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Solving Problems with Digital Computers
. . . Alston S. Householder
The Day of Reckoning
. . . Jackson W. Granholm
The Operation of a Computer Away from
a Central Staff
. . Howard Bromberg
Word Length
In
Digital Computers
.. D. D. McCracken
Free Use of the Toronto Computer, and
the Remote Programming of It (Part 2)
. . . c.
C. Gotlieb and others
putting
I
IDEAS
Ito work-research at I I
IBM
• Multi-Stable Work Horse: By employir:g a non-linear
load, new circuit permits two transistors to do the
work of ten. IBM Bulletin No. 200.
• Self-Complementary: New Gas Tube Counter subtracts by adding. IBM Bulletin No. 201.
• The Soft Touch: Ultrasonic cutting at IBM permits
devices to be cut from hard, brittle materials within 0.0002".
Multi-Stable Work Horse
As the size and complexity oflBM products increase, we are faced with growing
numbers of components-which means
increased cost. As part of our continuous
search for improvement and ways to
reduce the number of components, Robert Henle, one of our Transistor Circuit
Research people, undertook to get more
work out of a given number of transistors. The result is a two-transistor,
multi-stable circuit employing feedback
controlled by a non-linear load. Junction
transistors are naturally suited to this
new kind of circuit.
+$0 IIJIC
10 Sta~le State
~"it
A full report on this new idea from
IBM contains eight full-page circuit diagrams in addition to mathematical analyses of the operation of the circuit.
Write for your copy of IBM Bulletin
No. 200.
Gas Tube Counfer
Schematic
r---
The Soft Touch
1
I
I
I
II
... ---
I
'I
I
:
t"--:
I
1:
I
!
!
,
... --- t
COMl'L£M£nr--t---- -:•
1
I
I
C
t
INTEf!t.t£DlATE--~------
Self-Complementary
Accounting machines these days must
be able to do everything-even make
decisions. In order to get a machine to
do more in a day's time with little or no
increase in operating" cost, IBM Component Research people studied the idea
of using a multi-cathode gas tube. It's
good news that they came up with an
attractive approach, which Robert Koehler, of our Device Development Group,
then reduced to practice; it operates
faster than its electromechanical predecessor and, furthermore, with simple circuitry, can subtract. by adding. It can
read out in true number form both positive and negative balances. This is possible because a number stored in the tube
may be transposed to its 9's complement
(i.e., value subtracted from nine) by a
single electrical pulse.
If you'd like more information on the
basic principle, physical arrangement of
parts, and typical problems solved, write
for IBM Bulletin No. 201. If you are
fascinated by the theory of numbers, we
recommend this Bulletin.
DATA PROCESSING· ELECTRIC TYPEWRITERS· TIME EQUIPMENT. MILITARY PRODUCTS
In some of our studies of new components, at the IBM Research Laboratories
at Poughkeepsie, it is necessary to make
many different, small and intricately
shaped parts from brittle materials. Following the conventional approach, each
of these parts would require laborious
and costly machining and fabrication.
We turned to ultrasonic cutting; with
this tool we can make any shape or size
component in approximately a minutewith an accuracy five times greater than
previously possible! The ultrasonic cutter has helped us progress faster in our
development of new devices. RESEARCH
at IBM means IDEAS at work.
Schematic: of Uttro$onic Cutter
• For bulletins mentioned above, write
Dept. CA-7. International Business Machines Corp., 590 Madison Ave., New
York 22, N. Y.
11:)$1
DATA
PROCESSING
COMPUTERS
CYBERNETICS
'Vol.
5,
•
AUTOMATION
AND
ROBOTS
•
AUTOMATIC
CONTROL
July, 1956
No.7
ESTABLISHED SEPTEMBER, 1951
ARTICLES AND PAPEnS
SUJ.V:LdCJ Probleh1S .·d th Digi tal Computers
The Day of Reckoning
The Operation of a Computer Away from
a Central Staff
Word Length in Digital Computers
A General Curve-Fitting Subroutine
for Transcendental Functions
A Computer Program for Finding Roots
Free Use of the Toronto Computer. an~
the Remote Programmin~ of It (Part 2)
A. S. Householder
J. W. Granholm
H. Bromberg
6
10
12
D. D. McCracken
R. H. Bracken
14
16
A. D. Booth
C. C. Gotlieb
20
29
REFERENCE INFORMATION
New P[. ten ts
Who's Who in the Computer Field
(supplement)
••• R. R. Skolnick
22
32
Methods in High Speed Computation-Final Examination
Eastern Joint Computer Conference
December, 1956, New York
••• J. W. Carr, III
19
The Editor's Notes
Index of Notices
Advertising Index
38
4
28
44
Editor: Edmund C. Berkeley
Assistant Edi tors: Neil D. ~Jacdonald, F. L. Walker
Contributing Editors: Andrew D. Booth, John M. Breen, John W. Carr, III, Alston S. Householder
Advisory Comittee: Samuel B. Williams, Herbert F. Mitchell, Jr., Justin Oppenheim
Publisher: Berkeley Enterprises, Inc.
Main Office: 815 Washington Street, Newtonville 60, Mass. -- Decatur 2-5453 or 2-3928
Editorial Office: 36 West 11 Street, New York 11, N.Y. -- Gramercy 7-1157 or Algonquin 5-7177
•
Advertising Representatives:
San Francisco - W.A.Babcock, 605 Market St., San Francisco 5, Cali!.. Yukon 2-3954
Los Angeles - Wentworth F. Green, 439 So. Western Ave., Los Angeles 5, Calif., Dunkirk 7-R135
Elsewhere - the Publisher
(1)MPUTERS AND AUIDMATION is published monthly. Copyright, lY55, by Berkeley Enterprises, Inc.
Subscription rates: in the United States - one year $5.50, two years $10.50, in Canada - one year $6.00, two years $ll.~;
elsewhere - one year S6.~, two years
$12.50
Sulk subscription rates: see page 18
Advertising rates: see page 42
~tered as second class matter at·~~_~~P_o_st~O_f_fl_·c_e~,_N_e_w_l_o_r_k~,_N_._Y_.~~~~~~~~~~~~
- 3 -
The
Editor'~
Notes
OPPORTUNITY' TO
I. From Curtner B. Akin, Jr.,
Sewickley, Pa., to the Editor:
LEARN'
in your favor. Please accept my' appreciation:
you have no idea how tvonderfully surprised I
l\'as to find "Computers and Automation" in my
mailbox yesterday.
This letter'is merely an expression of
sincere thanks to you and YOUI policy of extending subscription privileges to everyone
l\'ho ldshes to read your fine magazine "Computers and Automation".
II.
From the Editor
Opportunities for education in ,the United
States, in the finest sense of the word "education", are far tess than they should be. Here
are three comparisons:
Union of Soviet
Socialist Republics United States
1. Average number of students
in class per
teacher
19 or 20 and
increasing
Denmark
2. Number of inhabitants for
every bookseller
Recently in these our United States,there
has been a great deal of consternation about
the number of scientists turned out, or manufactured, by Russia's system of education. It
has been brought to light that the young Russian in quest for knowledge has no problemfhrling reading material upon that subject which
holds for him the maximum interest. Isn't this
ideal? To me it seems a little hard to imagine
that a country as imperfect (to me) as Russia,
'has had the common sense to place before the
youth of its country the material they seek.
Let's turn to the U.S. and make a comparison. • •• As the ten or eleven-year old
grows a1'\'ay from his desire to live in a makebelieve world into a young roomber of adulthood, what does he find? Simply that he cannot Id th ease obtain the information lvhich he
seeks. The "educated" class closes its eyes
to his desires. His quest for learning "What
makes things tick" is nipped in the bud. The
adult world would rather he go through the required sequence necessary for becoming educated than satisfy his self-motivated thirst for
learning. Brother -- if that isn't crazy!:
7,000
No. of
Vacancies
3. In New York
650
City, on June 5,
1956, in regard
to competitive
examinations for
candidates who are
to teach mathematics in junior high
schools
34 or 35 and
incre~sing
[hi ted State s
100,000
No. of
Applicants
88
We earnestly hope that "Computers and Automation" may help in the cause of education of
men and women· in the United States, in the field
of computers and their applications and implications, including automation. And it 1s our
intention for the indefinite ·future that anyone
who wishes to, may subscribe to '''Computers and
Automation".
In closing, I would like to congratulate
you on a perhaps unrecognized wonderful point
- 4 -
Systems
Engineering
at The Ramo-Wooldridge
Corporation
The Intercontinental Ballistk Missile and the Intermediate Range
Ballistic Missile, Air Force programs for which we have over-all systems engineering and technical
direction responsibility, are prime examples of programs that require the systems engineering
approach. Most Ramo-Wooldridge work is of such a ~y~tems character, requiring the concurrent
solution of a wide variety of interrelated technical and operational problems. Additional examples
at R-W are communications, fire-control, and computer programs for the military, and automation and operations research projects for business and indmtry.
ICBM and IRBM are prime examples.
Successful execution of sy~tems engineering programs requires that the technical staff include experts in a considerable number of scientific and engineering speciaitie!>.
At Ramo-Wooldridge some of the pertinent fields are aerodynamics, propulsion, digital
computers, information theory, radio propagation, radar, infrared, servomechanisms, gyroscopy,
and nuclear physics.
Pertinent technical fields.
A qualified !>ystems engineering staff mu~t include unusually capable theoretidans and analysts who can predict the behavior of complex !>ystems, as well as ingenious
experimental physicists who can devise suitable new techniques for mea~uring actual physkal
parameters. In addition, the team must include experienced apparatus and equipment development
engineers, to insure a high level of practicability in the resulting end products.
