, w4);
not (Zero_b, Zero);
not (E_b, E);
and (w5, T1, Zero_b);
and (w6, T3, E_b);
or (D2, w5, w6);
buf (D3, T2);
endmodule
module DFF (output reg Q, input D, clock, reset_b);
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) Q <= 0;
else Q <= D;
endmodule
module DFF_S (output reg Q, input D, clock, set);
always @ (posedge clock, posedge set)
if (set == 1) Q <= 1;
else Q <= D;
endmodule
(c)
// Test plan for Control Unit
// Verify that state enters S_idle with reset_b asserted.
// With reset_b de-asserted, verify that state enters S_1 and asserts Load_Regs when
// Start is asserted.
// Verify that Incr_R2 is asserted in S_1.
// Verify that state returns to S_idle from S_1 if Zero is asserted.
// Verify that state goes to S_2 if Zero is not asserted.
// Verify that Shift_left is asserted in S_2.
// Verify that state goes to S_3 from S_2 unconditionally.
// Verify that state returns to S_2 from S_3 id E is not asserted.
// Verify that state goes to S_1 from S_3 if E is asserted.
// Test bench for One-Hot Control Unit
module t_Control_Unit ();
wire Ready, Load_regs, Incr_R2, Shift_left;
reg Start, Zero, E, clock, reset_b;
wire [3: 0] state = {M0.T3, M0.T2, M0.T1, M0.T0};
// Observe one-hot state bits
Controller_Gates_1Hot M0 (Ready, Load_regs, Incr_R2, Shift_left, Start, Zero, E, clock, reset_b);
initial #250 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial begin reset_b = 0; #2 reset_b = 1; end
initial fork
Zero = 1;
E = 0;
Start = 0;
#20 Start = 1; // Cycle from S_idle to S_1
#80 Start = 0;
#70 Zero = 0;
// S_idle to S_1 to S_2 to S_3 and cycle to S_2.
#130 E = 1;
// Cycle to S_3 to S_1 to S_2 to S_3
#150 Zero = 1; // Return to S_idle
join
endmodule
Note: simulation results match those for Prob. 8.34(d). See Prob. 8.34(c) for annotations.
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324
0
Name
60
120
180
Default
clock
reset_b
Start
Zero
E
1
state[3:0]
2
1
2
1
2
4
8
4
8
4
8
2
4
8
2
1
Ready
Load_regs
Incr_R2
Shift_left
(d) Datapath unit detail:
s1 = Shift_regs + Load_regs' Shift_regs'
s0 = Load_regs + Load_regs' Shift_regs'
Zero
8
R1
0
8
data
1
8
R1 << 1
8
R1
4x1
Mux
2
3
8
s1 s0
Register
(D-type
Flipflops)
8
R1
R1_7
D
Q
E
Q'
Shift_regs
clk
Load_regs
clock
4
0
4'b0001
+
1
2x1
Mux
sel
Register
(D-type
Flipflops)
R2
Incr_R2
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// Datapath unit – structural model
module Datapath_STR
#(parameter dp_width = 8, R2_width = 4)
(
output [R2_width -1: 0] count, output E, output Zero, input [dp_width -1: 0] data,
input Load_regs, Shift_left, Incr_R2, clock, reset_b);
supply1 pwr;
supply0 gnd;
wire [dp_width -1: 0] R1_Dbus, R1;
wire [R2_width -1: 0] R2_Dbus;
wire DR1_0, DR1_1, DR1_2, DR1_3, DR1_4, DR1_5, DR1_6, DR1_7;
wire R1_0, R1_1, R1_2, R1_3, R1_4, R1_5, R1_6, R1_7;
wire R2_0, R2_1, R2_2, R2_3;
wire [R2_width -1: 0] R2 = {R2_3, R2_2, R2_1, R2_0};
assign count = {R2_3, R2_2, R2_1, R2_0};
assign R1 = { R1_7, R1_6, R1_5, R1_4, R1_3, R1_2, R1_1, R1_0};
assign DR1_0 = R1_Dbus[0];
assign DR1_1 = R1_Dbus[1];
assign DR1_2 = R1_Dbus[2];
assign DR1_3 = R1_Dbus[3];
assign DR1_4 = R1_Dbus[4];
assign DR1_5 = R1_Dbus[5];
assign DR1_6 = R1_Dbus[6];
assign DR1_7 = R1_Dbus[7];
nor (Zero, R1_0, R1_1, R1_2, R1_3, R1_4, R1_5, R1_6, R1_7);
DFF D_E (E, R1_7, clock, pwr);
DFF DF_0 (R1_0, DR1_0, clock, pwr);
DFF DF_1 (R1_1, DR1_1, clock, pwr);
DFF DF_2 (R1_2, DR1_2, clock, pwr);
DFF DF_3 (R1_3, DR1_3, clock, pwr);
DFF DF_4 (R1_4, DR1_4, clock, pwr);
DFF DF_5 (R1_5, DR1_5, clock, pwr);
DFF DF_6 (R1_6, DR1_6, clock, pwr);
DFF DF_7 (R1_7, DR1_7, clock, pwr);
// Disable reset
DFF_S DR_0 (R2_0, DR2_0, clock, Load_regs); // Load_regs (set) drives R2 to all ones
DFF_S DR_1 (R2_1, DR2_1, clock, Load_regs);
DFF_S DR_2 (R2_2, DR2_2, clock, Load_regs);
DFF_S DR_3 (R2_3, DR2_3, clock, Load_regs);
assign DR2_0 = R2_Dbus[0];
assign DR2_1 = R2_Dbus[1];
assign DR2_2 = R2_Dbus[2];
assign DR2_3 = R2_Dbus[3];
wire [1: 0] sel = {Shift_left, Load_regs};
wire [dp_width -1: 0] R1_shifted = {R1_6, R1_5, R1_4, R1_3, R1_2, R1_1, R1_0, 1'b0};
wire [R2_width -1: 0] sum = R2 + 4'b0001;
Mux8_4_x_1 M0 (R1_Dbus, R1, data, R1_shifted, R1, sel);
Mux4_2_x_1 M1 (R2_Dbus, R2, sum, Incr_R2);
endmodule
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module Mux8_4_x_1 #(parameter dp_width = 8) (output reg [dp_width -1: 0] mux_out,
input [dp_width -1: 0] in0, in1, in2, in3, input [1: 0] sel);
always @ (in0, in1, in2, in3, sel)
case (sel)
2'b00: mux_out = in0;
2'b01: mux_out = in1;
2'b10: mux_out = in2;
2'b11: mux_out = in3;
endcase
endmodule
module Mux4_2_x_1 #(parameter dp_width = 4) (output [dp_width -1: 0] mux_out,
input [dp_width -1: 0] in0, in1, input sel);
assign mux_out = sel ? in1: in0;
endmodule
// Test Plan for Datapath Unit:
// Demonstrate action of Load_regs
//
R1 gets data, R2 gets all ones
// Demonstrate action of Incr_R2
// Demonstrate action of Shift_left and detect E
// Test bench for datapath
module t_Datapath_Unit
#(parameter dp_width = 8, R2_width = 4)
( );
wire [R2_width -1: 0] count;
wire
E, Zero;
reg [dp_width -1: 0] data;
reg
Load_regs, Shift_left, Incr_R2, clock, reset_b;
Datapath_STR M0 (count, E, Zero, data, Load_regs, Shift_left, Incr_R2, clock, reset_b);
initial #250 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial begin reset_b = 0; #2 reset_b = 1; end
initial fork
data = 8'haa;
Load_regs = 0;
Incr_R2 = 0;
Shift_left = 0;
#10 Load_regs = 1;
#20 Load_regs = 0;
#50 Incr_R2 = 1;
#120 Incr_R2 = 0;
#90 Shift_left = 1;
#200 Shift_left = 0;
join
endmodule
// Integrated system
module Count_Ones_Gates_1_Hot_STR
# (parameter dp_width = 8, R2_width = 4)
(
output [R2_width -1: 0] count,
input [dp_width -1: 0] data,
input
Start, clock, reset_b
);
wire Load_regs, Incr_R2, Shift_left, Zero, E;
Controller_Gates_1Hot M0 (Ready, Load_regs, Incr_R2, Shift_left, Start, Zero, E, clock, reset_b);
Datapath_STR M1 (count, E, Zero, data, Load_regs, Shift_left, Incr_R2, clock, reset_b);
endmodule
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// Test plan for integrated system
// Test for data values of 8'haa, 8'h00, 8'hff.
// Test bench for integrated system
module t_count_Ones_Gates_1_Hot_STR ();
parameter dp_width = 8, R2_width = 4;
wire [R2_width -1: 0] count;
reg [dp_width -1: 0] data;
reg Start, clock, reset_b;
wire [3: 0] state = {M0.M0.T3, M0.M0.T2, M0.M0.T1, M0.M0.T0};
Count_Ones_Gates_1_Hot_STR M0 (count, data, Start, clock, reset_b);
initial #700 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial begin reset_b = 0; #2 reset_b = 1; end
initial fork
data = 8'haa;
// Expect count = 4
Start = 0;
#20 Start = 1;
#30 Start = 0;
#40 data = 8'b00;
// Expect count = 0
#250 Start = 1;
#260 Start = 0;
#280 data = 8'hff;
#280 Start = 1;
#290 Start = 0;
join
endmodule
Note: The simulation results show tests of the operations of the datapath independent of the control unit, so
count does not represent the number of ones in the data.
Name
0
60
120
180
clock
reset_b
Load_regs
Incr_R2
Shift_left
Zero
E
aa
data[7:0]
R1[7:0]
xx
aa
54
a8
50
a0
40
80
00
R1[7]
R1[6]
R1[5]
R1[4]
R1[3]
R1[2]
R1[1]
R1[0]
R2[3:0]
x
f
0
1
2
3
4
5
6
count[3:0]
x
f
0
1
2
3
4
5
6
Digital
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Simulations results for the integrated system match those shown in Prob. 8.34(e). See those results for
additional annotation.
Name
0
150
300
450
600
clock
reset_b
Ready
Start
Load_regs
Shift_left
Incr_R2
Zero
E
state[3:0]
1
aa
data[7:0]
8.37
1
1
1
00
54
50
ff
R1[7:0]
xx
40
00
ff
fe
fc
f8
f0
e0
c0
80
R2[3:0]
x
f
0
1
2
3
4
f 0 f
0
1
2
3
4
5
6
7
00
8
count[3:0]
x
f
0
1
2
3
4
f 0 f
0
1
2
3
4
5
6
7
8
(a) ASMD chart:
reset_b
S_idle
/Ready
Start
Load_regs
1
S_running
1
Zero
R1 <= data
R2 <= 0
R2 <= R2 + R1[0]
R1 <= R1 >> 1
Add_shift
(b) RTL model:
module Datapath_Unit_2_Beh #(parameter dp_width = 8, R2_width = 4)
(
output [R2_width -1: 0]
count,
output
Zero,
input [dp_width -1: 0] data,
input
Load_regs, Add_shift, clock, reset_b
);
reg [dp_width -1: 0]
R1;
reg [R2_width -1: 0]
R2;
assign count = R2;
assign Zero = ~|R1;
always @ (posedge clock, negedge reset_b)
begin
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if (reset_b == 0) begin R1 <= 0; R2 <= 0; end else begin
if (Load_regs) begin R1 <= data; R2 <= 0; end
if (Add_shift) begin R1 <= R1 >> 1; R2 <= R2 + R1[0]; end // concurrent operations
end
end
endmodule
// Test plan for datapath unit
// Verify active-low reset action
// Test for action of Add_shift
// Test for action of Load_regs
module t_Datapath_Unit_2_Beh();
parameter R1_size = 8, R2_size = 4;
wire [R2_size -1: 0]
count;
wire
Zero;
reg [R1_size -1: 0]
data;
reg
Load_regs, Add_shift, clock, reset_b;
Datapath_Unit_2_Beh M0 (count, Zero, data, Load_regs, Add_shift, clock, reset_b);
initial #1000 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial fork
#1 reset_b = 1;
#3 reset_b = 0;
#4 reset_b = 1;
join
initial fork
data = 8'haa;
Load_regs = 0;
Add_shift = 0;
#10 Load_regs = 1;
#20 Load_regs = 0;
#50 Add_shift = 1;
#150 Add_shift = 0;
join
endmodule
Note that the operations of the datapath unit are tested independent of the controller, so the actions of
Load_regs and add_shift and the value of count do not correspond to data.
Name
0
50
100
150
clock
reset_b
Load R1, flush R2
Load_regs
R1 shifts, R2 adds
Add_shift
Zero
aa
data[7:0]
R1[7:0]
00
aa
55
2a
15
0a
05
02
01
00
R2[3:0]
0
1
2
3
4
count[7:0]
0
1
2
3
4
module Controller_2_Beh (
output
Ready,
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output reg Load_regs,
Add_shift,
input
Start, Zero, clock, reset_b
);
parameter S_idle = 0, S_running = 1;
reg
state, next_state;
assign
Ready = (state == S_idle);
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) state <= S_idle;
else state <= next_state;
always @ (state, Start, Zero) begin
next_state = S_idle;
Load_regs = 0;
Add_shift = 0;
case (state)
S_idle:
S_running:
if (Start) begin Load_regs = 1; next_state = S_running; end
if (Zero) next_state = S_idle;
else begin Add_shift = 1; next_state = S_running; end
endcase
end
endmodule
module t_Controller_2_Beh ();
wire Ready, Load_regs, Add_shift;
reg Start, Zero, clock, reset_b;
Controller_2_Beh M0 (Ready, Load_regs, Add_shift, Start, Zero, clock, reset_b);
initial #250 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial begin reset_b = 0; #2 reset_b = 1; end
initial fork
Zero = 1;
Start = 0;
#20 Start = 1; // Cycle from S_idle to S_1
#80 Start = 0;
#70 Zero = 0; // S_idle to S_1 to S_idle
#90 Zero = 1; // Return to S_idle
join
endmodule
Note: The state transitions and outputs of the controller match the ASMD chart.
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Name
0
50
100
150
clock
reset_b
Ready
Start
Load_regs
Add_shift
Zero
state
module Count_of_Ones_2_Beh #(parameter dp_width = 8, R2_width = 4)
(
output [R2_width -1: 0] count,
output Ready,
input [dp_width -1: 0] data,
input Start, clock, reset_b
);
wire Load_regs, Add_shift, Zero;
Controller_2_Beh M0 (Ready, Load_regs, Add_shift, Start, Zero, clock, reset_b);
Datapath_Unit_2_Beh M1 (count, Zero, data, Load_regs, Add_shift, clock, reset_b);
endmodule
// Test plan for integrated system
// Test for data values of 8'haa, 8'h00, 8'hff.
// Test bench for integrated system
module t_Count_Ones_2_Beh ();
parameter dp_width = 8, R2_width = 4;
wire [R2_width -1: 0] count;
reg [dp_width -1: 0] data;
reg Start, clock, reset_b;
Count_of_Ones_2_Beh M0 (count, Ready, data, Start, clock, reset_b);
initial #700 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial begin reset_b = 0; #2 reset_b = 1; end
initial fork
data = 8'haa;
// Expect count = 4
Start = 0;
#20 Start = 1;
#30 Start = 0;
#40 data = 8'b00; // Expect count = 0
#120 Start = 1;
#130 Start = 0;
#140 data = 8'hff;
#160 Start = 1;
#170 Start = 0;
join
endmodule
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Name
0
60
120
180
240
clock
reset_b
Start
Load_regs
Add_shift
Zero
Ready
state
aa
data[7:0]
00
00
aa
55
2a
15
0a
05
ff
07
03
01
00
R2[3:0]
0
1
2
3
4
0
1
2
3
4
5
6
7
8
count[3:0]
0
1
2
3
4
0
1
2
3
4
5
6
7
8
R1[7:0]
02
01
00
ff
7f
3f
1f
0f
(c) T0, T1 are to be asserted when the state is in S_idle, S_running, respectively. Let D0, D1 denote the inputs to
the one-hot flip-flops.