The kind of team required.
Sclentiltl lind en~ineerl whu (lfe experienced in l)'ltellls engineerinJ,: wurk. or who
lpeciali:.ed in certain technical /ieldl hilt IUB'e a hruad illterelt itl the interm tiom between their OW1l lpecialtiel and other /ield,\. are invited to explore the wide
"1111(1' v/ openinl(l tit The RtllnlJ- Wooldridge C orporatlCJTI ill:
'
ha~'e
Guided Missile Research and Development
•
Aerodynamics and Propulsion Systems
•
Automation and Data Processing
Digital Computers and Control Systems
Communications Systems
•
Airborne Electronic and Control Systems
The Ramo-Wooldridge Corporation
15730 ARBOR
VITAE
STREET
•
L.OS
ANGEL.ES
415.
CAL.IFORNIA
SOLVING
PROBLEMS
WITH
DIGITAL
COMPUTERS
ALSTON S. HOl'SElfOLHf:R
Mathematics Panel
Oak P.idge National Lahoratory
Oak Ridge, Tenn.
(Talk hefore American Physical Society, Washington
The speeds of "high speed" digital computers vary, from machine to machine, 0 v e r
several orders of magnitude, but for a fairly
representative group the multiplication time
is roughly half a millisecond. For the IBM
701, and for machines of the Princeton type,
the speed is slightly less; for the IBM 704 it
is rather greater, but this is perhaps a fair
round number. The Oracle at the Oak Rid g e
National LaboratorY,is a Princeton type machine and hence one of this class, and since it
is the machine with which I am most familiar,
and since "Oracle" is an easy tvord to say, I
wish to use the Oracle as representative of
this class.
D.C., April 26-28, 1956)
dimensions, and redefine it, freed from invidious implications. For this purpose I
shall consider the Horner to represent 106
multiplications or the equivalent thereof.
In these terms, Joe requires about 5 years to
produce a Horner, and the Oracle about 8 minutes. In the same terms, the NORC at Dahlgten
requires about one minute and the LARC, to be
delivered to Livermore two years hence, about
8 seconds. These last figures are very rough
and comparisons are difficult, since the NORC
and the LARC are floating point machines, which
gives them an effective speed that is perhaps
higher by an order of magnitude. On ~he other
hand, I am not at present considering the utility of the output, but seeking only some
gross, overall, and reasonably lyell-defined
measure of activity.
On the Oracle a division takes about the
same length of time as a multiplication, so we
can speak of multiplications and consider a
division as equivalent. In time, and in percentage of occurrences, a multiplication is
equivalent to about 10 single-address additive
operations. The ratio varies somewhat from
machine to machine, but in any case mUltiplications and divisions account for a substantial
percentage of most computing time.
A skilled human operator, let us call him
Joe for short, using a standard desk computer,
can- carry out about 1000 multiplications in a
working day, counting time to enter operands
and record results. This is steady going, and
if we allow time out for sickness, holidays,
and coffee breaks, 4000 per week is perhaps a
bette~ overall average.
This amounts to about
2xl05 multiplications in a working year, or
106 in five years. Considering 50 working yea~
as the productive human life time, if Joe spen~
his life doing multiplications on a desk calculator he will perform a total of about 107
of these.
There is a well knOlvn, but not well defined, unit of computational volume known as
the "Horner". I have never seen it in print,
but I understand it represents the amount of
computational labor required for solving an
algebraic equation of some given degree using
Horner's method, which is one of the more laborious and simple-minded of known methods.
I
should like to expand the unit to more practical
- 6 -
Returning to our friend Joe and his desk
computer, if we assume him to be a high school
graduate merely, with no special endowments
other than steadiness and dependability, his
salary and overhead would probably come to at
least $5,000 per year. Hence his output comes
at the rate of about $25,000 per Horner. While
Joe works a 40-hour week, the Oracle's week is
at present 120 hours long. If we figure depreciation at $200,000 per year, which is quire
excessive, this comes to about $30 per hour.
Normal operating costs run around $50 per hour,
and this adds up to about $10 per Horner. Ihe
LARe will cost about three times as much as
the Oracle. If we allow the same factor for
operating costs, and allow a factor of 60 for
speeds, lve come out with a cost of 50¢ per
Horner, a factor of 5.104 by comparison with
Joe. Perhaps I should emphasize again that
utility is not being considered. For a particular problem the number of Horners requited
can easily vary by an order of magnitude for
any single system depending upon the car e
taken in programming and analysis. But this
can be said for the output of any of the machines, that for an output of one Horner one does
not have to wait five years.
For Joe I have postulated very few skills,
the Oracle and the LARC have even fewer. If
we have a differential equation to be solved,
whether by Joe, by the Oracle, or by the LARC,
Solving Problems
lve have to program it properly since neither
one of the three knows any mathematics beyond
arithmetic. Suppose the problem requires about one Horner of computation. To compare
the programming of the problems for the LARC
wi th the prograrmning of the problem for Joe,
we must imagine that Joe is to be given his
data and instructions at the outset, and is
then to be left incommunicado for a period of
5 years at which time he suddenly emerges lvith
answers, which mayor may not be the correct
ones. The instructions must be explicit enough to guide him through all contingencies,
since by hypothesis all communication is severed for the period.
Ivhereas it is clear that numbers aclllally used
in real computations have a distribution that
is far,from simple. For example, the simple
rationals, certain transcendentals such as e
and Ir and simple functions of these, occur
wi th much more than random frequency. Having
recently formulated a pessimistic hypothesis
in this regard, I was informed by a Scotch
mathematician that my principle was already
well known in Scotland by the name of Ma cpherson's Law. In the original Scotch the
statement is, "Macpherson's piece aye fa's
jeelie side doon". There is another formulation of the same principle Which is known as
das Gesetz der Schtveinerei der Natur.
The parallel is not perfect, since either
the Oracle or the LARC can simply stop. A t
least it can be programmed to stop when~oub~
of a foreseeable character arise. But often
the troubles, if foreseeable, are neverthel~
not foreseen, and the machine d i 1 i g en t ly
P ro d u c es nonsense until the aberration is
discovered. Happily we can afford to squander
a few of the LARC's 50¢ Horners, as we could
not afford to squander Joe's $25,000 Horners.
But the fact, while ameliorating the difficulty, does not nullify it. Ultimately, for any
given problem, it is necessary to achieve a
program capable of directing the computer in
uninterrupted, valid performance for at least
a few seconds, and in the case of the LARC,
this would be equivalent to almost that many
years on the part of Joe. And whereas the
LARC will require 8 seconds to produce a Horner, there are machines in prospect for three
or four years hence that will produce a Honer
or more per second.
I can illustrate this with an occurrence
of several years ago when a floating-pointnutine was being prepared for a fixed-pointm~
ine. The results exhibited some obvious but
puzzling discrepanciesbQbut eventually it was
found that among the 2 possible number pai~
provided for, the routine gave the cor rec t
product for all but one, and this one 'pair
actually occurred in the computation. The
probability of the appearance ~ this pair at
anylgne time was, of course, 2 0, or, roughl~
10- ,on the assumption of a uniform distribution.
Recently at ORNL a routine for inverting
matrices was being tested by applying it to a
particular matrix tvhose inverse was obtainable
analytically. If a computed inverse is multiplied by the original matrix and the result
subtracted from the identity, it is possible
to compute quite easily and rigorously an upper limit to the error in the individual elements of that inverse. In this instance the
computed upper limit was exceeded by several
orders of magnitude by the errors actually
found in some of the elements. It turned out
that the discrepancy was due to the small residual error made in converting the elements
of the original matrix from decimal form to
binary. In other words, the matrix actually
inverted differed in the last few binary digits from the matrix whose inverse was known
theoretically, and this accounted for the
discrepancy.
These figures are introduced, not for
the purpose of bringing out what am azing achievements these computers are, but rather
tQ emphasize the difference between solving a
problem with Joe's help and solving it with
the lARC's help. The real, flesh and blood
Joes who actually pound Fridens and Marchants,
are not generally incarcerated, and, indeed,
they themselves can often see, as the LARC
cannot, when things go awry. In particular,
it is often possible to observe the build-up
of rounding errors in the course of a hand
computation and to take remedial measures,.
I am mildly distressed by the grot\' i ng
popularity of decimal machines for scientific
computation, and of floating-point machines.
It is a theorem that among all possible bases,
the base 2 minimizes the rate of growth of
generated error. In fact, the larger the b~e
the higher the rate. My objection to float~
ing point is based upon the fact that, to the
best of my knOtvledge, no one knows how to ptedic t the rate of growth of generated err 0 r
when floating point arithmetic is used.
It goes without saying that in the rotnse
of a Horner or two of computation, rounding
errors can build up very substantially and
possibly invalidate the entire result. Some
papers have been published attempting to derive statistical distributions of errors generated in the course of certain classes of
computation, but generally speaking I am
skeptical of the conclusions. For such,estimates some uniformity of the initial distributions of data and errors must be made,
In speaking of generated error I am not,
- 7 -
Computers and Automation
and zeros elseWhere,
of course, speaking of malfunctioning of the
machine, or of errors due to faulty coding, or
of the use of a fallacious formula. These ate
relatively easy to detect and correct. I am
not referring even to truncation errors. These
are also fairly easy to detect, generally, although I know of a case where several months
of IBM computations l~ere found to be invalid
because a Taylor series had been truncated too
soon, and another case where some months 0 f
coding time were wasted along with some machine time because a certain series was found to
converge too slowly to be usable at all. I n
both of these instances a sufficient amount m
fairly standard mathematical analysis could
have prevented the loss. The errors I refer
to, however, are those which result from rounding after every multiplication and division,
and in floating-point operations they appear
also when the exponents are adjusted by shifting before an addition or subtraction.