D0 = T0 Start' + T1 Zero
D1 = T0 Start + T1 E'
(d)
Gate-level one-hot controller
module Controller_2_Gates_1Hot
(
output
Ready, Load_regs, Add_shift,
input
Start, Zero, clock, reset_b
);
wire w1, w2, w3, w4;
wire T0, T1;
wire set;
assign Ready = T0;
assign Add_shift = T1;
and (Load_regs, T0, Start);
not (set, reset_b);
DFF_S M0 (T0, D0, clock, set);
// Note: reset action must initialize S_idle = 2'b01
DFF M1 (T1, D1, clock, reset_b);
not (Start_b, Start);
not (Zero_b, Zero);
and (w1, T0, Start_b);
and (w2, T1, Zero);
or (D0, w1, w2);
and (w3, T0, Start);
and (w4, T1, Zero_b);
or (D1, w3, w4);
endmodule
module DFF (output reg Q, input D, clock, reset_b);
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) Q <= 0;
else Q <= D;
endmodule
module DFF_S (output reg Q, input D, clock, set);
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always @ (posedge clock, posedge set)
if (set == 1) Q <= 1;
else Q <= D;
endmodule
// Test plan for Control Unit
// Verify that state enters S_idle with reset_b asserted.
// With reset_b de-asserted, verify that state enters S_running and asserts Load_Regs when
// Start is asserted.
// Verify that state returns to S_idle from S_running if Zero is asserted.
// Verify that state goes to S_running if Zero is not asserted.
// Test bench for One-Hot Control Unit
module t_Control_Unit ();
wire
Ready, Load_regs, Add_shift;
reg
Start, Zero, clock, reset_b;
wire [3: 0] state = {M0.T1, M0.T0};
// Observe one-hot state bits
Controller_2_Gates_1Hot M0 (Ready, Load_regs, Add_shift, Start, Zero, clock, reset_b);
initial #250 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial begin reset_b = 0; #2 reset_b = 1; end
initial fork
Zero = 1;
Start = 0;
#20 Start = 1; // Cycle from S_idle to S_1
#80 Start = 0;
#70 Zero = 0; // S_idle to S_1 to S_idle
#90 Zero = 1; // Return to S_idle
join
endmodule
Simulation results show that the controller matches the ASMD chart.
Name
0
60
120
180
clock
reset_b
Start
Zero
Load_regs
Add_shift
Zero
Ready
state[3:0]
1
2
1
2
1
2
1
// Datapath unit – structural model
module Datapath_2_STR
#(parameter dp_width = 8, R2_width = 4)
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(
output [R2_width -1: 0]
count,
output
Zero,
input [dp_width -1: 0]
data,
input
Load_regs, Add_shift, clock, reset_b);
supply1
pwr;
supply0
gnd;
wire [dp_width -1: 0] R1_Dbus, R1;
wire [R2_width -1: 0] R2_Dbus;
wire DR1_0, DR1_1, DR1_2, DR1_3, DR1_4, DR1_5, DR1_6, DR1_7;
wire R1_0, R1_1, R1_2, R1_3, R1_4, R1_5, R1_6, R1_7;
wire R2_0, R2_1, R2_2, R2_3;
wire [R2_width -1: 0] R2 = {R2_3, R2_2, R2_1, R2_0};
assign count = {R2_3, R2_2, R2_1, R2_0};
assign R1 = { R1_7, R1_6, R1_5, R1_4, R1_3, R1_2, R1_1, R1_0};
assign DR1_0 = R1_Dbus[0];
assign DR1_1 = R1_Dbus[1];
assign DR1_2 = R1_Dbus[2];
assign DR1_3 = R1_Dbus[3];
assign DR1_4 = R1_Dbus[4];
assign DR1_5 = R1_Dbus[5];
assign DR1_6 = R1_Dbus[6];
assign DR1_7 = R1_Dbus[7];
nor (Zero, R1_0, R1_1, R1_2, R1_3, R1_4, R1_5, R1_6, R1_7);
not
(Load_regs_b,
Load_regs);
DFF DF_0 (R1_0, DR1_0, clock, pwr);
DFF DF_1 (R1_1, DR1_1, clock, pwr);
DFF DF_2 (R1_2, DR1_2, clock, pwr);
DFF DF_3 (R1_3, DR1_3, clock, pwr);
DFF DF_4 (R1_4, DR1_4, clock, pwr);
DFF DF_5 (R1_5, DR1_5, clock, pwr);
DFF DF_6 (R1_6, DR1_6, clock, pwr);
DFF DF_7 (R1_7, DR1_7, clock, pwr);
// Disable reset
DFF DR_0 (R2_0, DR2_0, clock, Load_regs_b); // Load_regs (set) drives R2 to all ones
DFF DR_1 (R2_1, DR2_1, clock, Load_regs_b);
DFF DR_2 (R2_2, DR2_2, clock, Load_regs_b);
DFF DR_3 (R2_3, DR2_3, clock, Load_regs_b);
assign DR2_0 = R2_Dbus[0];
assign DR2_1 = R2_Dbus[1];
assign DR2_2 = R2_Dbus[2];
assign DR2_3 = R2_Dbus[3];
wire [1: 0]
wire [dp_width -1: 0]
wire [R2_width -1: 0]
sel = {Add_shift, Load_regs};
R1_shifted = {1'b0,
R1_7,
R1_6, R1_5,
R1_4,
R1_3,
R1_2,
R1_1};
sum = R2 + {3'b000,
R1[0]};
Mux8_4_x_1 M0 (R1_Dbus, R1, data, R1_shifted, R1, sel);
Mux4_2_x_1 M1 (R2_Dbus, R2, sum, Add_shift);
endmodule
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–
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Copyright
2012,
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rights
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335
module Mux8_4_x_1 #(parameter dp_width = 8) (output reg [dp_width -1: 0] mux_out,
input [dp_width -1: 0] in0, in1, in2, in3, input [1: 0] sel);
always @ (in0, in1, in2, in3, sel)
case (sel)
2'b00: mux_out = in0;
2'b01: mux_out = in1;
2'b10: mux_out = in2;
2'b11: mux_out = in3;
endcase
endmodule
module Mux4_2_x_1 #(parameter dp_width = 4) (output [dp_width -1: 0] mux_out,
input [dp_width -1: 0] in0, in1, input sel);
assign mux_out = sel ? in1: in0;
endmodule
// Test Plan for Datapath Unit:
// Demonstrate action of Load_regs
// R1 gets data, R2 gets all ones
// Demonstrate action of Incr_R2
// Demonstrate action of Add_shift and detect Zero
// Test bench for datapath
module t_Datapath_Unit
#(parameter dp_width = 8, R2_width = 4)
( );
wire [R2_width -1: 0] count;
wire
Zero;
reg [dp_width -1: 0] data;
reg
Load_regs, Add_shift, clock, reset_b;
Datapath_2_STR M0 (count, Zero, data, Load_regs, Add_shift, clock, reset_b);
initial #250 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial begin reset_b = 0; #2 reset_b = 1; end
initial fork
data = 8'haa;
Load_regs = 0;
Add_shift
=
0;
#10 Load_regs = 1;
#20 Load_regs = 0;
#50 Add_shift = 1;
#140 Add_shift = 0;
join
endmodule
Digital
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–
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2012,
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rights
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336
Name
0
50
100
150
clock
reset_b
Load_regs
Add_shift
Zero
aa
data[7:0]
R1[7:0]
xx
aa
55
2a
15
0a
05
02
01
00
R2[3:0]
x
0
1
2
3
4
count[3:0]
x
0
1
2
3
4
// Integrated system
module Count_Ones_2_Gates_1Hot_STR
# (parameter dp_width = 8, R2_width = 4)
(
output [R2_width -1: 0] count,
input [dp_width -1: 0] data,
input
Start, clock, reset_b
);
wire Load_regs, Add_shift,
Zero;
Controller_2_Gates_1Hot
M0 (Ready, Load_regs, Add_shift, Start, Zero, clock, reset_b);
Datapath_2_STR M1 (count, Zero, data, Load_regs, Add_shift, clock, reset_b);
endmodule
// Test plan for integrated system
// Test for data values of 8'haa, 8'h00, 8'hff.
// Test bench for integrated system
module t_Count_Ones_2_Gates_1Hot_STR
();
parameter
dp_width = 8, R2_width = 4;
wire [R2_width -1: 0] count;
reg [dp_width -1: 0] data;
reg
Start, clock, reset_b;
wire [1: 0]
state = {M0.M0.T1, M0.M0.T0};
Count_Ones_2_Gates_1Hot_STR
M0 (count, data, Start, clock, reset_b);
initial #700 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial begin reset_b = 0; #2 reset_b = 1; end
initial fork
data = 8'haa;
// Expect count = 4
Start = 0;
#20 Start = 1;
#30 Start = 0;
#40 data = 8'b00;
// Expect count = 0
#120 Start = 1;
#130 Start = 0;
#150 data = 8'hff;
// Expect count = 8
#200 Start = 1;
#210 Start = 0;
join
endmodule
Digital
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With
An
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HDL
–
Solution
Manual.
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Ciletti,
Copyright
2012,
All
rights
reserved.
337
Name
0
80
160
240
1
2
320
400
clock
reset_b
Start
Zero
Load_regs
Add_shift
1
state[1:0]
2
1
aa
data[7:0]
2
1
00
ff
R1[7:0]
xx
00
ff 7f 3f 1f 0f
R2[3:0]
x
0
1
2
3
4
0
1
2
3
4
5
6
7
00
8
count[3:0]
x
0
1
2
3
4
0
1
2
3
4
5
6
7
8
8.38
module Prob_8_38 (
output reg [7: 0]
Sum,
output reg
Car_Bor,
input [7: 0]
Data_A, Data_B);
reg [7: 0]
Reg_A, Reg_B;
always @ (Data_A, Data_B)
case ({Data_A[7], Data_B[7]})
2'b00, 2'b11:
begin
// ++, -{Car_Bor, Sum[6: 0]} = Data_A[6: 0] + Data_B[6: 0];
Sum[7] = Data_A[7];
end
default:
if (Data_A[6: 0] >= Data_B[6: 0]) begin
// +-, -+
{Car_Bor, Sum[6: 0]} = Data_A[6: 0] - Data_B[6: 0];
Sum[7] = Data_A[7];
end
else begin
{Car_Bor, Sum[6: 0]} = Data_B[6: 0] - Data_A[6: 0];
Sum[7] = Data_B[7];
end
endcase
endmodule
module t_Prob_8_38 ();
wire [7: 0] Sum;
wire
Car_Bor;
reg [7: 0]
Data_A, Data_B;
wire [6: 0] Mag_A, Mag_B;
assign
Mag_A = M0.Data_A[6: 0];
assign
Mag_B = M0.Data_B[6: 0];
wire
Sign_A = M0.Data_A[7];
wire
Sign_B = M0.Data_B[7];
wire
Sign = Sum[7];
wire [7: 0] Mag = Sum[6: 0];
// Hierarchical dereferencing
Prob_8_38 M0 (Sum, Car_Bor, Data_A, Data_B);
initial #650 $finish;
Digital
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An
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HDL
–
Solution
Manual.
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M.D.
Ciletti,
Copyright
2012,
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rights
reserved.
338
initial fork
// Addition
// A
B
#0 begin Data_A = {1'b0, 7'd25}; Data_B = {1'b0, 7'd10}; end
#40 begin Data_A = {1'b1, 7'd25}; Data_B = {1'b1, 7'd10}; end
#80 begin Data_A = {1'b1, 7'd25}; Data_B = {1'b0, 7'd10}; end
#120 begin Data_A = {1'b0, 7'd25}; Data_B = {1'b1, 7'd10}; end
// B
A
#160 begin Data_B = {1'b0, 7'd25}; Data_A = {1'b0, 7'd10}; end
#200 begin Data_B = {1'b1, 7'd25}; Data_A = {1'b1, 7'd10}; end
//+25, +10
// -25, -10
// -25, +10
// 25, -10
//+25, +10
// -25, -10
#240 begin Data_B = {1'b1, 7'd25}; Data_A = {1'b0, 7'd10}; end
#280 begin Data_B = {1'b0, 7'd25}; Data_A = {1'b1, 7'd10}; end
// Addition of matching numbers
// -25, +10
// +25, -10
#320 begin Data_A = {1'b1,7'd0}; Data_B = {1'b1,7'd0}; end
#360 begin Data_A = {1'b0,7'd0}; Data_B = {1'b0,7'd0}; end
#400 begin Data_A = {1'b0,7'd0}; Data_B = {1'b1,7'd0}; end
#440 begin Data_A = {1'b1,7'd0}; Data_B = {1'b0,7'd0}; end
// -0, -0
// +0, +0
// +0, -0
// -0, +0
#480 begin Data_B = {1'b0, 7'd25}; Data_A = {1'b0, 7'd25}; end
#520 begin Data_B = {1'b1, 7'd25}; Data_A = {1'b1, 7'd25}; end
// matching +
// matching –
// Test of carry (negative numbers)
#560 begin Data_A = 8'hf0; Data_B = 8'hf0; end
// Test of carry (positive numbers)
#600 begin Data_A = 8'h70; Data_B = 8'h70; end
join
endmodule
Name
0
// carry - // carry ++
190
Data_A[7:0]
19
Data_B[7:0]
0a
99
8a
0a
19
0a
8a
19
380
8a
0a
99
8a
80
19
80
00
00
80
570
80
19
99
f0
70
00
19
99
f0
70
Sign_A
Sign_B
Mag_A[6:0]
25
10
0
25
112
Mag_B[6:0]
10
25
0
25
112
Car_Bor
Sum[7:0]
23
a3
8f
0f
23
a3
8f
0f
80
00
80
32
b2
e0
60
Sign
Mag[7:0]
35
15
35
15
0
50
Digital
Design
With
An
Introduction
to
the
Verilog
HDL
–
Solution
Manual.
M.
Mano.
M.D.
Ciletti,
Copyright
2012,
All
rights
reserved.
96
8.39
339
Block diagram and ASMD chart:
data_AR data_BR
16
zero
16
Datapath
AR
Ld_regs
Controller
...
Add_decr
...
start
BR
...
done
reset_b
clock
PR
16
PR
reset_b
s0
done
AR <= data_A
BR <= data_B
PR <= 0
start
1
Ld_regs
PR <= PR + BR
AR <= AR -1
s1
Add_decr
Zero
1
module Prob_8_39 (
output [15: 0] PR, output done,
input
[7: 0] data_AR, data_BR, input start, clock, reset_b
);
Controller_P8_39 M0 (done, Ld_regs, Add_decr, start, zero, clock, reset_b);
Datapath_P8_39 M1 (PR, zero, data_AR, data_BR, Ld_regs, Add_decr, clock, reset_b);
endmodule
module Controller_P8_16 (output done, output reg Ld_regs, Add_decr, input start, zero, clock, reset_b);
parameter
s0 = 1'b0, s1 = 1'b1;
reg
state, next_state;
assign done = (state == s0);
Digital
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HDL
–
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2012,
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rights
reserved.
340
always @ (posedge clock, negedge reset_b)
if (!reset_b) state <= s0; else state <= next_state;
always @ (state, start, zero) begin
Ld_regs = 0;
Add_decr = 0;
case (state)
s0:
if (start) begin Ld_regs = 1; next_state = s1; end
s1:
if (zero) next_state = s0; else begin next_state = s1; Add_decr = 1; end
default: next_state = s0;
endcase
end
endmodule
module Datapath_P8_16 (
output reg
[15: 0] PR, output zero,
input
[7: 0] data_AR, data_BR, input Ld_regs, Add_decr, clock, reset_b
);
reg
[7: 0] AR, BR;
assign
zero = ~( | AR);
always @ (posedge clock, negedge reset_b)
if (!reset_b) begin AR <= 8'b0; BR <= 8'b0; PR <= 16'b0; end
else begin
if (Ld_regs) begin AR <= data_AR; BR <= data_BR; PR <= 0; end
else if (Add_decr) begin PR <= PR + BR; AR <= AR -1; end
end
endmodule
// Test plan – Verify;
// Power-up reset
// Data is loaded correctly
// Control signals assert correctly
// Status signals assert correctly
// start is ignored while multiplying
// Multiplication is correct
// Recovery from reset on-the-fly
module t_Prob_P8_16;
wire
done;
wire [15: 0] PR;
reg [7: 0] data_AR, data_BR;
reg
start, clock, reset_b;
Prob_8_16 M0 (PR, done, data_AR, data_BR, start, clock, reset_b);
initial #500 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial fork
reset_b = 0;
#12 reset_b = 1;
#40 reset_b = 0;
#42 reset_b = 1;
#90 reset_b = 1;
#92 reset_b = 1;
join
Digital
Design
With
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Verilog
HDL
–
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Manual.
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2012,
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rights
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341
initial fork
#20 start = 1;
#30 start = 0;
#40 start = 1;
#50 start = 0;
#120 start = 1;
#120 start = 0;
join
initial fork
data_AR = 8'd5;
data_BR = 8'd20;
// AR > 0
#80 data_AR = 8'd3;
#80 data_BR = 8'd9;
#100 data_AR = 8'd4;
#100 data_BR = 8'd9;
join
endmodule
Name
0
30
60
90
120
reset_b
clock
start
Ld_regs
Add_decr
zero
state
data_AR[7:0]
5
data_BR[7:0]
20
AR[7:0]
0
BR[7:0]
0
5
20
4 0
3
4
9
5
4
3
2
0
1
0
20
done
PR[15:0]
0
0
20
40
60
80
100
Digital
Design
With
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HDL
–
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2012,
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342
8.40
Data_in[7: 0]
8
Ready
Got_Data
Done_Product
Start
Run
Send_Data
Datapath
Shift_in
A
Shift_regs
Controller
Add_regs
B
Decr_P
Q
Shift_out
reset_b
P
C
clock
8
Zero
Q0
Note: Q0 = Q[0]
Data_out[7: 0]
Digital
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343
reset
S_idle
/Ready
B[7: 0] <= Data_in … B[31: 24] <= Data_in
Q[7: 0] <= Data_in … Q[31: 24] <= Data_in
Start
1
Shift_in
S_Ld_0...6
/Shift_in
S_Ld__7
/Got_Data
S_wait_1
Run
1
1
S_add
/ Decr_P
Q0
Run
The bytes of data will be read sequentially. Registers
Q and B are organized to act as byte-wide parallel
shift registers, taking 8 clock cycles to fill the pipe.
The least significant byte of the multiplicand enters
the most significant byte of Q and then moves
through the bytes of Q to enter B, then proceed to
occupy successive bytes of B until it occupies the
least significant byte of B, and so forth until both B
and Q are filled. Wait states are used to wait for Run
and Send_Data.
P <= P-1
1
{C, A} <= A + B
Add_regs
S_shift
/Shift_regs
Zero
1
S_product
/Done_Product
S_wait_2
Send_
Data
Send_
Data
1
Shift_out
1
Shift_out
S_Send_0...6
/Shift_out
Data_out <= P[7: 0] … P[31: 24]
Digital
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HDL
–
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344
module Prob_8_40 (
output [7: 0]
Data_out,
output
Ready, Got_Data, Done_Product,
input
[7: 0]
Data_in,
input
Start, Run, Send_Data, clock, reset_b
);
Controller M0 (
Ready, Shift_in, Got_Data, Done_Product, Decr_P, Add_regs, Shift_regs, Shift_out,
Start, Run, Send_Data, Zero, Q0, clock, reset_b
);
Datapath M1(Data_out, Q0, Zero, Data_in,
Start, Shift_in, Decr_P, Add_regs, Shift_regs, Shift_out, clock
);
endmodule
module Controller (
output reg Ready, Shift_in, Got_Data, Done_Product, Decr_P, Add_regs,
Shift_regs, Shift_out,
input Start, Run, Send_Data, Zero, Q0, clock, reset_b
);
parameter
reg
[4: 0]
S_idle = 5'd20,
S_Ld_0 = 5'd0,
S_Ld_1 = 5'd1,
S_Ld_2 = 5'd2,
S_Ld_3 = 5'd3,
S_Ld_4 = 5'd4,
S_Ld_5 = 5'd5,
S_Ld_6 = 5'd6,
S_Ld_7 = 5'd7,
S_wait_1 = 5'd8, // Wait state
S_add = 5'd9,
S_Shift = 5'd10,
S_product = 5'd11,
S_wait_2 = 5'd12, // Wait state
S_Send_0 = 5'd13,
S_Send_1 = 5'd14,
S_Send_2 = 5'd15,
S_Send_3 = 5'd16,
S_Send_4 = 5'd17,
S_Send_5 = 5'd18,
S_Send_6 = 5'd19;
state, next_state;
always @ (posedge clock, negedge reset_b)
if (~reset_b) state <= S_idle; else state <= next_state;
always @ (state, Start, Run, Q0, Zero, Send_Data) begin
next_state = S_idle;
// Prevent accidental synthesis of latches
Ready = 0;
Shift_in = 0;
Shift_regs = 0;
Add_regs = 0;
Decr_P = 0;
Shift_out = 0;
Got_Data = 0;
Done_Product = 0;
Digital
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HDL
–
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345
case (state)
S_idle:
S_Ld_0:
S_Ld_1:
S_Ld_2:
S_Ld_3:
S_Ld_4:
S_Ld_5:
S_Ld_6:
S_Ld_7:
S_wait_1:
S_add:
S_Shift:
S_product:
S_wait_2:
S_Send_0:
S_Send_1:
S_Send_2:
S_Send_3:
S_Send_4:
S_Send_5:
S_Send_6:
default:
endcase
end
endmodule
// Assign by exception to default values
begin
Ready = 1;
if (Start) begin next_state = S_Ld_0; Shift_in = 1; end
end
begin next_state = S_Ld_1; Shift_in = 1; end
begin next_state = S_Ld_2; Shift_in = 1; end
begin next_state = S_Ld_3; Shift_in = 1; end
begin next_state = S_Ld_4; Shift_in = 1; end
begin next_state = S_Ld_5; Shift_in = 1; end
begin next_state = S_Ld_6; Shift_in = 1; end
begin next_state = S_Ld_7; Shift_in = 1; end
begin Got_Data = 1;
if (Run) next_state = S_add;
else next_state = S_wait_1;
end
if (Run) next_state = S_add; else next_state = S_wait_1;
begin next_state = S_Shift; Decr_P = 1; if (Q0) Add_regs = 1; end
begin Shift_regs = 1; if (Zero) next_state = S_product;
else next_state = S_add; end
begin
Done_Product = 1;
if (Send_Data) begin next_state = S_Send_0; Shift_out = 1; end
else next_state = S_wait_2; end
if (Send_Data) begin next_state =S_Send_0; Shift_out = 1; end
else next_state = S_wait_2;
begin next_state = S_Send_1; Shift_out = 1; end
begin next_state = S_Send_2; Shift_out = 1; end
begin next_state = S_Send_3; Shift_out = 1; end
begin next_state = S_Send_4; Shift_out = 1; end
begin next_state = S_Send_5; Shift_out = 1; end
begin next_state = S_Send_6; Shift_out = 1; end
begin next_state = S_idle; Shift_out = 1; end
next_state = S_idle;
module Datapath #(parameter dp_width = 32, P_width = 6) (
output [7: 0]
Data_out,
output
Q0, Zero,
input
[7: 0]
Data_in,
input
Start, Shift_in, Decr_P, Add_regs, Shift_regs, Shift_out, clock
);
reg [dp_width - 1: 0]
A, B, Q;
// Sized for datapath
reg
C;
reg [P_width - 1: 0]
P;
assign
Q0 = Q[0];
assign
Zero = (P == 0);
// counter is zero
assign
Data_out = {C, A, Q};
always @ (posedge clock) begin
if (Shift_in) begin
P <= dp_width;
A <= 0;
C <= 0;
B[7: 0]
<= B[15: 8];
// Treat B and Q registers as a pipeline to load data bytes
B[15: 8] <= B[ 23: 16];
B[23: 16] <= B[31: 24];
B[31: 24] <= Q[7: 0];
Q[7: 0]
<= Q[15: 8];
Q[15: 8] <= Q[ 23: 16];
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Q[23: 16] <= Q[31: 24];
Q[31: 24] <= Data_in;
end
if (Add_regs) {C, A} <= A + B;
if (Shift_regs) {C, A, Q} <= {C, A, Q} >> 1;
if (Decr_P) P <= P -1;
if (Shift_out) begin {C, A, Q} <= {C, A, Q} >> 8; end
end
endmodule
module t_Prob_8_40;
parameter
dp_width = 32;
// Width of datapath
wire [7: 0]
Data_out;
wire
Ready, Got_Data, Done_Product;
reg
Start, Run, Send_Data, clock, reset_b;
integer
Exp_Value;
reg
Error;
wire [7: 0]
Data_in;
reg [dp_width -1: 0]
Multiplicand, Multiplier;
reg [2*dp_width -1: 0]
Data_register;
// For test patterns
assign
Data_in = Data_register [7:0];
wire [2*dp_width -1: 0]
product;
assign
product = {M0.M1.C, M0.M1.A, M0.M1.Q};
Prob_8_40 M0 (
Data_out, Ready, Got_Data, Done_Product, Data_in, Start, Run, Send_Data, clock, reset_b
);
initial #2000 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial fork
reset_b = 1;
#2 reset_b = 0;
#3 reset_b = 1;
join
initial fork
Start =0;
Run = 0;
Send_Data = 0;
#10 Start = 1;
#20 Start = 0;
#50 Run= 1;
#60 Run = 0;
#120 Run = 1;
#130 Run = 0;
// Ignored by controller
#830 Send_Data = 1;
#840 Send_Data = 0;
join
// Test patterns for multiplication
initial begin
Multiplicand = 32'h0f_00_00_aa;
Multiplier = 32'h0a_00_00_ff;
Data_register = {Multiplier, Multiplicand};
end
initial begin
// Synchronize input data bytes
@ (posedge Start)
repeat (15) begin
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@ (negedge clock)
Data_register <= Data_register >> 8;
end
end
endmodule
Simulation results: Loading multiplicand (0f0000aaH) and multiplier (0a0000ffH), 4 bytes each, in sequence,
beginning with the least significant byte of the multiplicand.
Note: Product is not valid until Done_Product asserts. The value of Product shown here (25510) reflects the
contents of {C, A, Q} after the multiplier has been loaded, prior to multiplication.
Note: The machine ignores a premature assertion of Run.
Note: Got_Data asserts at the 8th clock after Start asserts, i.e., 8 clocks to load the data.
Note: Product, Multiplier, and Multiplicand are formed in the test bench.
Launch activity
at rising edge of
clock
Name
Ignore Run
Loading 8 bytes
of data
0
Respond to
Run
Waiting for Run
40
80
120
160
clock
reset_b
Start
Run
Send_Data
Zero
Q0
Ready
Got_Data
Done_Product
Shift_in
Shift_regs
Add_regs
Decr_P
Shift_out
state[4:0]
20
Data_in[7:0]
170
P[31:0]
x
0
1
2
0
3
15
4
5
255
6
0
7
8
9
10
9
10
0
32
31
xxxxxxxx
B[31:0]
10
30
0f0000aa
C
00000000
A[31:0]
0a0000ff
Q[31:0]
Multiplicand[31:0]
0f0000aa
Multiplicand[31:0]
251658410
Multiplier[31:0]
0a0000ff
Multiplier[31:0]
167772415
000000000a0000ff
product[63:0]
product[63:0]
Data_out[7:0]
x
x
x
x
X
167772415
170
0
15
255
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127
348
Note: Product (64 bits) is formed correctly
Multiplication complete
Name
735
Begin sending data bytes
of product.
Waiting for Send_Data
785
835
885
935
clock
reset_b
Start
Run
Send_Data
Zero
Q0
Ready
Got_Data
Done_Product
Shift_in
Shift_regs
Add_regs
Decr_P
Shift_out
state[4:0]
10
9
10
11
12
13
14
15
16
17
18
19
20
0
Data_in[7:0]
1
P[31:0]
0
0f0000aa
B[31:0]
C
A[31:0]
00960015
Q[31:0]
9500a956
00000000
00000000
Multiplicand[31:0]
0f0000aa
Multiplicand[31:0]
251658410
Multiplier[31:0]
0a0000ff
Multiplier[31:0]
167772415
product[63:0]
009600159500a956
product[63:0]
42221339200760150
Data_out[7:0]
88
172
86
0
0
21
0
0
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349
Multiplication complete
Name
735
Begin sending data
bytes of product.
Waiting for Send_Data
785
Data sent - {C, A, Q}
empty. State = S_idle
835
885
935
clock
reset_b
Start
Run
Send_Data
Zero
Q0
Ready
Got_Data
Done_Product
Shift_in
Shift_regs
Add_regs
Decr_P
Shift_out
state[4:0]
10
9
10
11
12
13
14
15
16
17
18
19
20
0
Data_in[7:0]
1
P[31:0]
0
0f0000aa
B[31:0]
C
A[31:0]
00960015
Q[31:0]
9500a956
00000000
00000000
Multiplicand[31:0]
0f0000aa
Multiplicand[31:0]
251658410
Multiplier[31:0]
0a0000ff
Multiplier[31:0]
167772415
product[63:0]
009600159500a956
product[63:0]
42221339200760150
Data_out[7:0]
88
172
86
0
0
21
0
0
Digital
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8.41
350
(a)
Data
8
P1[7: 0]
P0[7: 0]
8
P1[7: 0]
P0[7: 0]
8
R0[15: 0]
{P1, P0} <= {0, 0}
S_idle
rst
1
Clr_P1_P0
1
En
Ld_P1_P0
P1 <= Data
P0 <= P1
{P1, P0} <= {0, 0}
1
P1 <= Data S_1
P0 <= P1
Ld_P1_P0
Clr_P1_P0
S_full
ld_P1_P0
S_wait
Ld
1
Ld
1
1
Ld_R0
P1 <= Data
P0 <= P1
En
R0 <= {P1, P0}
(b) HDL model, test bench and simulation results for datapath unit.
module Datapath_unit
(
output reg [15: 0] R0, input [7: 0] Data, input Clr_P1_P0, Ld_P1_P0, Ld_R0, clock, rst);
reg [7: 0]
P1, P0;
always @ (posedge clock) begin
if (Clr_P1_P0) begin P1 <= 0; P0 <= 0; end
if (Ld_P1_P0) begin P1 <= Data; P0 <= P1; end
if (Ld_R0) R0 <= {P1, P0};
end
endmodule
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// Test bench for datapath
module t_Datapath_unit ();
wire [15: 0] R0;
reg [7: 0]
Data;
reg
Clr_P1_P0, Ld_P1_P0, Ld_R0, clock, rst;
Datapath_unit M0 (R0, Data, Clr_P1_P0, Ld_P1_P0, Ld_R0, clock, rst);
initial #100 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial begin rst = 0; #2 rst = 1; end
initial fork
#20 Clr_P1_P0 = 0;
#20 Ld_P1_P0 = 0;
#20 Ld_R0 = 0;
#20
Data = 8'ha5;
#40 Ld_P1_P0 = 1;
#50
Data
=
8'hff;
#60 Ld_P1_P0 = 0;
#70 Ld_R0 = 1;
#80 Ld_R0 = 0;
join
endmodule
Name
0
50
100
clock
rst
Clr_P1_P0
Ld_P1_P0
Ld_R0
Data[7:0]
P1[7:0]
P0[7:0]
R0[15:0]
xx
a5
xx
ff
a5
xx
ff
a5
xxxx
ffa5
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(c) HDL model, test bench, and simulation results for the control unit.