The
analysis here is always tedious, and the mathematical techniques are by no means Ivell developed.
Then
A-I
l:vhere
J
In-l •
Hence, although every eigenvalue A = I for
A, nevertheless the last element of x - x*
will be 0< n-l times the first element of d.
If 0{ is large and n large the magnification 1vill be great.
This phenomenon is well known in the finite difference solution of differential equations. It goes by the name of instability. Actually, instability is a matter of degree, as
others have pointed out, and it should be ~eat
ed as such.
In some instances ~ posteriori estimates
of error can be made. I have already spoken
of the formula for obtaining an upper bound to
the error in the computed inverse of a matrix,
al though, as you recall, this refers to the
matrix actually in the machine which is not
always exactly -- in fact is seldom exactly the matrix you wish to invert. To the best of
my knmdedge, there is no Ivay of obtaining in
general a rigorous limit of errors in the solution of a sys tem of linear equations l.vith out
making u_se of a computed inverse. It doe.c: not suffice to substitute thecomput.ed solution inlo tile original equations. For suppose you do this, and
suppose you even find that to within rounding
errors the equations are exactly satisfied.
Th at is, suppose you ldsh to solve Ax" b, aId
you obtain for x a vector x* such that when
you take the machine product (Ax*) * of A
by x* you get exactly b. Nevertheless, in
general, the true product Ax* will differ
from the desired vector b by some vector d
of which you know only that each element of d
does not exceed the maximal error generated in
the machine computation. Then the error xx* is equal to A-ld. Now if it should happen that this unknown vector d has a large
component in the direction of the eigenvector
of A belonging to the smallest eigenvalue,
call it A, then the actual error vector xx* tVill be approximately ~ -la, and if ~
is small, the elements of )\-ld can be large.
This is what can happen in the case of s~alled
ill-conditioned systems. But the case can be
even worse. Consider the form
A;: I
= I + ex J + b(2 J 2 + ... + oc n - l
If the differential equation, 1\' h e the r
ordinary or partial, is linear, then the elements of the vector x of unknol.vns are the values of the dependent variable at mesh points of
the grid; the elements of the vector bare
determined by the boundary or initial values;
and the elements of the matrix A are determined by the method of approximating the derivatives by finite differences. For initial
value problems one generally tries to set up
a scheme whereby the dependent variable can be
evaluated by a straightforward recursion, beginning at a boundary or corner point and proceeding from point to point. One does not
generally Ivri te down the matrix explicitly, or
perhaps even think of the problem in these
terms, but in fact the matrix A is then a
triangular matrix, all of whose non-null ele. ments fallon the diagonal or not far below it.
Its form is only slightly more complicated than
that of the matrix jus t exhibited.
-O(J,
has ones just below the diagonal and
- 8 -
Now the order of the matri'x depends upon
the fineness of the grid. In general t he re
will be allinear combination of terms of the
f orm 0( n- ,~-,
n 1 ••• , Ivhere '~) J ur :: '3 (0(, ~,?()
technique for functions containing nonl inear p arameters in which accurate guesses of the fir s t
Then y -= Av + B w- + C
estimates are not necessary. All sums of squares
and cross products are computed in fixed-p 0 i n t
Assuming 0<. and f-> are constant, then the sum of
double-precision arithmetic which assures a highthe squares of the residuals will be a f unc t ion
degree of sensitivity to a fit and eliminates, in
of the three parameters A, B, and C only. Denotmost cases, the necessity for scaling the in d ependent variable.
ing this function by G(A,B,C) the normal equations
c an be obtained by setting the three parti al d erivatives of G to zero. Solving the normal equaDiscussion
tions yields the values for A, B, and C which can
then be used to compute the sum of squares of the
Inception
residuals. By applying a two-lvay searching technique, new values of 0< and (!J
are selec ted
A considerable amount of curve fitti n g i s
and the computations repeated until the sum 0 f
done using polynomials because of their simplicity
squares of the residuals has converged to a miniand flexibility, and computing installations have
mum. It should be noted that neither the partial
standard programs which can handle these problems
deri vati ves of y wi th respect to the non 1 in ear
from beginning to end by indicating only the degree
parameters nor estimates of the linear parameters
of the polynomial to be used. However, there are
were required. Justification for this method i s
numerous nonHnear relationships in scienc e i n
based on being able to eliminate these part i a 1
l'lhich a transcendental function is exp e c ted t 0
derivatives by utilizing the speed of modern computers with respect to trial and error solutions.
represent the relationship and l'lhich in most cases
cannot be reduced to a simpler form by considering
The searching technique assumes enough is known
functions of the variables as new variables. The
about 0< and ~
that upper and lower bounds may
problem of fitting these functions to a set 0 f
be assigned to each. The first values used will
points is not nearly as simple as that of fitting
then be ones which are half way between the upper
polynomials and can be solved only by tedious nuand lower bounds. Once the first sum of squares
merical methods. One of the most frequently apis obtained the initial values, IX, and~.
are
plied is the Least Squares Differential Correction
changed to 0(2. and ~2. res pecti vel y t
lvh ere
Method and is most useful when a function contains
several nonlinear par~meters. When applying the
o<~= O(,+AO~.
A second
sum of squares of the residuals is computed and
method to a high-speed computer using age n era 1
compared against the first. From this point the
purpose program, one must first code the prog ra m
logic of the search is best explained by the folsteps necessary to compute the given function and
lowing example.
the partial derivatives with respect to each parameter. Als 0 good ini ti al estimates 0 f e a c h
parameter must be used since the terms of degree
Let Ri equal the sum of squares of the residhigher than the first were neglected when us in g
uals at stage i (see Figure 1 on page 18).
Taylor's series expansion in linearizing the normal least square equations. The ideal programfor
If ~.c:::: RI , proceed in same direction.
this type of curve fitting would be one which required no additional coding by the user, but 0 f
If RI < R2 , reverse direction by set tin g
course is impractical if not impossible.
P<::a. ==- tX'. 60<.
and
(3'2. = tJ. - b.~ •
Assuming the former is true, then R3 is computed
.Consider nOlt only that class of transcendand compared with R2. If R3 c::::: R2, P roc ee din
ental functions containing two or less nonlinear
same direction. If R2~ R3' the logic of the
J
o
e
- 16 -
Curve-Fi ttinl! "u·'routine
search remembers that R2
~ Rl
~::a.-
i
the ref 0 r e ,
control card "tells" the curve fitting subroutine
o<~ =- o(~+AC)( ) ~~ -=
Ap .
No til, if
the number of linear and nonlinear parameters and
R4 ~ R2 , Rs will be computed.
Also R6 if R5 <: R4 •
the number of terms in a given function. It also
'%
~
%
R
'
t
d
If
R
--R
contains
the number of points -n tof be used in
N01'1 assum1ng
7 1S compu e •
5- 7 ,
1 the
,
f1t, the upper and lower bounds 0 each non inear
,
, '
R8 1S computed and 1f,less than R5 the se~r~h conparameter, the original deltas, and the number of
eludes t~at the funct10n G(A,B,C), has a m1n1m u m
times to decrease the original deltas. The final
when 0<. 1S equal to s~me value lyIng beu'lCen (O(I-+~)
step is the actual running of the problem by loadand ~,+4~OC) and fJ 1S equal to some value 1~1ng
ing the 'instructions, control card, and data into
between
~, , and (tl, - 2A~). A new s tar t 1 n g
the 701 and starting the computations.
point is then selected ldthin the nel'l bounds by
comparing the previous ly computed R lSi the original
An important function of the subroutin e i s
deltas are decreasedi and the search continued.
that all coefficients of the normal least squares
This process is repeated until satisfactory values
equations involving sums of squares and c r 0 s s
for 0< and ~ have been determined.
products are computed using fixed-point d 0 ubI eprecision arithmetic. Thus, it is possible t 0
It is important to note that when bad values
carry along 1 arge numbers in the comp uta t ion s
are initially used for ~ and ~ , the searching
tvithout having to drop significant digits. Also,
technique can very t'lell converge upon a false minonly those terms necessary in solving for the linear
imum. This does not me'an that good initial v a lparameters are computed. To clarify this remark,
ues must be used but rather that the best available
assume the parameter C is missing from a given
ones be used. False minimums become obvious when
function, then the terms ~ 'It ,,ZI.Ir,- and :2: ~i.
a computed parameter differs significantly from an
would not be computed as they are not use d i n
estimate of the same parameter obtained ex per isolving for A and B.
mentally.
Upon reaching a solution, the parameters,the
original x and y values, the computed y val u es,
Application to the IBM 701 Calculator
the squares of the residuals, and the sum 0 f
squares of the residuals will be printed. An adWhen coding the method for the IBM 701 C a 1di tional feature allows one to print the parameters
culator, the concepts of subroutines and programs
and the sum of squares of the residuals a tan y
were used. Possibly the term "subroutine program"
time during the computations. This f eat u rei s
should replace "subroutine" in the ti tie of th i s
used when there are nonlinear parameters in a funcpaper. However, since the method can be used to
tion, and it makes it possible for the mathematifit a general class of transcendental functions to
cian to watch the progress of the search.
a set of points when the functions themselves are
not explicitly defined, the term subroutine seems
It should be made clear that all input and
more appropriate.
output functions are included in the curve fitting
subroutine. Als 0, there are several b u i 1 t - i n
It is difficult to explain fully how the subchecking devices which will recognize errors made
routine is applied to a given curve fitting pro bby the coder or by the 701.
lem unless one goes into the details of the p r 0cedure, assuming of course, that not every reader
is familiar t'lTith the 701. However, a general deTiming Statistics
scription of the procedure will show that a minirmun
amount of effort is required when using the subThe following illustrative timing statistics,
routine.
obtained when using the curve fitting subroutine,
may best evaluate the subroutine with respect to
To begin t'li th, one needs to code only t h e
computing time.
necessary instructions for computing van d w •
Storage is available for any subroutine use din
Given y
A log x+Bx + C with N = 100 and
the computations, and the coder assumes that ()( ,~ ,
and % are available in three specific locations.