module Control_unit (output reg Clr_P1_P0, Ld_P1_P0, Ld_R0, input En, Ld, clock, rst);
parameter S_idle = 4'b0001, S_1 = 4'b0010, S_full = 4'b0100, S_wait = 4'b1000;
reg [3: 0] state, next_state;
always @ (posedge clock)
if (rst) state <= S_idle;
else state <= next_state;
always @ (state, Ld, En) begin
Clr_P1_P0 = 0;
// Assign by exception
Ld_P1_P0 = 0;
Ld_R0 = 0;
next_state = S_idle;
case (state)
S_idle:
if (En) begin Ld_P1_P0 = 1; next_state = S_1; end
else next_state = S_idle;
S_1:
begin Ld_P1_P0 = 1; next_state = S_full; end
S_full:
if (!Ld) next_state = S_wait;
else begin
Ld_R0 = 1;
if (En) begin Ld_P1_P0 = 1; next_state = S_1; end
else begin Clr_P1_P0 = 1; next_state = S_idle; end
end
S_wait:
if (!Ld) next_state = S_wait;
else begin
Ld_R0 = 1;
if (En) begin Ld_P1_P0 = 1; next_state = S_1; end
else begin Clr_P1_P0 = 1; next_state = S_idle; end
end
next_state = S_idle;
default:
endcase
end
endmodule
// Test bench for control unit
module t_Control_unit ();
wire Clr_P1_P0, Ld_P1_P0, Ld_R0;
reg En, Ld, clock, rst;
Control_unit M0 (Clr_P1_P0, Ld_P1_P0, Ld_R0, En, Ld, clock, rst);
initial #200 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial begin rst = 0; #2 rst = 1; #12 rst = 0; end
initial fork
#20 Ld = 0;
#20 En = 0;
#30 En = 1; // Drive to S_wait
#70 Ld = 1; // Return to S_1 to S_full tp S_wait
#80 Ld = 0;
#100 Ld = 1; // Drive to S_idle
#100 En = 0;
#110 En = 0;
#120 Ld = 0;
join
endmodule
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Name
0
50
100
150
clock
rst
En
Ld
Clr_P1_P0
Ld_P1_P0
Ld_R0
state[3:0]
x
1
2
4
8
2
4
8
1
(c) Integrated system Note that the test bench for the integrated system uses the input stimuli from the
test bench for the control unit and displays the waveforms produced by the test bench for the
datapath unit.:
module Prob_8_41 (output [15: 0] R0, input [7: 0] Data, input
En, Ld, clock, rst);
wire
Clr_P1_P0, Ld_P1_P0, Ld_R0;
Control_unit M0
(Clr_P1_P0, Ld_P1_P0, Ld_R0, En,
Ld,
clock, rst);
Datapath_unit M1 (R0, Data, Clr_P1_P0, Ld_P1_P0, Ld_R0, clock);
endmodule
module Control_unit (output reg Clr_P1_P0, Ld_P1_P0, Ld_R0, input En, Ld, clock, rst);
parameter S_idle = 4'b0001, S_1 = 4'b0010, S_full = 4'b0100, S_wait = 4'b1000;
reg [3: 0] state, next_state;
always @ (posedge clock)
if (rst) state <= S_idle;
else state <= next_state;
always @ (state, Ld, En) begin
Clr_P1_P0 = 0;
// Assign by exception
Ld_P1_P0 = 0;
Ld_R0 = 0;
next_state = S_idle;
case (state)
S_idle:
if (En) begin Ld_P1_P0 = 1; next_state = S_1; end
else next_state = S_idle;
S_1:
begin Ld_P1_P0 = 1; next_state = S_full; end
S_full:
if (!Ld) next_state = S_wait;
else begin
Ld_R0 = 1;
if (En) begin Ld_P1_P0 = 1; next_state = S_1; end
else begin Clr_P1_P0 = 1; next_state = S_idle; end
end
S_wait:
if (!Ld) next_state = S_wait;
else begin
Ld_R0 = 1;
if (En) begin Ld_P1_P0 = 1; next_state = S_1; end
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354
else begin Clr_P1_P0 = 1; next_state = S_idle; end
end
next_state = S_idle;
default:
endcase
end
endmodule
module Datapath_unit
(
output reg [15: 0] R0,
input [7: 0]
Data,
input
Clr_P1_P0,
Ld_P1_P0,
Ld_R0,
clock);
reg [7: 0]
P1, P0;
always @ (posedge clock) begin
if (Clr_P1_P0) begin P1 <= 0; P0 <= 0; end
if (Ld_P1_P0) begin P1 <= Data; P0 <= P1; end
if (Ld_R0) R0 <= {P1, P0};
end
endmodule
// Test bench for integrated system
module t_Prob_8_41 ();
wire [15: 0] R0;
reg [7: 0]
Data;
reg
En, Ld, clock, rst;
Prob_8_41 M0 (R0, Data, En, Ld, clock, rst);
initial #200 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial begin rst = 0; #10 rst = 1; #20 rst = 0; end
initial fork
#20 Data = 8'ha5;
#50 Data = 8'hff;
#20 Ld = 0;
#20 En = 0;
#30 En = 1; // Drive to S_wait
#70 Ld = 1; // Return to S_1 to S_full tp S_wait
#80 Ld = 0;
#100 Ld = 1; // Drive to S_idle
#100 En = 0;
#110 En = 0;
#120 Ld = 0;
join
endmodule
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Name
0
40
80
120
clock
rst
En
Ld
Clr_P1_P0
Ld_P1_P0
Ld_R0
state[3:0]
Data[7:0]
P1[7:0]
P0[7:0]
R0[15:0]
x
1
xx
2
4
8
a5
xx
4
ff
a5
xxxx
8
1
ff
a5
xx
2
00
ff
a5a5
00
ffff
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8.42
module Datapath_BEH
#(parameter dp_width = 8, R2_width = 4)
(
output [R2_width -1: 0] count, output E, //output reg E,
output Zero, input [dp_width -1: 0] data,
input Load_regs, Shift_left, Incr_R2, clock, reset_b);
reg [dp_width -1: 0] R1;
reg [R2_width -1: 0] R2;
assign E = R1[dp_width -1];
assign count = R2;
assign Zero = ~(| R1);
always @ (posedge clock) begin
// E <= R1[dp_width -1] & Shift_left;
// if (Load_regs) begin R1 <= data; R2 <= {R2_width{1'b1}}; end
if (Load_regs) begin R1 <= data; R2 <= {R2_width{1'b0}}; end
if (Shift_left) R1 <= R1 << 1;
//if (Shift_left) {E, R1} <= {E, R1} << 1;
if (Incr_R2) R2 <= R2 + 1;
end
endmodule
module Controller_BEH (
output
Ready,
output reg Load_regs,
output
Incr_R2, Shift_left,
input
Start, Zero, E, clock, reset_b
);
parameter S_idle = 0, S_1 = 1, S_2 = 2, S_3 = 3;
reg [1:0] state, next_state;
assign Ready = (state == S_idle);
assign Incr_R2 = (state == S_1);
assign Shift_left = (state == S_2);
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) state <= S_idle;
else state <= next_state;
always @ (state, Start, Zero, E) begin
Load_regs = 0;
case (state)
S_idle: if (Start) begin Load_regs = 1; next_state = S_1; end
else next_state = S_idle;
S_1:
if (Zero) next_state = S_idle; else next_state = S_2;
S_2:
//S_3:
S_3:
next_state = S_3;
if (E) next_state = S_1; else next_state = S_2;
if (E) next_state = S_1; else if (Zero) next_state = S_idle; else next_state = S_2;
endcase
end
endmodule
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// Integrated system
module Count_Ones_BEH_BEH
# (parameter dp_width = 8, R2_width = 4)
(
output [R2_width -1: 0]
count,
input [dp_width -1: 0]
data,
input
Start, clock, reset_b
);
wire Load_regs, Incr_R2, Shift_left, Zero, E;
Controller_BEH M0 (Ready, Load_regs, Incr_R2, Shift_left, Start, Zero, E, clock, reset_b);
Datapath_BEH M1 (count, E, Zero, data, Load_regs, Shift_left, Incr_R2, clock, reset_b);
endmodule
// Test plan for integrated system
// Test for data values of 8'haa, 8'h00, 8'hff.
// Test bench for integrated system
module t_count_Ones_BEH_BEH ();
parameter dp_width = 8, R2_width = 4;
wire [R2_width -1: 0] count;
reg [dp_width -1: 0] data;
reg Start, clock, reset_b;
Count_Ones_BEH_BEH M0 (count, data, Start, clock, reset_b);
initial #700 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial bebgin reset_b = 0; #2 reset_b = 1; enbd
initial fork
data = 8'haa;
// Expect count = 4
Start = 0;
#20 Start = 1;
#30 Start = 0;
#40 data = 8'b00; // Expect count = 0
#250 Start = 1;
#260 Start = 0;
#280 data = 8'hff;
#280 Start = 1;
#290 Start = 0;
join
endmodule
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Digital
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358
359
CHAPTER 9
9.1
Oscilloscope display:
clock
0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
QA
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
QB
0
QC
0
QD
0
BCD count: Oscilloscope displays from 0000 to 1001
Output pattern:
QA = alternate 1's and 0s
QB = Two 1's, two 0's, two 1's, four 0's
QC = Four 1's, six 0's
QD = Two 1's, eight 0's.
Other counts:
(a) 0101 must reset at 0110 – connect QB to R1, QC to R2
(b) 0111 must reset at 1000 – connect QD to both R1 and R2
(c) 1011 must reset at 1100 – connect QC to R1, QD to R2
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reserved.
9.2
360
Truth table:
Inputs
A
0
0
1
1
B
0
1
0
1
NAND
1
1
1
0
NOR NOT(A)
0
1
1
0
1
1
1
0
AND
0
0
0
1
OR XOR
0
0
1
1
1
1
1
0
Waveforms:
QA
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
QB
NAND(7400)
NOR(7492)
NOT( A (7404)
AND (7408)
OR (7432)
xOR (7486)
Digital
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361
9.3
Logic Diagram
x
y
yz
00
0
x
01
m0
m4
1
11
m1
m5
1
m3
m7
1
F = xy' + yz
x
10
m2
1
m6
1
F
y
z
7400
z
Boolean Functions:
AB
Boolean Functions:
CD
C
00
00
01
11
A
10
m0
m4
1
1
01
m1
m5
11
1
1
m3
m2
m7
m6
m15
m14
m8
m9
m11
m10
1
1
B
11
A
1
10
D
F1 = C' + AB'D'
C
00
01
m13
1
CD
00
m12
1
AB
10
01
11
m1
m3
m4
m5
m7
m12
m13
m15
m14
m8
m9
m11
m10
1
1
1
1
1
1
1
m2
m6
B
1
D
F2 = BD + CD + AB'D'
2 ICs: 7400, 7410
C
B
10
m0
F1
A
D
F2
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362
Complement:
AB
CD
C
00
00
01
11
A
10
m0
m4
01
m1
0
m5
0
11
m3
1
m7
1
10
D
1
B
m2
1
m6
1
m13
m15
m14
m8
m9
m11
m10
0
1
0
1
1
C
0
m12
F
B
0
1
F'
1
2 - 7400 ICs
D
F = D + B'C
F' = C'D' + BD'
9.4
Design Example:
AB
CD
C
00
00
01
11
A
10
m0
01
11
m1
10
m3
F = AB' + BC + BD
m2
A
m4
m5
m12
m13
m15
m14
m8
m9
m11
m10
1
m7
1
1
m6
1
1
1
1
1
1
B
B
C
F
D
1/3 7410
1
7400
D
Majority Logic
x
00
0
x
1
F = xy + xz + yz
y
yz
01
11
m0
m1
m3
m4
m5
m7
1
1
1
10
m2
m6
x
y
F
z
1
1/3 7410
7400
z
A
B
Peven
Podd
C
D
VCC
x
1 = x'
Digital
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363
Decoder Implementation
1
F1 = xz + x'y'z' = Σ (0, 5, 7)
x
y
z
F2 = x'y+ xy'z' = Σ (2, 3, 4)
F3 = xy+ x'y'z = Σ (1, 6, 7)
15
C1
C2
B
A
G1
74155
G2
9
10
11
12
7
6
5
4
0
1
2
3
4
5
6
7
9
6
4
F1
11
12
7
F2
10
5
4
F3
7410
8
9.5
Gray code to Binary – See solution to Prob. 4.7.
9's complementer – See solution to Prob. 4.18.
w = A'B'C'
x = BC' + B'C
y=C
z = D'
E = AB + AC
3 ICs: 7400, 7404, 7410
A
A'
B
B'
C
C'
w
B
C'
x
B'
C
D
y
z
A
B
E
A
C
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364
9.6
Four 7451's
See implementation
tables below
w
8
Mux A
A
8
Mux B
B
8
Mux C
C
8
Mux D
D
C
B
A
7447
7730
Fig. 11.8
x
y
z
A = ∑ (0, 2, 3, 6, 7, 8, 9, 12, 13)
B = ∑ (0, 2, 3, 4, 512, 13, 14)
C = ∑ (0, 1, 3, 5, 6, 9, 10, 13, 14)
D = ∑ (0, 7, 11)
Mux B
D0
D1
D2
Mux A
D3 D4
D5
D6
D7
D0
D1
D2
D3
D4
D5
D6
D7
1
w
w'
w'
w
w
w'
w'
w'
0
w'
w'
1
1
w
0
D0
D1
D2
Mux C
D3 D4
D5
D6
D7
D0
D1
D2
D3
D4
D5
D6
D7
w'
1
w
w'
1
1
0
w'
0
0
w
0
0
0
w'
0
Mux D
9.7
Half - Adder
x
y
S
C
Full- Adder
x
y
S
C
z
Parallel adder - See circuit of Fig. 9.10.
Adder-subtractor – See circuit of Fig. 9.11.
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365
Operation
9 + 5 = 14
9 + 9 = 19 = 16 + 2
9 + 15 = 24 = 16 + 8
9-5=4
9-9=0
9 - 15 = -6
A
4
B
4
Inputs
A
B
C0
S
0
0
0
1
1
1
1001
1001
1001
1001
1001
1001
0
0
0
1
1
1
1110
0010
1000
0100
0000
1010
0101
1001
1111
0101
1001
1111
Outputs
C4
0
1
1
1
1
0
sum < 15
sum > 15
sum > 15
A>B
A=B
AB y
A=B x
S1
M=1
9.8
M
SR Latch: See Fig. 5.4.
D Latch:
D
Q
Let CP = C, x = output of gate 4.
x = [(DC)'C]' = (D'C)'
C
4
Q'
x
Master-Slave D Flip-Flop: The circuit is as in Fig. 5.9.
The oscilloscope display:
Clock
Master Y
Slave Q
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Edge-Triggered D Flip-Flop: Circuit is shown in Fig. 5.10.
Clock
Output
IC Flip-Flops:
Connect all inputs to toggle switches, the clock to a pulser, and the outputs to indicator lamps.
9.9
Up-Down Counter with Enable:
B
A
7476
Q1
Q
Q1
Q
K
J
K
J
clock
E
x
7410
JB = KB = E (Complement B when E = 1)
JA = KA = E (Bx + B'x')
Complement A when E = 1 and:
B = 1 when x = 1 (Count up)
B = 0 when x = 0 (Count down)
State Diagram:
JA = B
KA = B'
JB = Ax + A'x' = (A ⊕ x)'
KB = Ax + A'x' = (A ⊕ x)'
Y=A⊕B⊕x
A
x
(A
x)' = JB = KB
Logic 1
y
B
Design of Counter: ABCD
JA = KA = B(CD)
JB = KB = CD
JC = D
JD = K D = 1
0000 → 0101 → 090
1000 → 1001 → 1010
KC = AD
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9.10
367
Ripple counter: See Fig. 6.8
Down counter: Either take outputs from Q' outputs or connect complement Q' to next clock input.
Synchronous counter: See Fig. 6.12.
BCD counter: See solution to Prob. 6.19.
Unused states:
10
11
6
12
13
4
14
15
2
Binary counter wth parallel load:
Connect QA and QD through a NAND gate to the load. See Fig. 6.15.
9.11
Ring counter:
See Fig. 6.17(a).
States of register:
QA QB QC QD
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
Switch-tail ring counter: See Fig. 6.18(a). Connect (QD)' at pin 12 to the serial input at pin 4. State
sequence as in Fig. 6.18(b).
Feedback shift register: Serial input = QC ⊕ QD (Use 7486).
Sequence of states:
QA QB QC QD
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
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Bidirectional shift register with parallel load:
Function table:
74195
Clear Clock
0
1
1
1
1
74157
SH/LD
x
STROBE SELECT
x
1
0
0
0
*
x
x
0
0
1
x
x
1
0
x
Function
Async clear
Shift right (QA QB)
Shift left (Select B)*
Parallel Load (Select A)
Synchronous clear
B inputs come from QA-QD shifted by one position.
9.12
To serial input of 74197
QD
x
74197
(QD)'
x'
J
y
QD
74197
(QD)'
Q
K
y'
M = 0 for add,
1 for subtract
9.13
Testing the RAM:
To 4 switches
From pulser
A
QA
D1 D2 D3 D4
A
B
QB
B
QC
C
QD
WE
D
S1 S2 S3 S4
R1
7493
R2
GND
vcc
7447
7730
Fig. 11.8
VCC
GND
Read
ME
To pulser
Write
7404
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Memory Expansion:
Input
address
A
B
C
D
ME 7489
Input
data
D1
D2
D3
D4
Output
data to
indicator
lamps
WE
A
B
C
D
ME 7489
Read
D1
D2
D3
D4
WE
Pulser
Write
9.14
Circuit Analysis – Answers to questions:
1) Resets to 0 the two 74194 ICs, the two D flip-flops, and the start SR latch. This makes S1S0 = 11
(parallel load).