10 ~ x ~ 10,000 :> 500
y ~ 1200
The linkage between the coding and the curve fitting subroutine is supplied by 21 basic instrucSince there were no nonlinear parameters in t his
tions. These instructions also contain informatim
function, the searching technique was ignored, and
used by the subroutine l1/hich allows for c omp lete
the normal equations solved for A, B, and C. The
flexibility in assigning the decimal point to all
actual computing time was 3 seconds, while readmg
data, variables, constants, and parameters. Th e
in the data and printing the results took approxinstructions and any subroutines are then put into
imately 54 seconds. The same function was use d
machine language by an assembly program. The time
wi th 189 data sets, of 10 points each, and the
required to complete the coding will vary dependtotal time for card reading, computing I and printing on the function being used. In fitting the
ing was 23 minutes.
curve
-1It.?('
-~')('
-«-x
~ = Ae
+ B2.
+ C
Given y = Ae
+ C
=
=
~
wi th N
the coding time would be approximately 30 minutes.
=
16 and 0
<
eX ~
5 ,
.h.o< = 0.2,
.6.0( divided by 10 three times,
After coding, a control card is prepared, and
the x and y observations punched on cards using a
standard input card form. The information on the
O. 05 ~ x ~
- 17 -
1. 4,
0.1 ~ Y ~ 0.3 .
Computers and ,.\utomation
Finally, it is believed that the subroutine
has the ability to solve a general class of curve
fit ting problems and at the same time reduce the
effort normally applied in their solution.
The above function required a one-way search for
0<
and total computing time tfaS approximate 1 y
12 seconds.
Gi ven y = __.....;A~_.....-....",..._ _ _ + C
(1
+
P
cXx 2)
using this function with the same data as
single exponential with
o
..c::::.
0<
.c:::;,
o c::
78,
~ ~
L:\r -
..60( = 0.5
Figure 1:
1
the
(Ju
0.8
-t------- ----------1-----:-I
I
I
I
I
I
0.010
1
I
I
R~
I
I
I
I
Applying the two-way search, the total computing
time tvas 12 seconds; however, the first estimates
of both 0( and p turned out to be exceptionally
good. When using "bad" initial values of 0< and
~
,the computing time increased to 40 seconds.
Gi ven y = Ae
tvi th N
=
-p(I)(:
25 and 0 <::
,Ao< = 0.025,
o~
x
~
+
24,
Be
D<
-P« +
~
I
I
:
I
1
R,
~
y
~
I
I
I
I
I
I
C
1, 0 <: ~ c:::::. 2)
Ar = 0.05
25
R7' II
~l ---~-- - - --I
:
I
I
Rs
R,
I
I
I
I
I
I
I
I
130
:
I
('9.. ---r- - - - -1----- ---------1------
This function is a solution, under c ert a in
conditions, of a second-order-differential he a tflow equation. The temperature, (y), is a function
of time, (x).
I
t
- END -
*--------------------*
Computing time for the curve fitting procedure ranged from 30 to 90 seconds, depending on the
initial estimates of ~ and ~
For this particul ar function 0< tvas extremely sens i t i v e and
bad guesses of both 0< 1 and AO( sometimes resuI ted in false solutions. Also, the min i mum
seemed to be in a steep tvalled trough, and in some
cases, the search would converge to the bottom of
the trough and decrease the deltas before it found
out that it would have to continue dotYn the trough,
at which time the deltas tvere too small for rapid
convergence.
*
BULK SUBSCRIPTION RATES
These rates apply to prepaid subscriptions canirg in
together direct to the publisher. For example,
if 7 subscriptions come in together, the saving on each one-year subscription will be 24
percent, and on each th'o-year subscription will
be 31 percent. The bulk subscription rate s,
depending on the number of simultaneous s u bscriptions received, follow:
Bulk Subscription Rates
COni ted States)
Summary
In summary then, the curve fitting meth 0 d
obtains' a least squares fi t to .!l points, using a
general class of transcendental functions by utilizing a searching technique which minimizes the
sum of squares of the residuals. The method, tvhich
requires a high-speed computer, has been coded in
subroutine form and used successfully on the IBM
701 Calculator. When using the subroutine, since
it represents a general solution for a curve fitting problem when the function to be fit has not
yet been defined, a certain amount of coding, independent of the subroutine, is required. However,
this coding is kept to a minimum as the me tho d
eliminates the necessity of taking partial derivati ves t'Vi th respect to nonlinear parameters. Estimates of linear parameters are not required, but
the upper and 10l1er bounds must be given for nonlinear parameters. All computations are don e in
either single-precision or double-prec~ion fixedpoint arithmetic, since the 701 operates muc h
faster when computing in fixed point.
- 18 -
Number of
Rate for Each Subscription, and
Simul taneous Resulting Saving to Subscriber
Subscriptions
One Year
1\VQ Years
7 or more
4 to 6
3
2
$ 4.20, 24 %
4.60, 16
5.00, 9
5.25, 5
$ 7.25, 31 %
8.00, 24
8.80, 16
9.55,
9
For Canada, add 50 cents for each year; 0 u tside of the Onited States and Canada, add $1.00
for each year.
METHODS IN HIGH SPEED COMPUTATION
FINAL EXAMINATION
JOHN W. CARR, III
Uni versi ty of Michig-an
Ann Arbor, Michi~n
Here is a copy of the final (closed boo k )
examination given January, 1956, in Mat h 1 7 3 ,
"Methods of High Speed Computation". It may be of
interest to readers of "Computers and Automation".
It is mainly self-explanatory, except for problem
5, which describes the 384-bi t MIDAC roorcury delay
line storage uni ts, tvi th 48-bi t words inc 1 ud i n ~
45 bits of information, and a 46th bit pari t y
digit for ~ parity.
1.
(c) Program four separate floating-point subroutines, in a standard subroutine for m
of your OlVn choosing, for add, subtrac t,
multiply, and divide.
(d) Spdcify your own conventions for and then
program a subroutine which, upon overflow,
automatically prints out the machine's
ins truc tion counter, contents of its pertinent arithmetic registers, and instruction
being performed along with the word "overflow", and stops. Upon restarting it t\fill
read in a new program from magnetic tape,
perform a memory sum, print out the sum,
and stop.
(One Hour) In Problem 2 you will be asked to
program one of several alternative problems.
In this problem you are asked to des i g n
a
computer and set up an instruction cod e to
solve one of these problems. Your procedur e
should be as foll~~:
(e) Evaluate the following logical functio n
for all possible truth table combinations:
Pick a problem in 2 that you will sol ve.
(2) Set up the specifications and instruction code for your computer. These
specifications must include:
0)
(a)
(b)
(c)
(d)
[ (A • B)
6~
-1. 7x - .80
=
°.
(g) Perform social security calculations for
a list of 20,000 employees stored on magnetic tape, insert the newly-calculate d
values on the tape, and print out a social
security record with man's name, year-todate total pay, and total deductions.
(11)
(a) Read in a matrix and vector in decim a1.
Perform the matrix by vector nmltiplication
Program a routine to obtain the mean and
standard deviation for 1000 numbers. Do
not program the square root, but instead
set up complete specifications for such a
subroutine and inclUde it in the program
as a block.
Remember, Problems 1 and 2 will be judged on hOh'
well I can follol'l and understand t"hat you did,
as well as how sound and imaginative a job you
do.
n
=1
+ 3. 6~
Print out the answer in decimal.
(30 Minutes) Using the instruction code and
computer devised in Problem 1, solve ~ of
the following problems.
j
0) 1 v [(A • C) ~ (B • 0)]
(f) Write a program to find a real roo t between 0 and 1 for the polynomial equation:
Remember, I must be able to follow and understand
the program you write in Problem 2, so please give
me complete specifications. You have had enoug h
experience by now to devise a reasonable computer.
Include a description of your input-output devices
and internal" registers involved in instructions.
(N~TE: I do not want detailed hardware discussions).
:!£...
(C,
(Your machine is allowed only one logical
operation relating storage and arithmetic
uni t) •
Fixed point.
Single address instruction code.
Satisfactory input-output.
Methods to alter addresses.
(3) I will not accept any freak instruction
types such as "Solve Problem 2C. "
Nor can I permit a complete a r ray
of logical operations in Part 2e.
2.
~
ai· Xj
J
for an arbitrary value of n, and p r i n t
out the result in decimal. Use a cycling
procedure. Do not forget scaling.
3.
(20 Minutes)
Derive a procedure for:
(a) Decimal to binary conversion 0 f mix e d
(integer plus fraction) numbers;
(b) Read in a sequence of 256 20-cha r ac t e r
alphanumeric words. Sort them in pro per
alphanumerical sequence, 0-9, a-Z. Print
out the sorted results in alpha n u me ric
form. You may use any method for sorting
that you see fit, irrespective of the time
required for sorting.
(b) Binary to dec i-mal conversion
numbers.
0
f mix e d
In other words, present a method for each and
give a mathematical justification for it.