2) The start switch sets the SR latch to 1. The clock pulses load 0000_0001 into the 8-bit register. If the
start switch stays on, the register never clears to all 0s when S1S0 = 11 (right-most QD stays on).
3) Pressing the pulser makes S1S0 = 10 and the light shifts left. When QC becomes 1, the start SR latch
is cleared to 0. When QA of the left 74194 becomes 1, it changes S1 to 0 (through the PR input) and
S0 to 1 (through the CLR input. with S1S0 = 01, the single light shifts right.
4) If the pulser is pressed while the light is moving to the left or the right, S1S0 becomes 11 and all 0s
are loaded into the register in parallel. The light goes off.
5) When the right-most QD becomes a 1, S1S0 changes from 01 (shift right) to 11 (parallel load). If the
pulser is pressed before the next clock pulse, S1S0 goes to 10 (shift left). If not pressed, an all 0s
value is loaded into the register in parallel. (Provided the start switch is in the logic 1 position.)
Lamp Ping-Pong
Add a left pulser. Three wire changes to the D flip-flop on the left:
1) Connect the clock input of the flip-flop to the pulser.
2) Connect the D input to the QA of the left 74197
3) Connect the input of the inverter (that goes to PR) to ground.
Counting the Losses
QD
Right-most
flip-flop of
shift register
A
7493
Fig. 11.8
Fig. 11.4
S1 S0
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9.15
370
Clock Pulse Generator
tL = 0.693 RBC = 10-6
RB = 10-6 /(0.693 x 0.001 x 10-6) = 103 / 0.693 = 1.44 KΩ (Use RB = 1.5 KΩ)
tH/tL = 0.693 (RA + RB)C /(0.693 RB C) = (RA + RB) / RB = 9/ 1 = 9
9 RB = RA + RB RA = 8 RB = 8 x 1.5 KΩ = 12 KΩ
Oscilloscope Waveforms (Actual results may be off by + 20 %.)
5V
Pin 3
output
0V
1 µs
9 µs
Pin 2 or 6
across C
3.3 V = 0.66 VCC
1.1 V = 0.22 VCC
3.3 V
1.7 V
Pin 7
Collector
0V
Variable Frequency Pulse Generator:
20 KHz: 10-3 / 20 = 0.05 x 10-3 = 50 µs
100 KHz: 10-3 / 100 = 10-5 = 10 µs
tH = 49 µs: (RA + RP + RB) / RB = 49/ 1 = 49
RP = 48 RB – RA = 48 x 1.5 – 11 = 60 KΩ
9.16
Control of Register
7476
Cout
J
Q
Carry
CP
K QB
74194
SW1
S1
SW2
S2
SW1
0
0
1
SW2
0 No change
1 shift right
1 Load
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Checking the Circuit:
Initial
+ 0110
+ 1110
+ 1101
+ 0101
+ 0011
Carry
0
0
1
1
0
0
Register
0000
0110
0100
0001
0110
1001
Circuit Operation:
Address
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
9.17
Carry RAM
0
0110
0
0110
0
0011
1110
1
0001
1
1000
1101
1
0101
1
1010
0101
0
1111
0
0111
0011
0
1010
0
0101
RAM Value
RAM + Register
Shfit Register
RAM Value
RAM + Register
SHIFT
RAM Value
RAM + Register
SHIFT
RAM Value
RAM + Register
SHIFT
RAM Value
RAM + REgiser
SHIFT
Multiplication Example (11 x 15 = 165)
Multiplicand B = 1111
C
Initial:
T2 = 1
T1= 1
Add B; P <= P+1
T3 = 1
T2 = 1
Shift CAQ
Add B; P <= P+1
T3 = 1
T2 = 1
Shift CAQ
P <= P+1
T3 = 1
T2 = 1
Shift CAQ
Add B; P <= P+1
T3 = 1
Shift CAQ
T0 = 1
(Because PC = 1)
A
0 0000
1111
0 1111
0 0111
1111
1 0110
0 1011
0 1011
Q
P
1011 0000
1011 0001
1101 0001
1101 0010
0110 0010
0110 0011
0 0101 1011 0011
1111
1 0100 1011 0100
0 1010 0101 0100
1010 0101 = Product
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372
Data Processor Design
Load Q Load A Shift AQ
T1
T2Q1
T3
0
1
0
0
0
0
1
0
Register Q
S1 S0
0
0
0
1
0
1
0
0
S1(Q) = T1
S4(Q) = T1 + T3
0
1
0
1
Register A
S1 S0
0
0
1
0
0
0
1
1
S1(A) = T2Q1
S0(A) = T2Q1 + T3
T1
S1
T2
S0
of Q
Q1
S1
of A
S0
T3
7474
74161
Asynchronous
clear P, A, and E
P
T
D
Cout
E
CP
Design of Control: See Section 8.8.
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373
SOLUTIONS FOR SECTION 9.19
Supplement to Experiment 2:
(a)
w3
x
w1
F=x
y
w2
y
w4
Initially, with xy = 00, w1 = w2 = 1, w3 = w4 = 0 and F = 0. w1 should change to 0 10ns after xy
changes to 01. w4 should change to 1 20 ns after xy changes to 01. F should change from 0 to 1 30 ns
after w4 changes from 0 to 1, i.e., 50 ns after xy changes from 00 to 01. w3 should remain unchanged
because x = 0 for the entire simulation.
(b)
`timescale 1ns/1ps
module Prob_3_33 (output F, input x, y);
wire w1, w2, w3, w4;
and #20 (w3, x, w1);
not #10 (w1, x);
and #20 (w4, y, w1);
not #10 (w2, y);
or #30 (F, w3, w4);
A
endmodule
module t_Prob_3_33 ();
reg x, y;
wire F;
Prob_3_33 M0 (F, x, y);
initial #200 $finish;
initial fork
x = 0;
y = 0;
#100 y = 1;
join
endmodule
(c) To simulate the circuit, it is assumed that the inputs xy = 00 have been applied sufficiently long for
the circuit to be stable before xy = 01 is applied. The testbench sets xy = 00 at t = 0 ns, and xy = 1 at t =
100 ns. The simulator assumes that xy = 00 has been applied long enough for the circuit to be in a stable
state at t = 0 ns, and shows F = 0 as the value of the output at t = 0. The waveforms show the response to
xy = 01 applied at t = 100 ns.
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374
Name
0.000ns
66.670ns
133.340ns
200.010ns
x
y
w1
w2
w3
w4
F
Δ = 50 ns
Supplement to Experiment 4:
(a)
// Gate-level description of circuit in Fig. 4-2
module Circuit_of_Fig_4_2 (
output F1, F2,
input
A, B, C);
wire T1, T2, T3, F2_not, E1, E2, E3;
or G1 (T1, A, B, C);
and G2 (T2, A, B, C);
and G3 (E1, A, B);
and G4 (E2, A, C);
and G5 (E3, B, C);
or G6 (F2, E1, E2, E3);
not G7 (F2_not, F2);
and G8 (T3, T1, F2_not);
or G9 (F1, T2, T3);
endmodule
module t_Circuit_of_Fig_4_2;
reg [2: 0] D;
wire F1, F2;
parameter stop_time = 100;
Circuit_of_Fig_4_2 M1 (F1, F2, D[2], D[1], D[0]);
initial # stop_time $finish;
initial begin
// Stimulus generator
D = 3'b000;
repeat (7)
#10 D = D + 1'b1;
end
initial begin
$display ("A
B C
$monitor ("%b
%b
end
endmodule
F1 F2");
%b %b %b", D[2], D[1], D[0], F1, F2);
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375
/*
A
0
0
0
0
1
1
1
1
B
0
0
1
1
0
0
1
1
C
0
1
0
1
0
1
0
1
F1
0
1
1
0
1
0
0
1
F2
0
0
0
1
0
1
1
1
*/
The simulation results demonstrate the behavior of a full adder, with F1 = sum, and F2 – carry.
Name
0
60
A
B
C
F1
F2
(b)
// 3-INPUT MAJORITY DETECTOR CIRCUIT.
// Circuit implements F = xy + xz +yz.
module Majority_Detector (output F, input x, y, z);
wire wl, w2, w3;
nand
nl(wl, x, y),
n2(w2, x, z),
n3(w3, y, z),
n4(F, wl, w2, w3) ;
endmodule
// Test bench
//Treating inputs to majority detector as a vector, reg [2:0]D; //D[2] = x, D[l] = y, D[0] = z. wire F;
module t_Majority_Detector ();
wire F;
reg [2: 0] D;
wire x = D[2];
wire y = D[1];
wire z = D[0];
Majority_Detector M0 (F, x, y, z);
initial #100 $finish;
initial $monitor ($time,, "xyz = %b F = %b", D, F);
Digital
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376
initial begin
D = 0;
repeat (7)
#10 D = D + 1;
end
endmodule
Simulation results:
0
xyz
=
000
F
=
0
10
xyz
=
001
F
=
0
20
xyz
=
010
F
=
0
30
xyz
=
011
F
=
1
40
xyz
=
100
F
=
0
50
xyz
=
101
F
=
1
60
xyz
=
110
F
=
1
70
xyz
=
111
F
=
1
Name
0
60
x
y
z
F
Supplement to Experiment 5: See the solution to Prob. 4.42.
Supplement to Experiment 7:
(a)
//BEHAVIORAL DESCRIPTION OF 7483 4-BIT ADDER,
module Adder_7483 (
output S4, S3, S2, S1, C4,
input A4, A3, A2, A1, B4, B3, B2, B1, C0, VCC, GND
);
// Note: connect VCC and GND to supply1 and supply0 in the test bench
wire [4: 1] sum;
wire [4: 1] A = {A4, A3, A2, A1};
wire [4: 1] B = {B4, B3, B2, B1};
assign S4 = sum[4];
assign S3 = sum[3];
assign S2 = sum[2];
assign S1 = sum[1];
assign {C4, sum} = A + B + C0;
endmodule
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377
module t_Adder_7483 ();
wire S4, S3, S2, S1, C4;
wire A4, A3, A2, A1, B4, B3, B2, B1;
reg C0;
supply1 VCC;
supply0 GND;
reg [4:1] A, B;
assign A4 = A[4];
assign A3 = A[3];
assign A2 = A[2];
assign A1 = A[1];
assign B4 = B[4];
assign B3 = B[3];
assign B2 = B[2];
assign B1 = B[1];
Adder_7483 M0 (S4, S3, S2, S1, C4, A4, A3, A2, A1, B4, B3, B2, B1, C0, VCC, GND);
initial #2600 $finish;
initial begin
A = 0; B = 0; C0 = 0;
repeat (256) #5 {A, B} = {A, B} + 1;
A = 0; B = 0; C0 = 1;
repeat (256) #5 {A, B} = {A, B} + 1;
end
endmodule
(b)
module Supp_9_17b (output [4: 1] S, output carry, input [4: 1] A, B, input M, VCC, GND);
wire B4, B3, B2, B1;
xor (B4, M, B[4]);
xor (B3, M, B[3]);
xor (B2, M, B[2]);
xor (B1, M, B[1]);
Adder_7483 M0 (S[4], S[3], S[2], S[1], carry, A[4], A[3], A[2], A[1], B4, B3, B2, B1, M, VCC, GND);
endmodule
module Adder_7483 (
output S4, S3, S2, S1, C4,
input A4, A3, A2, A1, B4, B3, B2, B1, C0, VCC, GND
);
// Note: connect VCC and GND to supply1 and supply0 in the test bench
wire [4: 1] sum;
wire [4: 1] A = {A4, A3, A2, A1};
wire [4: 1] B = {B4, B3, B2, B1};
assign S4 = sum[4];
assign S3 = sum[3];
assign S2 = sum[2];
assign S1 = sum[1];
assign {C4, sum} = A + B + C0;
endmodule
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378
module t_Supp_9_17b ();
wire [4: 1] S;
wire carry;
reg C0;
reg [4: 1] A, B;
reg M;
supply1 VCC;
supply0 GND;
Supp_9_17b M0 (S, carry, A, B, M, VCC, GND);
initial #2600 $finish;
initial begin
A = 0; B = 0; M = 0;
repeat (256) #5 {A, B} = {A, B} + 1;
A = 0; B = 0; M = 1;
repeat (256) #5 {A, B} = {A, B} + 1;
end
endmodule
(c), (d)
module supp_9_7c (output S3, S2, S1, S0, C, V, input A3, A2, A1, A0, B3, B2, B1, B0, M);
wire [3: 0] Sum, B;
assign S3 = Sum[3];
assign S2 = Sum[2];
assign S1 = Sum[1];
assign S0 = Sum[0];
wire [3:0] A = {A3, A2, A1, A0};
xor(B[3], B3, M);
xor(B[2], B2, M);
xor(B[1], B1, M);
xor(B[0], B0, M);
xor (V, C, C3);
ripple_carry_4_bit_adder M0 (Sum, C, C3, A, B, M);
endmodule
module t_supp_9_7c ();
wire S3, S2, S1, S0, C, V;
reg A3, A2, A1, A0, B3, B2, B1, B0, M;
wire [3: 0] sum = {S3, S2, S1, S0};
wire [3: 0] A = {A3, A2, A1, A0};
wire [3: 0] B = {B3, B2, B1, B0};
supp_9_7c M0 (S3, S2, S1, S0, C, V, A3, A2, A1, A0, B3, B2, B1, B0, M);
initial #2600 $finish;
initial begin
{A3, A2, A1, A0, B3, B2, B1, B0} = 0; M = 0;
repeat (256) #5 {A3, A2, A1, A0, B3, B2, B1, B0} = {A3, A2, A1, A0, B3, B2, B1, B0} + 1;
{A3, A2, A1, A0, B3, B2, B1, B0} = 0; M = 1;
repeat (256) #5 {A3, A2, A1, A0, B3, B2, B1, B0} = {A3, A2, A1, A0, B3, B2, B1, B0} + 1;
end
endmodule
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module half_adder (output S, C, input x, y);
// Instantiate primitive gates
xor (S, x, y);
and (C, x, y);
endmodule
// Verilog 2001, 2005 syntax
module full_adder (output S, C, input x, y, z);
wire S1, C1, C2;
// Instantiate half adders
half_adder HA1 (S1, C1, x, y);
half_adder HA2 (S, C2, S1, z);
or G1 (C, C2, C1);
endmodule
// Modify for C3 output
module ripple_carry_4_bit_adder ( output [3: 0] Sum, output C4, C3, input [3:0] A, B, input C0);
wire
C1, C2; // Intermediate carries
// Instantiate chain of full adders
full_adder FA0 (Sum[0], C1, A[0], B[0], C0),
FA1 (Sum[1], C2, A[1], B[1], C1),
FA2 (Sum[2], C3, A[2], B[2], C2),
FA3 (Sum[3], C4, A[3], B[3], C3);
endmodule
Addition:
Name
312
332
352
3
A[3:0]
B[3:0]
372
4
15
0
1
2
3
4
5
6
7
8
9
10
11
12
2
4
5
6
7
8
9
10
11
12
13
14
15
0
M
sum[3:0]
1
C
V
Subtraction:
Name
1740
1760
5
A[3:0]
B[3:0]
1780
1800
6
12
13
14
9
8
7
15
0
1
2
3
4
5
6
7
8
9
5
4
3
2
1
0
15
14
13
M
sum[3:0]
6
C
V
Digital
Design
With
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380
Supplement to Experiment 8:
(a)
module Flip_flop_7474 (output reg Q, input D, CLK, preset, clear);
always @ (posedge CLK, negedge preset , negedge clear)
if (!preset)
Q <= 1'b1;
else if (!clear)
Q <= 1'b0;
else
Q <= D;
endmodule
module t_Flip_flop_7474 ();
wire Q;
reg D, CLK, preset, clear;
Flip_flop_7474 M0 (Q, D, CLK, preset, clear);
initial #150 $finish;
initial begin CLK = 0; forever #5 CLK = ~CLK; end
initial fork
preset = 0; clear = 0;
#20 preset = 1;
#40 clear = 1;
join
initial begin D = 0; #60 forever #20 D = ~D; end
endmodule
0
60
Name
120
CLK
preset
clear
D
Q
(b)
//Solution to supplement Experiment 8(b)
//Behavioral description of a 7474 D flip-flop with Q_not
module Flip_Flop_7474_with_Q_not (output reg Q, Q_not, input D, CLK, Preset, Clear);
always @ (posedge CLK, negedge Preset, negedge Clear)
/* case ({Preset, Clear})
2'b00: begin Q <= 1; Q_not <= 1; end
2'b01: begin Q <= 1; Q_not <= 0; end
2'b10: begin Q <= 0; Q_not <= 1; end
2'b11: begin Q <= D; Q_not <= ~D; end
// NOTE: Q_not <= ~Q will produce a pipeline effect and delay Q_not by one clock
endcase*/
if (Preset == 0) begin Q <= 1; if (Clear == 0) Q_not <= 1; else Q_not <= 0; end
else if (Clear == 0) begin Q <= 0; Q_not <= 1; end
else begin Q <= D; Q_not <= ~D; end
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381
endmodule
// Note: this model will not work if Preset and Clear are // both brought low and then high again.