- 19 -
(cont'd on page 21)
A COMPUTER PROGRAM FOR FINDING ROOTS
ANDREW D. 'lOOTfl, Direc tor
Rirkhack College Computational Laboratory
Uni v. of London
London, W. C. 1., England
In recent years there has been considerab 1 e
discussion about automatic programming. Unfortunately most of the published data on this subject
has been of a very general kind and gives 1 it tl e
information regarding the manner in which a rea 1
automatic program actually works.
It is the purpose of this paper to desc r ibe
a program which has been used on A.P.E.{X.) C. (an
electronic digital computer at this Laborator0 for
the investigation of the real roots of polynomials.
The only claim that this particular program has to
be called "automatic" lies in the facts, th a tit
determines the degree of the polynomial from the
co-efficients which are given, and that it locates
the roots accurately after making a prelim ina ry
survey. Since it was originally designed toevaluate the roots of the confluent hyper-geometr i c
func.tions IFl(a,l,z) tvhere a;:. -1, -2, -3, etc.,
it is assured known that the roots are real and
posi tive; and the machine automatically stops when
they have all been determined.
The only human step is to insert the tap e
containing the coefficients into the reader, and
the program is capable of dealing with polynomials
of degree not exceeding 31. From this point onwards the operation is entirely automatic and proceeds as follows:
1)
The machine reads the tape into the coefficient storage locations after passing the data
through the decimal-binary conversion sub-routin~.
but if P(z - 2-3) is negative, P(z - 2-3 -2-4) is the
next trial. This process continues until the interval
2-31 has been reached at wgfch point the
value of (zr= z::2-3 :f:.2-4 • • • 2- ) is passed
to the binary-decimal conversion routine and is
then printed. It is followed by the value of the
residual, that is of P (zr). Unity is now s u btracted from a root-count number and the res u 1 t
is tested by means of a conditional transfer i nstruction. If the result is negative, all of the
roots have been found and the program stops. If,
however, the result is positive, it is stored for
future use, and the program passes to 7).
=
7)
The values of z and of P(z) are passe d
through the binary-decimal conversion routine and
are printed out. The program then returns to 4)
at an appropriate point.
It should be mentioned that since A.P.E.(X.)C.
operates wi th numbers in the ran 9 e -1 ~ z ~ l,
suitable scale factors are applied to z and to the
coefficients so that the results of the calculations remain wi thi,n range. Normally this process
must be carried out by the programmer, but if a
considerable slowing down of the calculation can
be tolerated, the relevant instJ;uctions i nth e
following program may be modified to use f10atingpoint routines.
Since most readers will not be familiar with
the A.P.E. (X.)C. code, the program is written in
a verbal form which can readily be trans for me d
into a real machine code.
2) At the same time it counts the number of
co-efficients, (n+1) , and by this means de t e rmines the degree (n) of the polynomial.
A.l
A.2
3) Wi th the count number evaluated in 2),
the polynomial evaluation routine is set so as to
use just the (n+1) input coefficients and notthe
(30 - n) other values possible to the program.
A.3
Storage locations for z, P(z - 2-2 )
cleared to zero
Coefficient count location c 1 ear e d to
zero
Decimal-binary conversion sub-ro uti n e
modified to come out at B.5
B.l
B.2
Tape read
Result non-zero, proceed to B.3. Result
zero, end of coefficients, proceed to
B.7
B.3 9 lines of tape read (i.e. 8 decimal
digits of coefficient and sign)
B.4 Data converted to binary
B.5 Coefficient count location con ten t s
added into storage location digits of
recora instruction, which is then executed. This records the coefficient
in its correct place
B.6 Coefficient count location contents increased by unity. Proceed to B.l
B.7 Coefficient Gount used to set C.3 and
0.15 to correct initial values
4) The program eval ua es tie pol y nom i a 1
P(z) at intervals Z = 0, 2- , 2~ , 3.2-2 •••. n.2-2
2
5) The machine compares the s i g n 0 f the
latest value of p(z) with the sign of that previously calculated. If a change in sign has occurred, the program for finding the exact root is
suitably modified according to the sense of the
change + -=> -, or - ~+. In the event of a si g n
change the machine next proceeds to 6), otherwise
to 7) •
6) The root is evaluated to 31 bit P re c ision. This is done by the process of "successive
trial an~ comparison" in whiCh, for example, i f
P (z - 2-) is positive and P (z) is negative the
value of P(z - 2- 3) is calculated; if th i s i s
positive, P(z - 2-3 +2-4) is next calculated,
C.l
- 20 -
C.6 restored to correct initial for m
(See 0.2)
Finding Roots
C.2
C.3
C.4
C.S
C.6
C.7
C.8
C.9
C.IO
C.ll
C.12
C.13
C.14
C.lS
0.1
0.2
0.3
0.4
O.S
0.6
Accumulator cleared and Z sen t to
mUltiplier register
an added to accumulator contents
Accumulator contents transferred to
regis ter (R)
Order C.3 modified to refer tolocation a 1.
Resul t o?-C.5 tested to sense end of
evaluation cycle. Cycle un-finished, C.7. Cycle complete, C.8
R times z formed in accumulator C.3
Sign of number P(z - 2-2) tested and
compared wi th that of P (z) c 0 ntained in register. If signs are
same,proceed to C.9. If different,
proceed to C. 15
P(z - 2-2) tested replaced by P(z).
Binary-decimal convert and p r i n t
sub-routines modified to come out
at C.12
Z storage location contents c 0 nverted and printed
Binary-decimal convert and p r i n t
sub-routines modified to come out
at C.14
Value of P (z) converted and printed
followed by tabulation symbo 1 s
for page layout
Contents of Z s~orage location increased by 2-. Proceed to C.2
P(z) positive, 0.10 set to com e
out at 0.4. P(z) negative, 0.10
set to come out at 0.3
O.lS set to coefficient count -2.
Probe location set to 2-3 • zr set
with value of z reached in tabulation program
Instruction C.6 modified to 0 utp ut
to 0.8 for completed cycle. Proceed to 0.6
Accumulator contents positive, proceed to O.S. If negative, p r 0ceed to 0.6
Accumulator contents positive, proceed to 0.6. If negative, p roceed to O.S
Probe added to zr
Probe subtracted from zr
0.14
Value of P (zJ converted and printed
follol\led by tabulation s y mb 01 s
for page layout
O.lS Uni ty subtrac ted from root-c 0 u n t
number
0.16 Result tested, if positive, proceed
to C.IO; if negative, proceed to
0.17
0.17 Stop
- END -
*-------------------*-------------------*
FINAL EXAMINATION
(cont'd from page lQ)
4.
(10 Minutes) Draw a flow or sequence diagram
for either 3(a) or 3(b).
S.
(30 Minutes) The follOldng
pendent system of equations
ally an important element 0
Identify the element in the
in English what it does:
Xn= (~-384 • W
n) v
Boolean tim e derepresents logicf the MI 0 A C •
machine and explain
(Y n • Wn)
X48K+46 = ( .... «(X48K~ X48K+l)¢ X48K+2)
1=
X48K+3) •••
=I: X48K+4S)
State what function the pulses Xn , Wn , Yn , and
X48K+46 perform. Here:
K= 0, 1, 2, ••• 7
6.
0.7
Accumulator cleared and new val u e
of zr written in multiplier register. Program sent to C.3
0.8 Probe shifted one place rig h t and
re-recorded
0.9 Probe tested. If> 0, p roc eed to
0.10. If zero, proceed to 0.11
0.10 P(zr) to accumulator. Proceed t 0
0.3 or 0.4. (See C.1S)
0.11 Binary-dec imal convert and p r i n t
routine modified to come 0 u t at
0.13
0.12 zr storage location contents c 0 nverted and printed
Binary-decimal convert and p r in t
routine modified to come out a t
O.lS
(30 Minutes)
Write a subroutine, in standard
MIOAC conventional subroutine form,' to rea d
in a block of words from the drum, perform a
memory sum, taking account of any po s sib 1 e
overflows, on the first n-l words, and compare
the anSlver wi th the number stored in the n-th
\·wrd by a similar previous subroutine. In case
they do not agree, print out the hexadec im a 1
word "badbadbadba" and stop the machine.
If
they do agree, jump out of the subroutine i n
the usual fashion. Set up pertinent specifications for the subroutine. Since you do not
have a code list (closed book), do the b est
you can. 00 not use "present address reI ative" but code in floating address instead.
- END -
- 21 -
NEW PATENTS
RAYMOND R. SKOLNICK, Reg. Patent Agent
Ford Inst. Co., Div. of Sperry nand Corp.
Long Island City 1, New York
The following is a compilation of patents pertaining to computers and associated equipmen t
from the Official Gazette of the United States
Patent Office, dates of issue as in d i cat e d.
Each entry consists of: patent number / inventores) / assignee / invention.
April 10. 1956: 2,741,734 / Edward O. Johnson
and William M. Webster, Jr., Princeton, N.J. /
Uni ted States of America / An inverter c i rcuit.
2,741,756 / Arthur C. Stocker, Collingswood,
N. J. / Radio Corp .. of America, Del. / An
electrical data storage circuit.
2,741,757 / George C.. Devol, Greenwich, and
Erik B. Hansell, East Hartford, Conn .. / George
C. Devol / A magnetic storage and sen sin g
device.
2,741,758 / Seymour R. Cray, MinneaJX> 1is , Minn. /
Sperry Rand Corp., Netf York, N. Y. / A magnetic core logical circuit.
April 17. 1956: 2,742,227 / Frank W. Bub b,
Dayton, Ohio / Phillips Petroleum Co., Del. /
An electrical computer for solving simultaneous equations.