// A case statement for both Q and Q_not is also OK.
module t_Flip_Flop_7474_with_Q_not ();
wire Q, Q_not;
reg D, CLK, Preset, Clear;
Flip_Flop_7474_with_Q_not M0 (Q, Q_not, D, CLK, Preset, Clear);
initial #250 $finish;
initial begin CLK = 0; forever #5 CLK = ~CLK; end
initial fork
Preset = 1; Clear = 1;
#50 Preset = 0;
#80 Clear =
Name
0
80
160
240
CLK
Preset
Clear
D
Q
Q_not
Supplement to Experiment #9:
(a)
module Figure_9_9a (output reg y, input x, clock, reset_b);
reg [1: 0] state, next_state;
parameter S0 = 2'b00, S1 = 2'b01, S2 = 2'b10, S3 = 2'b11;
always @ (posedge clock, negedge reset_b) if (reset_b == 0) state <= S0; else state <= next_state;
always @ (state, x) begin
y = 0;
case (state)
S0: if (x) begin next_state = S0; y = 1; end else begin next_state = S1; y = 0; end
S1: if (x) begin next_state = S3; y = 0; end else begin next_state = S2; y = 1; end
S2: if (x) begin next_state = S1; y = 0; end else begin next_state = S0; y = 1; end
S3: if (x) begin next_state = S2; y = 1; end else begin next_state = S3; y = 0; end
endcase
end
endmodule
module t_Figure_9_9a ();
wire y;
reg x, clock, reset_b;
Figure_9_9a M0 (y, x, clock, reset_b);
initial #200 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial fork
reset_b = 0;
Digital
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x = 0;
// S0. S1, S2 after release of reset_b
#10 reset_b = 1;
#40 x = 1;
// Stay in S0
#60 x= 0;
// S1, S2
#80 x = 1;
// s1, S3,
#100 x = 0; // S3
#130 x = 1;
// S2, S1, S3 cycle
join
endmodule
Name
0
60
120
180
clock
reset_b
x
state[1:0]
0
1
2
0
1
2
1
3
2
1
3
2
1
3
y
(b) The solution depends on the particular design.
(c, d)
Note: The HDL description of the state diagram produces outputs T0, T1, and T2. Additional logic must
form the signals that control the datapath unit (Load_regs, Incr_P, Add_regs, and Shift_regs). An
alternative controller that generates the control signals, rather than the states, as the outputs is given
below too. It produces identical simulation results.
module Supp_9_9cd # (parameter dp_width = 5)
(
output [2*dp_width - 1: 0]
Product,
output
Ready,
input
[dp_width - 1: 0]
Multiplicand, Multiplier,
input
Start, clock, reset_b
);
wire Load_regs, Incr_P, Add_regs, Shift_regs, Done, Q0;
Controller M0 (
Ready, Load_regs, Incr_P, Add_regs, Shift_regs, Start, Done, Q0,
clock, reset_b
);
Datapath M1(Product, Q0, Done, Multiplicand, Multiplier,
Start, Load_regs, Incr_P, Add_regs, Shift_regs, clock, reset_b);
endmodule
/* // This alternative controller directly produces the signals needed to control the datapath.
module Controller (
output Ready,
output reg Load_regs, Incr_P, Add_regs, Shift_regs,
input Start, Done, Q0, clock, reset_b
);
parameter
S_idle =
3'b001,
// one-hot code
S_add = 3'b010,
S_shift = 3'b100;
reg [2: 0]
state, next_state;
// sized for one-hot
assign
Ready = (state == S_idle);
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always @ (posedge clock, negedge reset_b)
if (~reset_b) state <= S_idle; else state <= next_state;
always @ (state, Start, Q0, Done) begin
next_state = S_idle;
Load_regs = 0;
Incr_P = 0;
Add_regs = 0;
Shift_regs = 0;
case (state)
S_idle:
if (Start) begin next_state = S_add; Load_regs = 1; end
S_add:
begin next_state = S_shift; Incr_P = 1; if (Q0) Add_regs = 1; end
S_shift: begin Shift_regs = 1;
if (Done) next_state = S_idle;
else next_state = S_add;
end
default: next_state = S_idle;
endcase
end
endmodule
*/
// This controller has an embedded unit to generate T0, T1, and T2 and additional logic to form // // the
signals needed to control the datapath.
module Controller (
output Ready, Load_regs, Incr_P, Add_regs, Shift_regs,
input Start, Done, Q0, clock, reset_b
);
State_Generator M0 (T0, T1, T2, Start, Done, Q0, clock, reset_b);
assign Ready = T0;
assign Load_regs = T0 && Start;
assign Incr_P = T1;
assign Add_regs = T1 && Q0;
assign Shift_regs = T2;
endmodule
module State_Generator (output T0,T1, T2, input Start, Done, Q0, clock, reset_b);
parameter
S_idle = 3'b001,
// one-hot code
S_add = 3'b010,
S_shift = 3'b100;
reg [2: 0]
state, next_state;
// sized for one-hot
assign T0 = (state == S_idle);
assign T1 = (state == S_add);
assign T2 = (state == S_shift);
always @ (posedge clock, negedge reset_b)
if (~reset_b) state <= S_idle; else state <= next_state;
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always @ (state, Start, Q0, Done) begin
next_state = S_idle;
case (state)
S_idle:
if (Start) next_state = S_add;
S_add:
next_state = S_shift;
S_shift: if (Done) next_state = S_idle; else next_state = S_add;
default: next_state = S_idle;
endcase
end
endmodule
module Datapath #(parameter dp_width = 5, BC_size = 3) (
output [2*dp_width - 1: 0] Product, output Q0, output Done,
input [dp_width - 1: 0] Multiplicand, Multiplier,
input Start, Load_regs, Incr_P, Add_regs, Shift_regs, clock, reset_b
);
// Default configuration: 5-bit datapath
reg [dp_width - 1: 0]
A, B, Q;
// Sized for datapath
reg
C;
reg [BC_size - 1: 0]
P;
// Bit counter
assign Q0 = Q[0];
assign Done = (P == dp_width );
// Multiplier is exhausted
assign Product = {C, A, Q};
always @ (posedge clock, negedge reset_b)
if (reset_b == 0) begin
// Added to this solution, but
P <= 0;
// not really necessary since Load_regs
B <= 0;
// initializes the datapath
C <= 0;
A <= 0;
Q <= 0;
end
else begin
if (Load_regs) begin
P <= 0;
A <= 0;
C <= 0;
B <= Multiplicand;
Q <= Multiplier;
end
if (Add_regs) {C, A} <= A + B;
if (Shift_regs) {C, A, Q} <= {C, A, Q} >> 1;
if (Incr_P) P <= P+1 ;
end
endmodule
module t_Supp_9_9cd;
parameter
wire [2 * dp_width - 1: 0]
wire
reg [dp_width - 1: 0]
reg
integer
reg
dp_width = 5;
// Width of datapath
Product;
Ready;
Multiplicand, Multiplier;
Start, clock, reset_b;
Exp_Value;
Error;
Supp_9_9cd M0(Product, Ready, Multiplicand, Multiplier, Start, clock, reset_b);
initial #115000 $finish;
initial begin clock = 0; #5 forever #5 clock = ~clock; end
Digital
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initial fork
reset_b = 1;
#2 reset_b = 0;
#3 reset_b = 1;
join
always @ (negedge Start) begin
Exp_Value = Multiplier * Multiplicand;
//Exp_Value = Multiplier * Multiplicand +1;
end
always @ (posedge Ready) begin
# 1 Error <= (Exp_Value ^ Product) ;
end
// Inject error to confirm detection
initial begin
#5 Multiplicand = 0;
Multiplier = 0;
repeat (32) #10 begin
Start = 1;
#10 Start = 0;
repeat (32) begin
Start = 1;
#10 Start = 0;
#100 Multiplicand = Multiplicand + 1;
end
Multiplier = Multiplier + 1;
end
end
endmodule
Name
47359
47399
47439
47479
clock
reset_b
Ready
Start
Load_regs
Add_regs
Shift_regs
Incr_P
Q0
Done
1
state[2:0]
2
4
2
4
2
4
2
4
2
4
1
2
4
T0
T1
T2
Multiplicand[4:0]
11
12
13
13
Multiplier[4:0]
Product[9:0]
Exp_Value
143
143
13
397
198
99
483
241
625
312
156
13
156
Error
Digital
Design
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429
169
386
Supplement to Experiment #10:
module Counter_74161 (
output
QD, QC, QB, QA,
output
COUT,
input
D, C, B, A,
input
P, T,
L,
CK,
CLR
);
// Data output
// Output carry
// Data input
// Active high to count
// Active low to load
// Positive edge sensitive
// Active low to clear
reg [3: 0] A_count;
assign QD = A_count[3];
assign QC = A_count[2];
assign QB = A_count[1];
assign QA = A_count[0];
assign COUT = ((P == 1) && (T == 1) && (L == 1) && (A_count == 4'b1111));
always @ (posedge CK, negedge CLR)
if (CLR == 0)
A_count <= 4'b0000;
else if (L == 0)
A_count <= {D, C, B, A};
else if ((P == 1) && (T == 1)) A_count <= A_count + 1'b1;
else A_count <= A_count; // redundant statement
endmodule
module t_Counter_74161 ();
wire
QD, QC, QB, QA;
wire [3: 0] Data_outputs = {QD, QC, QB, QA};
wire
Carry_out;
// Output carry
reg [3:0]
Data_inputs;
// Data input
reg
Count,
// Active high to count
Load,
// Active low to load
Clock,
// Positive edge sensitive
Clear;
// Active low to clear
Counter_74161 M0 (QD, QC, QB, QA, Carry_out,
Data_inputs[3], Data_inputs[2], Data_inputs[1], Data_inputs[0], Count, Count, Load, Clock, Clear);
initial #200 $finish;
initial begin Clock = 0; forever #5 Clock = ~Clock; end
initial fork
Clear = 0;
Load = 1;
Count = 0;
#20 Clear = 1;
#40 Load = 0;
#50 Load = 1;
#80 Count = 1;
#180 Count = 0;
Data_inputs = 4'ha;
join
endmodule
// 10
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Name
0
70
140
Clock
Clear
Load
Count
a
Data_inputs[3:0]
Data_outputs[3:0]
0
a
b
c
d
e
f
0
1
2
3
Supplement to Experiment #11.
(a)
// Note: J and K_bar are assumed to be connected together.
module SReg_74195 (
output reg QA, QB, QC, QD,
output QD_bar,
input A, B, C, D, SH_LD, J, K_bar, CLR_bar, CK
);
assign QD_bar = ~QD;
always @ (posedge CK, negedge CLR_bar)
if (!CLR_bar) {QA, QB, QC, QD} <= 4'b0;
else if (!SH_LD) {QA, QB, QC, QD} <= {A, B, C, D};
else case ({J, K_bar})
2'b00: {QA, QB, QC, QD} <= {1'b0, QA, QB, QC};
2'b11: {QA, QB, QC, QD} <= {1'b1, QA, QB, QC};
2'b01: {QA, QB, QC, QD} <= {QA, QA, QB, QC}; // unused
2'b10: {QA, QB, QC, QD} <= {~QA, QA, QB, QC}; // unused
endcase
endmodule
module t_SReg_74195 ();
wire QA, QB, QC, QD;
wire QD_bar;
reg A, B, C, D, SH_LD, CLR_bar, CK;
reg Serial_Input;
wire J = Serial_Input;
wire K_bar = Serial_Input;
wire [3: 0] Data_inputs = {A, B, C, D};
wire [3: 0] Data_outputs = {QA, QB, QC, QD};
SReg_74195 M0 (QA, QB, QC, QD, QD_bar, A, B, C, D, SH_LD, J, K_bar, CLR_bar, CK);
initial #200 $finish;
initial begin CK = 0; forever #5 CK = ~CK; end
initial fork
{A, B, C, D} = 4'ha;
CLR_bar = 0;
Serial_Input = 0;
SH_LD = 0;
#30 CLR_bar = 1;
#60 SH_LD = 1;
#120 Serial_Input = 1;
join
endmodule
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4
388
Name
0
60
120
180
CK
CLR_bar
SH_LD
Serial_Input
A
B
C
D
QA
QB
QC
QD
QD_bar
a
Data_inputs[3:0]
Data_outputs[3:0]
0
a
5
2
1
0
8
c
e
f
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(b)
module Mux_74157 (
output reg Y1, Y2, Y3, Y4,
input A1, A2, A3, A4, B1, B2, B3, B4, SEL, STB
);
wire [4: 1] In_A = {A1, A2, A3, A4};
wire [4: 1] In_B = {B1, B2, B3, B4};
always @ (In_A, In_B, SEL, STB)
if (STB) {Y1, Y2, Y3, Y4} = 4'b0;
else if (SEL) {Y1, Y2, Y3, Y4} = In_B;
else {Y1, Y2, Y3, Y4} = In_A;
endmodule
module t_Mux_74157 ();
wire Y1, Y2, Y3, Y4;
reg A1, A2, A3, A4, B1, B2, B3, B4, SEL, STB;
wire [4: 1] In_A = {A1, A2, A3, A4};
wire [4: 1] In_B = {B1, B2, B3, B4};
wire [4: 1] Y = {Y1, Y2, Y3, Y4};
Mux_74157 M0 (Y1, Y2, Y3, Y4, A1, A2, A3, A4, B1, B2, B3, B4, SEL, STB);
initial #200 $finish;
initial fork
{A1, A2, A3, A4} = 4'ha;
{B1, B2, B3, B4} = 4'hb;
STB = 1;
SEL = 1;
#50 STB = 0;
#100 SEL = 0;
#150 STB = 1;
join
endmodule
Name
0
60
120
In_A[4:1]
a
In_B[4:1]
b
180
STB
SEL
Y[4:1]
0
b
a
0
(c)
module Bi_Dir_Shift_Reg (output [1: 4] D_out, input [1: 4] D_in, input SEL, STB, SH_LD, clock,
CLR_bar);
wire
QD_bar;
wire [1: 4] Y;
SReg_74195 M0 (D_out[1], D_out[2], D_out[3], D_out[4], QD_bar, Y[1], Y[2], Y[3], Y[4],
SH_LD, D_out[4], D_out[4], CLR_bar, clock
);
Mux_74157 M1 (Y[1], Y[2], Y[3], Y[4], D_in[1], D_in[2], D_in[3], D_in[4],
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390
D_out[2], D_out[3], D_out[4], D_out[1], SEL, STB
);
endmodule
module SReg_74195 (
output reg QA, QB, QC, QD,
output
QD_bar,
input
A, B, C, D, SH_LD, J, K_bar, CLR_bar, CK
);
assign
QD_bar = ~QD;
always @ (posedge CK, negedge CLR_bar)
if (!CLR_bar) {QA, QB, QC, QD} <= 4'b0;
else if (!SH_LD) {QA, QB, QC, QD} <= {A, B, C, D};
else case ({J, K_bar})
2'b00: {QA, QB, QC, QD} <= {1'b0, QA, QB, QC};
2'b11: {QA, QB, QC, QD} <= {1'b1, QA, QB, QC};
2'b01: {QA, QB, QC, QD} <= {QA, QA, QB, QC}; // unused
2'b10: {QA, QB, QC, QD} <= {~QA, QA, QB, QC}; // unused
endcase
endmodule
module Mux_74157 (
output reg Y1, Y2, Y3, Y4,
input A1, A2, A3, A4, B1, B2, B3, B4, SEL, STB
);
wire [4: 1] In_A = {A1, A2, A3, A4};
wire [4: 1] In_B = {B1, B2, B3, B4};
always @ (In_A, In_B, SEL, STB)
if (STB) {Y1, Y2, Y3, Y4} = 4'b0;
else if (SEL) {Y1, Y2, Y3, Y4} = In_B;
else {Y1, Y2, Y3, Y4} = In_A;
endmodule
// SEL = 1
// SEL = 0
module t_Bi_Dir_Shift_Reg ();
wire [1: 4] D_out;
reg [1: 4] D_in;
reg SEL, STB, SH_LD, clock, CLR_bar;
Bi_Dir_Shift_Reg M0 (D_out, D_in, SEL, STB, SH_LD, clock, CLR_bar);
initial #200 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial fork
D_in = 4'h8;
// Data for walking 1 to right
CLR_bar = 0;
STB = 0;
SEL = 0;
// Selects D_in
SH_LD = 0;
// load D_in
#10 CLR_bar = 1;
#20 STB = 1;
#40 STB = 0;
#30 SH_LD = 1;
#50 SH_LD = 0; // Interrupt count to load
#60 SH_LD = 1;
#80 SEL = 1;
#100 STB = 1;
#130 STB = 0;
#140 SH_LD = 0;
//#150 SH_LD = 1;
join
endmodule
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Asynchronous clear
Synchronous clear
60
0
Name
No effect
Reload
120
180
clock
CLR_bar
SH_LD
STB
SEL
8
D_in[1:4]
8
Y[1:4]
D_out[1:4]
0
0
8
8
0
8
2
4
2
1
0
8
4
2
1
1
2
4
8
1
2
8
1
2
4
8
1
QD
Shifting towards D_out[4]
Shifting towards D_out[1]
The behavioral model is listed below. The two models have matching simulation results.