2,742,566 / Frederick V. Hunt, Belmont, Norman
B.. Saunders, Weston, and Robert E. Kirkland,
Dorchester, Mass. / United States of America/
A demodulator device..
'
2,742,588 / Arthur V. ' Hollenberg, Morris Plains,
N. J . / Bell Telephone Lab., Inc., New York,
N.. Y. / An Electronic amplifier ..
2,742,599 / Horst M. Schweighofer, Cedar Rapids,
Iotl'a / Collins Radio Co .. , Cedar Rapids, Iowa /
A shaft positiQning device.
2,742,615 / Joseph O. Preisig, Mercervill e ,
A
N. J .. / Radio Corp .. of America, Del.. /
frequency selective circuit ..
2,742,632 / 'Ric.hard L. Whitely, Haddonfield,
N. J. / Radio Corp. of America, Del. /
A
magnetic switching circuit.
2,743,367 / Edwin P. Felch and Francis G. Merrill, Chatham, N. Y. / Bell Telephone Lab.,
Inc., New York, N. Y. / A frequency mu 1 t iplier apparatus.
2,743,401 / Raymond W. Moore and Willia m D.
King, Buffalo, N. Y.. , and James T. Carleton
and Loren F. Stringer, Pittsburg h , P a. /
Westinghouse Electric Corp., East Pittsburgh,
Pa. / A magnetic amp!ifier control system.
2,743,430 / Melvin L. Schultz and George A.
Morton, Princeton, N. J. / Radio Cor p. of
America, Del. / An information storage device.
2,743,434 / Hugh B. Flemdng, Burlingame,Calif./
- / A system of carrier current distribution.
2,743,436 / David Gale, Netf York, N. Y./United
States of America / A navigation computer.
May 1. 1956: 2,743,867 / Germain Gervais,
Riviere-a-Pierre, Quebec, Canada / - An integrating counter mechanism.
2,743,868 / William Wockenfuss, Brooklyn, N.Y./
Burroughs Corp., Mich. / A sensing device
for a perforated card.
2,744,169 / Charles Reed Deming, Venice, Calif./
Hughes Aircraft Co., Culver City, Cal if. /
A pulse amplifier circuit.
2,744,196 / Conrad H. Hoeppner, Washington,
D.. C. , and Carl Harrison Smith, Jr., Arlington, Va. / - / A pulse width discriminator.
e,744,197/ Roland Marshall Gogolick and James
Gilmore Tabler, East Cleveland, Ohio / GlobeUnion Inc., Milwaukee, Wis. / A fre que ncy
stabilizer.
2,744,223 / James F. English, Jr., Lakewood,
and Anthony J .. Hornfeck, Lyndhurst, Ohio /
Bailey Meter Co., Del. / A servo sy s te m
including an electrical inverter circuit •.
2,744,227 / Charles W. Spindler, Jr., Norristown, Pa. / Leeds and Northrup Co., Philadelphia, Pa. / A compensated null-balance
servo sys tem.
2,744,240 / Guy N. Hughes, Maryville, and
Ralph N. Harder, Alcoa, Tenn. / Aluminum Co.
of America, Pittsburgh, Pa. / A system for
integrating D. C.. values.
2,744,242 / Seymour B. Cohn, Flushing, N. Y. /
Sperry Rand Corp., Del .. / A wave guide delay
line.
April 24. 1956: 2,743,355 / Robert L. Sin k,
Altadena, Calif .. / General Electric Company,
N. Y. / An automatic gain control circui t fo~
pulse receivers.
2,743,359 / David Sayre, Philadelphia, Pa. /
United States of America / A counting circuit.
May 8. 1956: 2,744,683 / John W. Gray, White
2,743,360 / Russell S. Stanton and GeorgeYucht,
Plains, N. Y. / General Precision Lab. Inc.,
Los Angeles, Calif. / Hughes Aircraf teo. ,
N. Y. / A navigational resolver-integrator
Del. / A pulse-length switching circuit.
computer.
2,743,362 / Daniel Leed, New York, N. Y.. / Bell
2,744,955 / Arthur Eugene Canfora, Brooklyn,
Telephone Lab., Inc., New York, N.. Y. / An
N.Y .. , Anthony Liguori, Hackensack, an d
automatic frequency control ..
- 22 (cont'd on page 39)
AIRCRAFT-MARINE PRODUCTS. INC. ~
H ARRISBURC. PA.
).'''-,
,
THE
CELLULAR,
SHIELDED
FATCHCORD
SYSTElM:
revolutionary Cellular, Shielded
Patchcord Progra:r:n.rn.ing System.
is constructed of molded nylon blocks alternated
with interlocking metal strips. The hole in each
block accommodates: standard patchcords, coaxial (shielded) patchcords, or special "L" type
shielded patchcords.
This cellular system of construction prevents current leakage from one circuit to another, while providing all the advantages of
a metal patchboard. Its insulated surface and
flexibility of arrangement, spacing and color
The illustration shows how Berkeley Division
of Beckman Instruments, Inc.
is using A-MP's new Patchcord System
in its new EASE* 1200 Analog Computer.
coding offer exceptional versatility on computers, test equipment, business machines,
and all types of automated industrial and
militaryequiplnent .
.
~~li.E
~~S+~l'"
Aircra:ft-Marine Products, Inc.
GENERAL OFFICE: HARRISBURG, PA.
A-M,;) of Canada, Ltd., Toronto, Canada
A-MP-Holland N.V., 's-Hertogenbosch, Holland
Aircraft-Marine Products (G.B.) Ltd., London, England
Societe A-MP de France, Courbevoie, Seine, France
shield
-----r~~_+_-~~-spring
c e l l - - - -...
contact tip
*Trade mark, Berkeley Division of Beckman Instruments, Inc.
(cont'd from page 13)
Operation of a Computer
Unless there is a good guess to begin wit h ,
this iterative procedure can be excruciati n g
because of the relatively large number of steps
necessary. However, it can be effective when
applied to a sequence of problems each of which
involves only a small variation in design or
composition from its predecessor. This als 0
makes input preparation much simpler as it is
prepared from previous problems.
For MUG
problems, computations require, on the average,
about an hour and a half per problem.
Our third problem is a two dimensional
problem called BETTIS 54. In this the bas i c
equations are IOOre or less the same as those
of BETTIS 57. The Geometry used is X Y rather
than the r 9 or r g previously used. In this
problem the description of the reactor use d
is more flexible. The problem utilizes a uniform mesh with boundaries allowed a Ion g the
mesh and it may progress automatically from a
course mesh to a fine mesh. With such a two
group code it is often necessary to spend two
full shifts in the solution of one pro b I em
consisting of 12 or 13 power iterations. This
is, of course, dependent upon the n um be r of
points and the rate of convergence.
Bot h
BETTIS 57 and MUG problems involve the simultaneous solution of two partial differenti a 1
equations over fairly large regions.
The design of reactors creates more problems to be done than there is machine time with
which to carry out their solutions. Our difficul ties, consequently, are not If i t h the
problems themselves, for they are a Ire a d y
coded, but with the factors involved in their
solution. This, however, does not prec 1 ude
the possibility of difficulties tdth a coded
program. We may then divide the princ i pal
difficulties into three main categories: personnel failure, priori ty demands, and computer
failure. Personnel failure must be subdivided
into two categories, namely loss of time while
actually on the machine and errors in inp u toutput preparation. The former is relatively
common. This involves using the wrong tapes,
not being familiar enough with the operati n g
manual and, in our case, not knowing where the
person, who was running these same problems
previously, left off. Our personnel vary from
week to week and often time from day t 0 day.
This is, of course, dependent upon the needs
of the various laboratories involved - The
David Taylor Model Basin in Washington, Westinghouse Atomic Power Division in Pittsburg h
and General Electric's Knolls Atomic Power
Laboratory in Schenectady, each of who m is
physically responsible for one shift. We are
at present also doing another type problem for
Combustion Engineering of New York. Each week
the Model Basin works its shift for e i the r
Westinghouse or General Electric so that every
other week one of the laboratories con t r 0 1 s
two-thirds of all available time. All of our
problems originate in ei ther Pittsbu r g h 0 r
Schenectady, and since they are of the ty p e
that there are more problems to be done t han
there is computer time 1\'1 th which to sol v e
them, we are able to accumulate a sufficient
backlog. The lack of centralization involves
us in a difficul ty with communication, w h ic h
in turn has a tendency to invite the sec 0 n d
type of personnel failure. This inv ita tion,
I must say, for the most part goes unanswered.
Yet, the transmittal of quanti ties of in put
data by telephone to a person who may not be
familiar wi th the problem in question is at
best hazardous. The nature of these problems
is such that in any homogeneous group e a c h
problem depends upon the result of its prede~
cessor. In examining the results of a problem
it may be found that any further computa ti 0 n
along the same lines may be so unnecessary and
wasteful that immediate changes must be effected. In this way the means are justified. The
correc t acceptance of input data by no means
precludes the possibility for error, for while
running problems each person must un i t Y P e
these changes or new data and do the pro 0 freading. Running between computer and type r
is certainly trying and even after th e s e obstacles are effectively met a problem ma y be
pulled off the computer and replaced with one
of higher priori ty. The procedure for th is
substitution varies with each type problem and
with the amount of time spent on the problem.
It is understood that each, person be familiar with every type problem that is run.