SH_LD
SEL
STB
D_in[1: 4]
D_out[ 4]
0
D_out[1: 4]
74157
74195
Parallel
load
1
{D[2], D[3], D[4], D[1]}
Note: CLR_b provides active-low asynchronous
clear of D_out , overriding the functionality
shown in the table below.
SH_LD
STB
SEL
0
0
0
1
0
0
1
x
0
1
x
x
D_out <= D_in
Shift_D_out towards D[1] (left)
Synchronous clear: D_out <= 4'b0
Shift towards D_out[4] (right)
module Bi_Dir_Shift_Reg_beh (output reg [1: 4] D_out, input [1: 4] D_in, input SEL, STB, SH_LD, clock,
CLR_bar);
always @ (posedge clock, negedge CLR_bar)
if (!CLR_bar) D_out <= 4'b0;
else if (SH_LD ) D_out <= {D_out[4], D_out[1], D_out[2], D_out[3]};
else if (!STB) D_out <= SEL ? {D_out[2: 4], D_out[1]}: D_in;
else D_out <= 4'b0;
endmodule
module t_Bi_Dir_Shift_Reg_beh ();
wire [1: 4] D_out;
reg [1: 4] D_in;
reg SEL, STB, SH_LD, clock, CLR_bar;
Bi_Dir_Shift_Reg_beh M0 (D_out, D_in, SEL, STB, SH_LD, clock, CLR_bar);
initial #200 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial fork
D_in = 4'h8;
// Data for walking 1 to right
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CLR_bar = 0;
STB = 0;
SEL = 0;
// Selects D_in
SH_LD = 0;
// load D_in
#10 CLR_bar = 1;
#20 STB = 1;
#40 STB = 0;
#30 SH_LD = 1;
#50 SH_LD = 0; // Interrupt count to load
#60 SH_LD = 1;
#80 SEL = 1;
#100 STB = 1;
#130 STB = 0;
#140 SH_LD = 0;
//#150 SH_LD = 1;
join
endmodule
Supplement to Experiment #13.
module RAM_74189 (output S4, S3, S2, S1, input D4, D3, D2, D1, A3, A2, A1, A0, CS, WE);
// Note: active-low CS and WE
wire [3: 0]
address = {A3, A2, A1, A0};
reg [3: 0]
RAM [0: 15];
// 16 x 4 memory
wire [4: 1]
Data_in = { D4, D3, D2, D1}; // Input word
tri [4: 1]
Data;
// Output data word, three-state output
assign S1 = Data[1];
// Output bits
assign S2 = Data[2];
assign S3 = Data[3];
assign S4 = Data[4];
always @ (Data_in, address, CS, WE) if (~CS && ~WE) RAM[address] = Data_in;
assign Data = (~CS && WE) ? ~RAM[address] : 4'bz;
endmodule
module t_RAM_74189 ();
reg [4: 1] Data_in;
reg [3: 0] address;
reg CS, WE;
wire S1, S2, S3, S4;
wire D1, D2, D3, D4;
wire A0, A1, A2, A3;
wire [4: 1] Data_out = {S4, S3, S2, S1};
assign D1 = Data_in [1];
assign D2 = Data_in [2];
assign D3 = Data_in [3];
assign D4 = Data_in [4];
assign A0 = address[0];
assign A1 = address[1];
assign A2 = address[2];
assign A3 = address[3];
wire [3: 0] RAM_0 = M0.RAM[0];
wire [3: 0] RAM_1 = M0.RAM[1];
wire [3: 0] RAM_2 = M0.RAM[2];
wire [3: 0] RAM_3 = M0.RAM[3];
wire [3: 0] RAM_4 = M0.RAM[4];
wire [3: 0] RAM_5 = M0.RAM[5];
wire [3: 0] RAM_6 = M0.RAM[6];
wire [3: 0] RAM_7 = M0.RAM[7];
wire [3: 0] RAM_8 = M0.RAM[8];
wire [3: 0] RAM_9 = M0.RAM[9];
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wire [3: 0] RAM_10 = M0.RAM[10];
wire [3: 0] RAM_11 = M0.RAM[11];
wire [3: 0] RAM_12= M0.RAM[12];
wire [3: 0] RAM_13 = M0.RAM[13];
wire [3: 0] RAM_14 = M0.RAM[14];
wire [3: 0] RAM_15 = M0.RAM[15];
wire [4: 1] word = ~Data_out;
RAM_74189 M0 (S4, S3, S2, S1, D4, D3, D2, D1, A3, A2, A1, A0, CS, WE);
initial #110 $finish;
initial fork
WE = 1;
CS = 1;
address = 0;
Data_in = 3;
#10 CS = 0;
#15 WE = 0;
#20 WE = 1;
#25 address = 14;
#25 Data_in = 1;
#30 WE = 0;
#35 WE = 1;
#40 CS = 1;
#50 address = 0;
#60 CS = 0;
#70 CS = 1;
#80 address = 14;
#90 CS = 0;
join
endmodule
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Write
Name
Hi-Z
0
Read
30
60
90
CS
WE
address[3:0]
0
Data_in[4:1]
3
14
0
x
RAM_0[3:0]
3
RAM_1[3:0]
x
RAM_2[3:0]
x
RAM_3[3:0]
x
RAM_4[3:0]
x
RAM_5[3:0]
x
RAM_6[3:0]
x
RAM_7[3:0]
x
RAM_8[3:0]
x
RAM_9[3:0]
x
RAM_10[3:0]
x
RAM_11[3:0]
x
RAM_12[3:0]
x
x
RAM_13[3:0]
x
RAM_14[3:0]
1
x
RAM_15[3:0]
x
word[4:1]
Data_out[4:1]
14
1
z
3
x
z
12
x
x
z
1
x
3
x
1
14
z
12
z
14
Note: Data_out is the complement of the stored value
Supplement to Experiment #14.
module Bi_Dir_Shift_Reg_74194 (
output reg QA, QB, QC, QD,
input
A, B, C, D, SIR, SIL, s1, s0, CK, CLR
);
always @ (posedge CK, negedge CLR)
if (!CLR) {QA, QB, QC, QD} <= 4'b0;
else case ({s1, s0})
2'b00: {QA, QB, QC, QD} <= {QA, QB, QC, QD};
2'b01: {QA, QB, QC, QD} <= {SIR, QA, QB, QC};
2'b10: {QA, QB, QC, QD} <= {QB, QC, QD, SIL};
2'b11: {QA, QB, QC, QD} <= {A, B, C, D};
endcase
endmodule
module t_Bi_Dir_Shift_Reg_74194 ();
wire QA, QB, QC, QD;
reg A, B, C, D, SIR, SIL, s1, s0, clock, CLR;
Bi_Dir_Shift_Reg_74194 M0 (QA, QB, QC, QD, A, B, C, D, SIR, SIL, s1, s0, clock, CLR);
initial #250 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
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initial fork
CLR = 0;
{A, B, C, D} = 4'hf;
s1 = 0;
s0 = 0;
SIL = 0;
SIR = 0;
#10 CLR = 1;
#30 begin s1 = 1; s0 = 1; end// load
#40 s1 = 0; // shift right
#100 s1 = 1; // load
#110 begin s1 = 0; s0 = 0; end
#140 s1 = 1; // shift left
#160 s1 = 0; // pause
#180 s1 = 1; // resume
join
endmodule
Load
Load
Shift right, filling 0
Shift left, filling 0
Pause
Name
0
70
140
Shift left, filling 0
210
clock
CLR
s1
s0
A
B
C
D
SIR
QA
QB
QC
QD
SIL
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Supplement to Experiment #16.
The HDL behavioral descriptions of the components in the block diagram of Fig. 9.23 are described in the
solutions of previous experiments, along with their test benches and simulations results: 74189 is described
in Experiment 13(a); 74157 in Experiment 11(b); 74161 in Experiment 10; 7483 in Experiment 7(a); 74194
in Experiment 14; and 7474 in Experiment 8(a). The structural description of the parallel adder instantiates
these components to show how they are interconnected (see the solution to the supplement for Experiment 17
for a similar procedure). A test bench and simulation results for the integrated unit are given below.
// LOAD condition for 74194: s1 = 1, s0 = 1
// SHIFT condition: s1 = 0, s0 = 1
// NO CHANGE condition: s1 = 0, s0 = 0
module Supp_9_16 (
output [3: 0] accum_sum,
output carry,
input [3: 0] Data_in, Addr_in,
input SIR, SIL, CS, WE, s1, s0, count, Load, select, STB, clock, preset, clear, VCC, GND
);
wire B4 = Data_in[3]; // Data world to memory
wire B3 = Data_in[2];
wire B2 = Data_in[1];
wire B1 = Data_in[0];
wire S4, S3, S2, S1;
wire D4, D3, D2, D1;
wire S4b = ~S4; // Inverters
wire S3b = ~S3;
wire S2b = ~S2;
wire S1b = ~S1;
wire D = Addr_in[3]; // For parallel load of address counter
wire C = Addr_in[2];
wire B = Addr_in[1];
wire A = Addr_in[0];
wire Ocar, Y1, Y2, Y3, Y4, QA, QB, QC, QD, A3, A2, A1, A0;
assign accum_sum = {D4, D3, D2, D1};
Flip_flop_7474 M0 (Ocar, carry, clock, preset, clear);
Adder_7483 M1 (D4, D3, D2, D1, carry, S4b, S3b, S2b, S1b, QD, QC, QB, QA, Ocar, VCC, GND);
Mux_74157 M2 (Y4, Y3, Y2, Y1, QD, QC, QB, QA, B4, B3, B2, B1, select, STB);
Counter_74161 M3 (A3, A2, A1, A0, COUT, D, C, B, A, count, count, Load, clock, clear);
RAM_74189 M4 (S4, S3, S2, S1, Y4, Y3, Y2, Y1, A3, A2, A1, A0, CS, WE);
Reg_74194 M5 (QD, QC, QB, QA, D4, D3, D2, D1, Ocar, SIL, s1, s0, clock, clear);
endmodule
module t_Supp_9_16 ();
wire [3: 0] sum;
wire carry;
reg [3: 0] Data_in, Addr_in;
reg SIR, SIL, CS, WE, s1, s0, count, Load, select, STB, clock, preset, clear;
supply1 VCC;
supply0 GND;
wire [3: 0] RAM_0 = M0.M4.RAM[0];
wire [3: 0] RAM_1 = M0.M4.RAM[1];
wire [3: 0] RAM_2 = M0.M4.RAM[2];
wire [3: 0] RAM_3 = M0.M4.RAM[3];
wire [3: 0] RAM_4 = M0.M4.RAM[4];
wire [3: 0] RAM_5 = M0.M4.RAM[5];
wire [3: 0] RAM_6 = M0.M4.RAM[6];
wire [3: 0] RAM_7 = M0.M4.RAM[7];
wire [3: 0] RAM_8 = M0.M4.RAM[8];
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wire [3: 0] RAM_9 = M0.M4.RAM[9];
wire [3: 0] RAM_10 = M0.M4.RAM[10];
wire [3: 0] RAM_11 = M0.M4.RAM[11];
wire [3: 0] RAM_12= M0.M4.RAM[12];
wire [3: 0] RAM_13 = M0.M4.RAM[13];
wire [3: 0] RAM_14 = M0.M4.RAM[14];
wire [3: 0] RAM_15 = M0.M4.RAM[15];
wire [4: 1] word = {M0.S4b, M0.S3b,M0.S2b, M0.S1b};
wire [4: 1] mux_out = { M0.Y4, M0.Y3, M0.Y2, M0.Y1};
wire [4: 1] Reg_Output = {M0.QD, M0.QC, M0.QB, M0.QA};
Supp_9_16 M0 (sum, carry, Data_in, Addr_in, SIR, SIL, CS, WE, s1, s0, count, Load,
select, STB, clock, preset, clear, VCC, GND);
integer k;
initial #600 $finish;
initial begin clock = 0; forever #5 clock = ~clock; end
initial fork
#10 begin preset = 1; clear = 0; s1 = 0; s0 = 0; Load = 1; count = 0; CS = 1; WE = 1; STB = 0; end
// initialize memory
#10 begin k = 0; repeat (16) begin M0.M4.RAM[k] = 4'hf; k = k + 1; end end
#20 begin Data_in = 4'hf; Addr_in = 0; select = 1; end
#30 begin clear = 1; WE = 0; end
// load memory
#40 begin
count = 1;
CS = 0;
begin
repeat (16) @ (negedge clock) Data_in = Data_in + 1;
count = 0;
@ (negedge clock) CS = 1;
end
end
#200 count = 1;
// Establish address
#240 count = 0;
#250 WE = 1;
#260 CS = 0;
// Read from memory
#280 clear = 0;
#290 clear = 1;
#300 count = 1;
// Establish address
#340 begin s1 = 1; s0 = 1; count = 0; end
#390 CS = 0;
#400 clear = 0;
// Clear the registers
#410 clear = 1;
#420 begin count = 1; CS = 0; end
// Accumulate values
#490 begin count = 0; CS = 1; end
join
endmodule
module Flip_flop_7474 (output reg Q, input D, CLK, preset, clear);
always @ (posedge CLK, negedge preset , negedge clear)
if (!preset)
Q <= 1'b1;
else if (!clear)
Q <= 1'b0;
else
Q <= D;
endmodule
module Adder_7483 (
output S4, S3, S2, S1, C4,
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input A4, A3, A2, A1, B4, B3, B2, B1, C0, VCC, GND
);
// Note: connect VCC and GND to supply1 and supply0 in the test bench
wire [4: 1] sum;
wire [4: 1] A = {A4, A3, A2, A1};
wire [4: 1] B = {B4, B3, B2, B1};
assign S4 = sum[4];
assign S3 = sum[3];
assign S2 = sum[2];
assign S1 = sum[1];
assign {C4, sum} = A + B + C0;
endmodule
module Mux_74157 (
output reg Y1, Y2, Y3, Y4,
input A1, A2, A3, A4, B1, B2, B3, B4, SEL, STB
);
wire [4: 1] In_A = {A1, A2, A3, A4};
wire [4: 1] In_B = {B1, B2, B3, B4};
always @ (In_A, In_B, SEL, STB)
if (STB) {Y1, Y2, Y3, Y4} = 4'b0;
else if (SEL) {Y1, Y2, Y3, Y4} = In_B;
else {Y1, Y2, Y3, Y4} = In_A;
endmodule
module Counter_74161 (
output QD, QC, QB, QA,
// Data output
output COUT,
// Output carry
input
D, C, B, A,
// Data input
input
P, T,
// Active high to count
L,
// Active low to load
CK,
// Positive edge sensitive
CLR
// Active low to clear
);
reg [3: 0] A_count;
assign QD = A_count[3];
assign QC = A_count[2];
assign QB = A_count[1];
assign QA = A_count[0];
assign COUT = ((P == 1) && (T == 1) && (L == 1) && (A_count == 4'b1111));
Digital
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HDL
–
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Manual.