Considering that a good maj ori ty of our p e rsonnel are not acquainted with the field, we
have a problem wi th what I would call "scholarship" which, most generally spe a king, involves attention to detail. This implies a n
intimacy with particularsj it is conce rned
wi th the many ramifications a given s ubj e c t
might have. When one dedicates himself to such
a task he ceases, for a tirre, to relate the
imroodiate subject of his study to wha tever
else he knows. He must temporarily sus pen d
judgment of his subject in order to be better
able to discover all that it is and all th a t
it involves. The neophyte, however, m u s t
limi t himself knowingly, not forgetting t hat
he may have certain reservations ab 0 u t the
meaning of his subject, but simply suspending
them until his understanding of his subj e c t
is thorough enough to permit him to m a k e a
judgrren~.
Thus, the development of some form
of scholarship is a mastery of particulars before the generalities. It is, in a 1 a r 9 e r
sense, essential to all of human thought, acti vi ty and learning and is by no means CI1 overnight occurrence. The particular with which
we are concerned is that which involves p r 0duction in the solution of problems.
I tis
perhaps not the best of all possible systems
to acquaint people with a field in which they
must accurately carry out solutions to problems
- 25 -
Computers and Automation
which, at first, they know nothing about.
man's prowess. In this installation we recognize the computer'~ capacity on problems tried
and true so that most organization and analysis
involves the continuous desire to increase the
stabili ty of the input-output system.
T his
brings up the question of remote data processing. With the perfection of such a system, a
computer installation away from a central staff
becomes even more satisfactory as the time required for input preparation and input-outp u t
transmittal becomes negligible. The bigge s t
si_ngle factor which governs the effectivenes s
of a production installation is the speed with
which all the processes concerned with a given
problem are carried out. Judging from our effeciency reports which account for each minute
of computer time, I maintain we look like any
other computer installation.
There is no doubt but that cal cuI at ion
admi ts of error. This, however, differs fro m
computation tvhich contains no human e 1 erne n t.
The very nature of this installation is s u c h
that in order to be effective, the source of
error must be recognized immediately and th en
removed. In our case it is necessary to oversimplify operational procedures. This attitude
of simplicity has been with us from the start.
When we first ini tiated proceedings, w e had
sdme input data already typed and a tap e of
service routines. We were able to correct our
data and test tapes so th~t inside of the first
hour of the first day tire had started in operation. Instead of beginning at the beginni n g,
we jumped in somewhere near the middle tv! th a
good bi t of programming, that would norm a 11 y
have to be done, all set up. We do not, by any
means, advocate the abolition of programming.
We do say that, in such an installation c 0 ncerned only with production runs, the nonresidency of programmers tends to remove complexities and reduce non-productivity.
The p r 0grammers who did the original coding are called
upon as consultants from time to time and they
are now at liberty to work on improvements and
better codes.
As a result of the facts regarding th i s
particular electronic computer installation, I
should like to suggest that some of the impressions and opinions presently held by many people must now, in the light of the e vi den c e
presented, be considered to be either amy t h
or at least suspect. Such opinions to be questioned inclUde:
To sum up, in slightly over nine month s
we have utilized close to five thousand hour s
of computer time and have successfully solve d
over three thousand problems. We have see n
tvhere a computer installation is not constrained
by necessity to have programmers, to do coding,
or to have experienced pers'onnel to carry 0 u t
p~oblem solutions.
And, the lack of proximity
to headquarters, tvhich in some t'\tays must retard
the input-output set-up, coupled with the urgency
of the problems involved, nevertheless does not
detract from that which is accomplished.
In the nine month duration of this computer
installation, we have attempted to achieve the
optimum use of human as well as ma te ria 1 resources. The basic principles of automa t ion
seem to concede the human use of human beings
as a fulfilled prerequisite for bigger and
better things. In an organization de v 0 ted
solely to production work, however, this cannot
be considered as an accomplished condition precedent. In any attempt to control resources as
a means to increased productivity the role of
the machine cannot be overlooked. It can be
mistaken. A computer is a catalyst p 1 ace d
into the scheme of things in order to li~t the
human element out of the slow, tedious, unartistic approach for maximum efficiency if h i c h
seems to serve as a universal panacea. I f we
consider the computer's role to be constant,
that is, it can altfays do a job fas ter and
perhaps better than the human element, we may
then concern ourselves with "homo-automation"
and effect the most advantageous uti 1 i t Y of
1.
Experienced personnel are a necessary
prerequisi te for a successful hi g hspeed computer installation.
2.
No computer installation can opera t e
effectively outside a general s t a f f
or staffs.
3.
Programmers and programming are the
heart of all computer installations.
4.
Only ideal conditions produce ide a 1
resul ts.
- ENJl -
*-------------------*------------------*
Hawaii Firm interested in representing Computer Manufacturer.
Executive staff qualified in Business Machines and Electronic
Engineering Fields. Maintenance
staH experienced in Electronics.
Teleprinters and Precision Equipment.
Reply to
COMPUTERS and AUTOMATION
- 26 -
(cont'd from page 11)
Day of fleckoning
The right part of the balcony had been reserved for the gentlemen of the press. The
rest had been left free so that the many visi tors could file through, observing the calculator in operation briefly.
The spools of the tape servos spun rapidly.
Blue dots scintillated on the faces of the
cathode ray tubes. The purple light marked
DATA IN lvas glowing.
At precisely ten a.m. Dr. Amos K. Hommel
turned to us.
In a moment the tape servos hal ted. The
blue dots glolved steadily.. The information
was ld thin the memory of the machine. The
problem had been accepted.
"Gentlemen," he said, "we are ready
begin."
t
0
"Describe the detailed design of y ou r
mvn superior successor!" SUPERVAC had bee n
asked.
He put on his pince-nez glasses.
"Miss Campylos, if you please." he said,
turning to his secretary.
The blue light labeled WAITING blinked
insistently ..
Miss Campylos took the twelve reels 0 f
magnetic tape. One at a time she threaded
their ends through the spools of the in p utoutput servos. She closed the glass doors.
LATE.
Hommel pushed the button marked CALCUFor some five minutes the machine was observed to perform in very even fashion.. The
dots on the tube faces blinked bright, then
dim in orderly rows. The tape servos spun in
unison. The monitor lights formed eve rchanging symmetrical patterns across the face
of the console.
"Ready with the data, Dr. Hommel." she
said.
"Ready Mr .. Barnes?" said Hommel ..
"Ready, Sir," s aid Barnes at the ma i n
pmver frame monitor panel.
The yellow light marked CHECK DATA glowed continually.
"Proceed!" said Hommel.
Barnes threw three switches in quick succession. Grasping the oversize lever of the
main circuit breaker with both hands he pushed
it firmly home. The crackling sound of clooing
relays and solenoids came from the main power
frame.. An all-pervading hum filled the room,
accompanied by the ever higher-pitched whine
of shaft bearings as the massive direct current generators which powered SUPERVAC spun
into action.
Dr. Hommel sat at the main console. He
pressed a number of buttons.. The great steel
drum began to turn. Lights blinked on and
off. Hommel spoke into the console m i c rophone.
"Mr. Nugent, memory check please .. "
Nugent gazed rapidly at the tube faces _
and dials before him, scanning each in turn.
"Main store empty, Sir," he said.
Hommel worked from a typed list, checking
off the functions of the machine one at a time
as they were found to be in order. At least
he put down his list. Before him glowed the
orange lights labeled MAIN POWER ON, AUXILIARY
POWER ON, DRUM ON, and AIR CONDITIONING ON, as
lvell as the green light marked READY.
Hommel pushed the button labeled READ.
Suddenly the demeanor of the m ac hi n e
changed. No longer did tube faces s h i f t
their dots in orderly fashion. Now the scintillation went on haphazardly over the entire
display. Monitor lights flickered in strange
and weird patterns. The machine was sorting
and classifying its information. At Hommel's
elbow shone a chartreuse light labeled FORMULATING PROBLEM.
After some twenty minutes the mode of
operation of the calculator again changed.
Now familiar patterns were seen repeating
themselves on the faces of the memory tubes.
They grew ever more complex. Occasionally
they could be recognized racing madly through
the monitor lights as the machine took cogn:izance of them. On the console an amber light
proclaimed the word MULL.
For some hours the machine continued in
MULL mode, calculating at fantastic speeds,
grinding relentlessly through the morass of
digits toward a solution. Hommel watched the
calculator's every move. At one-thirty in tie
afternoon Bardney relieved Hommel at the console for an hour. Still the machine ground
on relentlessly with no sign of nearing completion.
As evening neared most of the visitors
had left the building. A few reporters nodded
sleepily on the balcony. Suddenly we noticed
Hommel stiffen. The MULL light had gone out!
(cont'd on page 28)
- 27 -
DAY OF
RE(]{rnI~G
Computers and Au toma tion
(cont'd from page 27)
In its place glO1~ed the siooster, magneta-colored RECHECK DATA light. The machine's operation shifted to the patterns of data checking.
after two minutes the MULL light came on again.
Hommel relaxed. The machine resumed its calculation.
Engineers
Mathematicians
At seven P.M., however, the machine again
suspended calculation and entered into five ~
utes of RECHECK DATA. This tirre Hommel became
visibly concerned and he left the console for
a hurried consultation with Bardney.
Physicists
TRANSLATE ADVANCED
ENGINEERING INTO
MATHEMATICAL TERMS
As the evening wore on, the performance of
the machine became more and more erratic. It
went into frequent and prolonged periods of RECHECK DATA.
At precisely ten-thirty every eye Ivas fixed upon SUPERVAC as the MULL light again Ivent
out. This time, however, its place Ivas taken
by the voilet WRITE light.