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Copyright
2012,
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rights
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399
always @ (posedge CK, negedge CLR)
if (CLR == 0)
A_count <= 4'b0000;
else if (L == 0)
A_count <= {D, C, B, A};
else if ((P == 1) && (T == 1))
A_count <= A_count + 1'b1;
else
A_count <= A_count; // redundant statement
endmodule
module RAM_74189 (output S4, S3, S2, S1, input D4, D3, D2, D1, A3, A2, A1, A0, CS, WE);
// Note: active-low CS and WE
wire [3: 0] address = {A3, A2, A1, A0};
reg [3: 0]
RAM [0: 15];
// 16 x 4 memory
wire [4: 1] Data_in = { D4, D3, D2, D1}; // Input word
tri [4: 1]
Data;
// Output data word, three-state output
assign S1 = Data[1];
// Output bits
assign S2 = Data[2];
assign S3 = Data[3];
assign S4 = Data[4];
always @ (Data_in, address, CS, WE) if (~CS && ~WE) RAM[address] = Data_in;
assign Data = (~CS && WE) ? ~RAM[address] : 4'bz; // Note complement of data word
endmodule
module Reg_74194 (
output reg QA, QB, QC, QD,
input
A, B, C, D, SIR, SIL, s1, s0, CK, CLR
);
always @ (posedge CK, negedge CLR)
if (!CLR) {QA, QB, QC, QD} <= 4'b0;
else case ({s1, s0})
2'b00: {QA, QB, QC, QD} <= {QA, QB, QC, QD};
2'b01: {QA, QB, QC, QD} <= {SIR, QA, QB, QC};
2'b10: {QA, QB, QC, QD} <= {QB, QC, QD, SIL};
2'b11: {QA, QB, QC, QD} <= {A, B, C, D};
endcase
endmodule
Simulation results: initializing memory to 4'hf, then writing to memory. Note: the values of the inputs are
ambiguous until the clear signal is asserted. Signals Ocar and carry are ambiguous because the output of
memory is high-z until memory is read is read.
Digital
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400
Name
0
60
120
180
clock
preset
clear
CS
WE
s1
s0
Load
count
select
STB
x
Addr_in[3:0]
address[3:0]
0
x
0
x
Data_in[3:0]
1
f
0
2
1
3
2
4
5
3
6
4
5
6
8
7
9
8
10
9
11
a
12
b
13
c
14
d
15
e
0
f
x
word[4:1]
Reg_Output[4:1]
7
x
0
Ocar
x
accum_sum[3:0]
carry
RAM_0[3:0]
x
RAM_1[3:0]
x
RAM_2[3:0]
x
RAM_3[3:0]
x
RAM_4[3:0]
x
RAM_5[3:0]
x
RAM_12[3:0]
x
RAM_13[3:0]
x
RAM_14[3:0]
x
RAM_15[3:0]
x
f
0
f
1
f
2
f
3
f
4
f
5
f
c
f
d
f
e
f
Initialize memory
f
Write to memory
Digital
Design
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An
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401
Sequence through addresses and
accumulate the sum
Clear registers
Name
258
318
378
438
clock
preset
clear
CS
WE
s1
s0
Load
count
select
STB
Addr_in[3:0]
address[3:0]
Data_in[3:0]
word[4:1]
Reg_Output[4:1]
Ocar
accum_sum[3:0]
carry
RAM_0[3:0]
RAM_1[3:0]
RAM_2[3:0]
RAM_3[3:0]
RAM_4[3:0]
RAM_5[3:0]
RAM_12[3:0]
RAM_13[3:0]
RAM_14[3:0]
RAM_15[3:0]
0
3
0
1
2
3
4
0
1
f
3
0
1
2
3
0
x
0
1
2
3
4
4
8
4
12
0
5
0
8
12
0
5
9
1
0
0
0
1
2
3
4
5
c
d
e
f
Digital
Design
With
An
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HDL
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1
402
Clear registers
Name
Read and accumulate values
372
432
492
552
clock
preset
clear
CS
WE
s1
s0
Load
count
select
STB
0
Addr_in[3:0]
4
address[3:0]
0
1
2
3
5
6
7
f
Data_in[3:0]
4
word[4:1]
Reg_Output[4:1]
4
0
0
5
5
9
1
0
2
3
4
5
6
1
3
6
10
15
3
6
10
15
5
x
5
x
Ocar
accum_sum[3:0]
0
1
x
carry
RAM_0[3:0]
0
RAM_1[3:0]
1
RAM_2[3:0]
2
RAM_3[3:0]
3
RAM_4[3:0]
4
RAM_5[3:0]
5
RAM_12[3:0]
c
RAM_13[3:0]
d
RAM_14[3:0]
e
RAM_15[3:0]
f
Supplement to Experiment #17.
The HDL behavioral descriptions of the components in the block diagram of Fig. 9.23 are described in
the solutions of previous experiments, along with their test benches and simulations results: 74161 in
Experiment 10; 7483 in Experiment 7(a); 74194 in Experiment 14; and 7474 in Experiment 8(a). The
structural description of the parallel adder instantiates these components to show how they are
interconnected (see the solution to the supplement for Experiment 17 for a similar procedure). A test
bench and simulation results for the integrated unit are given below.
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//
Control
unit
is
obtained
by
modifying
the
solution
to
Prob.
8.24.
//
Datapath
is
implemented
with
a
structural
HDL
model
and
IC
components.
//
LOAD
condition
for
74194:
s1
=
1,
s0
=
1
//
SHIFT
condition:
s1
=
0,
s0
=
1
//
NO
CHANGE
condition:
s1
=
0,
s0
=
0
module Supp_9_17_Par_Mult # (parameter dp_width = 4)
(
output [2*dp_width - 1: 0]
Product,
output
Ready,
input
[dp_width - 1: 0]
Multiplicand, Multiplier,
input
Start, clock, reset_b, VCC, GND
);
wire Load_regs, Incr_P, Add_regs, Shift_regs, Done, Q0;
Controller M0 (
Ready, Load_regs, Incr_P, Add_regs, Shift_regs, Start, Done, Q0,
clock, reset_b);
Datapath M1(Product, Q0, Done, Multiplicand, Multiplier,
Start, Load_regs, Incr_P, Add_regs, Shift_regs, clock, reset_b, VCC, GND);
endmodule
module Controller (
output Ready,
output reg Load_regs, Incr_P, Add_regs, Shift_regs,
input Start, Done, Q0, clock, reset_b
);
parameter
S_idle = 3'b001,
// one-hot code
S_add = 3'b010,
S_shift = 3'b100;
reg [2: 0] state, next_state;
// sized for one-hot
assign
Ready = (state == S_idle);
always @ (posedge clock, negedge reset_b)
if (~reset_b) state <= S_idle; else state <= next_state;
always @ (state, Start, Q0, Done) begin
next_state = S_idle;
Load_regs = 0;
Incr_P = 0;
Add_regs = 0;
Shift_regs = 0;
case (state)
S_idle: if (Start) begin next_state = S_add; Load_regs = 1; end
S_add:
begin next_state = S_shift; Incr_P = 1; if (Q0) Add_regs = 1; end
S_shift: begin
Shift_regs = 1;
if (Done) next_state = S_idle;
else next_state = S_add;
end
default: next_state = S_idle;
endcase
end
endmodule
module Datapath #(parameter dp_width = 4, BC_size = 3) (
output [2*dp_width - 1: 0] Product, output Q0, output Done,
input [dp_width - 1: 0] Multiplicand, Multiplier,
input Start, Load_regs, Incr_P, Add_regs, Shift_regs, clock, clear, VCC, GND
);
wire C;
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404
wire Cout, Sum3, Sum2, Sum1, Sum0, P3, P2, P1, P0, A3, A2, A1, A0;
wire Q3, Q2, Q1;
wire [dp_width -1: 0] A = {A3, A2, A1, A0};
wire [dp_width -1: 0] Q = {Q3, Q2, Q1, Q0};
assign Product = {C, A, Q};
wire [ BC_size -1: 0] P = {P3, P2, P1, P0};
// Registers must be controlled separately to execute add and shift operations correctly.
// LOAD condition for 74194: s1 = 1, s0 = 1
// SHIFT condition: s1 = 0, s0 = 1
// NO CHANGE condition: s1 = 0, s0 = 0
wire B3 = Multiplicand[3];
// Data word to adder
wire B2 = Multiplicand[2];
wire B1 = Multiplicand[1];
wire B0 = Multiplicand[0];
wire Q3_in = Multiplier[3];
wire Q2_in = Multiplier[2];
wire Q1_in = Multiplier[1];
wire Q0_in = Multiplier[0];
assign Done = ({P3, P2, P1, P0} == dp_width);
// Counts bits of multiplier
wire s1A = Load_regs || Add_regs;
// Controls for A register
wire s0A = Load_regs || Add_regs || Shift_regs;
wire s0Q = Load_regs || Shift_regs;
// Controls for Q register
wire s1Q = Load_regs;
wire Pout;
// Unused
wire clr_P = clear && ~Load_regs;
Flip_flop_7474 M0_C (C, Cout, clock, VCC, clr_P);
Adder_7483 M1 (Sum3, Sum2, Sum1, Sum0, Cout, A3, A2, A1, A0, B3, B2, B1, B0, GND, VCC, GND);
Counter_74161 M3_P (P3, P2, P1, P0, Pout, GND, GND, GND, GND, Incr_P, Incr_P, VCC, clock,
clr_P);
Reg_74194 M4_A (A3, A2, A1, A0, Sum3, Sum2, Sum1, Sum0, C, GND, s1A, s0A, clock, clr_P);
Reg_74194 M5_Q (Q3, Q2, Q1, Q0, Q3_in, Q2_in, Q1_in, Q0_in, A0, GND, s1Q, s0Q, clock, clear);
endmodule
module t_Supp_9_17_Par_Mult;
parameter
dp_width = 4;
// Width of datapath
wire [2 * dp_width - 1: 0] Product;
wire
Ready;
reg [dp_width - 1: 0]
Multiplicand, Multiplier;
reg
Start, clock, reset_b;
integer
Exp_Value;
reg
Error;
supply0
GND;
supply1
VCC;
Supp_11_17_Par_Mult M0 (Product, Ready, Multiplicand, Multiplier, Start, clock, reset_b, VCC, GND);
wire [dp_width -1: 0] sum = {M0.M1.Sum3, M0.M1.Sum2, M0.M1.Sum1, M0.M1.Sum0};
initial #115000 $finish;
initial begin clock = 0; #5 forever #5 clock = ~clock; end
initial fork
reset_b = 1;
#2 reset_b = 0;
#3 reset_b = 1;
join
always @ (negedge Start) begin
Exp_Value = Multiplier * Multiplicand;
//Exp_Value = Multiplier * Multiplicand +1; // Inject error to confirm detection
end
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always @ (posedge Ready) begin
# 1 Error <= (Exp_Value ^ Product) ;
end
initial begin
#5 Multiplicand = 0;
Multiplier = 0;
repeat (32) #10 begin
Start = 1;
#10 Start = 0;
repeat (32) begin
Start = 1;
#10 Start = 0;
#100 Multiplicand = Multiplicand + 1;
end
Multiplier = Multiplier + 1;
end
end
endmodule
module Flip_flop_7474 (output reg Q, input D, CLK, preset, clear);
always @ (posedge CLK, negedge preset , negedge clear)
if (!preset)
Q <= 1'b1;
else if (!clear)
Q <= 1'b0;
else
Q <= D;
endmodule
module Adder_7483 (
output S4, S3, S2, S1, C4,
input A4, A3, A2, A1, B4, B3, B2, B1, C0, VCC, GND
);
// Note: connect VCC and GND to supply1 and supply0 in the test bench
wire [4: 1] sum;
wire [4: 1] A = {A4, A3, A2, A1};
wire [4: 1] B = {B4, B3, B2, B1};
assign S4 = sum[4];
assign S3 = sum[3];
assign S2 = sum[2];
assign S1 = sum[1];
assign {C4, sum} = A + B + C0;
endmodule
module Counter_74161 (
output QD, QC, QB, QA,
// Data output
output
COUT,
// Output carry
input
D, C, B, A,
// Data input
input
P, T,
// Active high to count
L,
// Active low to load
CK,
// Positive edge sensitive
CLR
// Active low to clear
);
reg [3: 0] A_count;
assign QD = A_count[3];
assign QC = A_count[2];
assign QB = A_count[1];
assign QA = A_count[0];
assign COUT = ((P == 1) && (T == 1) && (L == 1) && (A_count == 4'b1111));
always @ (posedge CK, negedge CLR)
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if (CLR == 0)
A_count <= 4'b0000;
else if (L == 0)
A_count <= {D, C, B, A};
else if ((P == 1) && (T == 1))
A_count <= A_count + 1'b1;
else
A_count <= A_count; // redundant statement
endmodule
module Reg_74194 (
output reg QA, QB, QC, QD,
input A, B, C, D, SIR, SIL, s1, s0, CK, CLR
);
always @ (posedge CK, negedge CLR)
if (!CLR) {QA, QB, QC, QD} <= 4'b0;
else case ({s1, s0})
2'b00: {QA, QB, QC, QD} <= {QA, QB, QC, QD};
2'b01: {QA, QB, QC, QD} <= {SIR, QA, QB, QC};
2'b10: {QA, QB, QC, QD} <= {QB, QC, QD, SIL};
2'b11: {QA, QB, QC, QD} <= {A, B, C, D};
endcase
endmodule
Name
41353
41403
41453
41503
Ready
Start
Load_regs
Shift_regs
Add_regs
Q0
s1A
s0A
s1Q
s0Q
Done
state[2:0]
4
1
2
4
2
4
2
4
2
4
1
2
4
2
Incr_P
clr_P
4
P[2:0]
0
1
2
3
4
0
1
C
sum[3:0]
A[3:0]
6
Q[3:0]
f
Multiplicand[3:0]
8
6
12
9
15
10
8
14
10
7
14
10
3
0
6
3
9
4
2
8
4
0
7
3
7
b
5
5
a
5
2
b
6
d
7
11
Multiplier[3:0]
Product[7:0]
55
Exp_Value
55
11
53
74
37
66
11
66
Error
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61
77
407
CHAPTER 10
10.1
7400
7404
1
2
3
&
4
6
8
12
13
11
1
4
3
=1
4
5
9
6
9
10
8
8
12
13
11
10
12
13
See textbook.
10.3
10.4
x
y
z
G1
V2
N3
x
y
z
A
B
C
1
2
3
A
B
C
BCD-to-decimal decoder (similar to IC 7442)
BCD/DEC
A
B
C
D
10.5
1
2
4
8
BIN-OCT
1
2
4
E3
10.6
0
1
2
3
4
5
6
7
8
9
D0
D1
D2
D3
D4
D5
D6
D7
D8
D9
Similar to 7438:
E1
E2
6
5
11
10.2
1
2
3
5
9
10
7486
2
1
&
EN
0
1
2
3
4
5
6
7
IC type 74153.
Digital
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408
s2
s1
0
1
} G 03
EN
1
2
MUX
4
EN
1
2
4
10.7
(a)
(b)
1S
C1
1R
1D
C1
10.8
(c)
1T
C1
The common control block is used when the circuit has one or more inputs that are common to all lower
sections.
10.9
load
clock
M1 [Load]
C2
I1
I2
I3
1, 2D
A1
A2
A3
I4
10.10
A4
See textbook.
10.11
UP/DOWN
COUNT
ENABLE
CLOCK
CTR DIV 16
M1 [Up]
M2 [Down] 1, 3 CT = 15
G3
2, 3 CT = 0
C/1, 3+/2,3-
Carry out for count-up
Carry out for count-down
0
CT
3
10.12
RAM 256 X 1
Address
Select
Read/Write
Data input
0
1
2
0
3
A
255
4
5
6
7
G1
1EN [READ]
1C2 [WRITE]
A, 2D
Carry out for count-up
Carry out for count-down
Α
Data output
Digital
Design
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HDL
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rights
reserved.
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