Professional engineers and
scientists with a strong
interest in digital applications
are needed at GE's expanding
Aircraft Nuclear Propulsion
Department. Advanced
engineering or scientific
knowledge is necessary, as
well as the ability to analyze
engineering problems. While
computer experience is
desirable, it is not essential.
"A result!" shouted Hommel, jumping up
from his chair.
We all ran to the printer which had clattered into operation. The typebars t~hacked
atvay. The paper rolled up from the platen. We
bent over to read the cryptic message:
"12 OCTOBER 1957," SUPERVAC had written,
"2230 PM CST, O:.}30 AM GCT -- PROBLEM 198BC12XA -- RECKON HAVE EXCELLENT POSITION HERE. NOT
WISH RELINQUISH IT AT THIS TIME, THANX. ROGER.
-- PDX~.c*EM -- OUT. "
Specifically, the men who
undertake this work must be
_ able to take a physical
problem an,d translate it into
mathematical terms suitable
for digital programming
analysis and solution.
The impassive faces of the cathode ray
tubes went suddenly dark. The tape servos
were not turning. On the console there burned a single, bright-red light labeled AUTOMATIC STOP!
- FNn -
...
~:;----------
IND:E1X OF NOTICES
For Informat'ioiCcfri:-
Advertising Index
Advertising Rates and
Specifications
Back Copies
Bulk Subscript jon Rates
Manuscripts
Reader's Inquiry Form
*
See Page:
44
42
Some of the most extensive
and modern computer
facilities in industry are at
your service at GE's Cincinnati
plant. You may also do
graduate work in your field
under GE's re-imbursed
tuition plan. And the city
itself, one of the country's
well-known cultural centers,
is a fine place to live.
Please write full details, including salary 1'equirements to:
40
Mr. W. J. Kelly
18
Aircraft Nuclear Propulsion Dept.
35
44
GENERAL. ELECTRIC
I
j
Address Changes: If your address changes, please
send us both your new and your old address, ttorn
off from the Ivrapper if possible), and allow three
h'eeks for the change.
- 28-
Cincinnati 15, Ohio
'I
Free
and
Use
the
of
the
Remote
Toronto
Computer,
Programming
of
It
C. C. GOTLJEB and others
Computation Centre
University of Toronto
Toronto, Canada
PA'lT 2
Continued from May, 1956 Issue of Computers and Automation
CHAPTER 4.
(n ~
EXAMPLES
In this Chapter we give details of s ever a 1
small problems- illus trating the use 0 f v a rio u s
techniques in coding, ending wi th a somewhat larger
problem followed through from the time it was first
received until final printed results were obtained.
1)
!
is then calculated as
ci-!) --:-
(n+
1) •
Note that no HALT order is included, sin c e
the pr~gram is not intended to terminate a t any
pre-set point.
For Examples 2 and 3, see the original manual.
Example 1.
The first example, a tabulation of! ,shows
the use of a loop.
n!
'n' takes successive integral values, and the tabulation is required to five significant dec i mal
places, four entries to a line, and in blocks of
four lines. The program could be written as f 0 1lows:
001
002
003
004
INST
OVER
OVER
OVER
LOOP
005
DIVD Z02.0 Z03.0
011
COl.O
ZOl.O
ZOl.O
016.0
000.0
000.0
000.0
000.5
ZOl.O Place 1 in ZOl
Z02.0 Place 1 in Z02
Z03.0 Place 1 in Z03
000.0 Set B5 to co u n t
16
(n + 1)
Z02.0 1
-;
CO:)
.
replaces
X16.5 1
006
OVER Z02.U 000.0
007
ADDN Z03.0 ZOl.O
'Z03.0
008
TRl'B 005.0 000.5
000.0
009
PRNT 016.4
005.0
X01.0
010
TRNS 004.0 000.0
000.0
011
QUIT 000.0 000.0
000.0
Cl'BT 1
STOP
ENTR
1
Ii:
("iii. 1) : placed in
one of XOl, ••• ,X16
(n -T 1) + 1 replaces
n+l
Reduce B5 and return to 005 if
B5 ~ 0
Print tab Ie 0 f
last 16 values
Return to insU:uction 004
End of code
-+ + "
The method used is quite direct. Answers are
stored in sets of sixteen on the X page, and printed out when each set is complete. ZOI is used to
retain T 1. At any instant, Z02 contains ~
and
Z03 contains (n + 1).
n:
- 29 -
CHAPTER 5.
LIBRARY FUNCTIONS
A number of tapes have been prepared i n a
library form which allows them to be incorporated
directly into Transcode programs as FUNCT IONS.
This chapter is a description of the Tra n s' cod e
library so that programmers can uselliese FUNCTIONS
without knowledge of the working details. Additions will be made to this library as new routines
become available.
Transcode library programs will be described
under the following headings.
1.
Title. The library tape will be labelled with
this title.
2.
"Tape Control -- Standard"
This !reans that the tape for the f,u n c tion,
which is to be used as FNTN oof, is to be reperforated into the program exac tly as it comes fr 0 m
the library cabinet, immediately following
FFFF oof Spaces
If the Tape Control is not standard, alternative
notes are given.
3.
"Program Entry -- Standard"
This means that the function oof is to b e
called into action as required by the program b y
means of the instruction
FNTN oof.O
aaa.A
ddd.D
Where the argument is to be found in address a a a
(modified by B-line A) and the function of thi s
argument is to be placed in address ddd (modified)
by B-line D). Notation as on Summary Sheet, A ppendix V. If the Program Entry is not S tan dard,
alternative notes are given.
4.
Time. This is generally given in milliseconds*
(msec .)
Computers and Automation
It is the time to execute the routine once, and
includes the time required to call in the function
routine and to restore the master program in the
electronic store.
APPENDIX III. TIMES OF TRANSCODE
OPERATIONS
Reading-in Instructions
Other headings may be present in particula r
cases.
Two routines (Te: CONVERSION/L and TC: CONVERSION/S) are available for converting Transcode
numbers from their floating binary form t~ fixedpoint binary form for output in fixed-point decimal form. These require a knowledge of real code,
and so will not be described here. Other routines,
including ones for inverting matrices, sol v in g
linear equations and integrating systems of differential equations are available. These r e qui r e
detailed information which can be obtained fro m
the librarian.
*
1 msec.
=
1
1000
sec.
The library functions arctan, arccotan,check
sum, cosine, exponential, natural logarithm, and
sine are described. See the original manual.
APPENDIX I.
For Output
5 or 6 instructions
per sec.
Reading-in NUMB or CNST - 27 msec. per decimal
digit. *
4 or 5 instructions
Translation into machine
per sec.
code 5 msec.
ZERO
100 msec.
COKE
73 to 89 msec.
ADDN, KOMP, SUBT
63 msec.
MULT.
141 to 216 msec.
DIVN
181 to 311 msec.
~QRT
75 msec.
READ
108 msec.
WRTE
50 msec.
TRNS
(4 msec. if back to sam c
segroont)
0.96 msec.
B-line INST
1 to 2 sec.
QUIT
6 2/3 characters per sec.
*Printing
24 characters per sec.
*Punching
=1=
There is a delay for conversion of numbe r s
with decimal exponents larger than about 10. For
exponents of the order of 1000, this delay is about
6 sec. In the case of output, maximum conversion
time is 1 sec. Zero and infinity are output without conversion. ++is input ldthout conversion.
MAGNITUDE RESTRICTIONS
on a Transcode Number having absolute value n.
10-75 ,000 < n < 1075 ,000
For Input
Input time oc I exponent r •
Noticeable loss of speed
for 10-10 > n > 101U.
Use + + for zero.
During
Calculation
-
APPENDIX IV. GLOSSARY OF TERMS
USED IN TRANSCODE
10-153 < n < 106~0
If n becomes < 10-153 ,
the number is
replaced by _10-10 ,000.
If n becomes> 10660 ,
IF/G stop occurs, and a
prepulse causes the
number tu be replaced
by 102 6tjtj.
10-100 < n < 10100 , n;: zero or infinity.
Let ab = correct exponent modulolOO.
If n < 10-llJlJ, 0.0. 8+00-4-is output.
If 10-199 < n" 10-10 , 0.0 •• ().tab
- is output.
+ + and Transcode zero are output
as 8.00 •• O+O~A
If 101 0 ~ n < 1066v, correct mantissa and ab+ is output.
If n >,,10 660 , 8.88 •• 89.ab+ is output.
Transcode infinity is output a s
8.88 •• 89.88 + •
APPENDIX II. FERUT OPERATING SHEET
FOR TRANSCODE, AND OPERATOR INSTRUCTIONS
FOR TRANSCODE
See the original manual.
- 30 -
bit - binary digit, a unit of binary information,
represented by 0 or 1.
character - 5 bits, a unit of information in the
scale of 32, represented by a teleprint symbol.
line - 20 bits, a unit of information in a FERUT
electronic store or B-register.
address - the label which identifies a s tor age
unit.
electronic storage location - the normal location
of a Transcode number, referred to by an address of the type XOl, X02, ••• YOl, Y02 ••••
etc. It occupies three lines in the ele ctronic store.
page - a set of electronic storage locations r elated to one electronic storage tube of the
computer, containing 64 lines. The X and Y
pages each contain 21 electronic storage locations, the Z page only 13.
magnetic storage or drum location - a unit of drum
storage, norml1ly Llt~rchangeable with a page
of electronic information.
control unit - that part of the computer w h i c h
directs the sequence of operations.
instruction - a command to the arithmetical, control or output units of the computer; in d icating the function to be performed, the address of all numbe~s involved, and any other
relevant information.
instruction code - the available set of instructions.
tape control - a command to the input unit of the
computer, indicating the manner of reading-in
instructions and nuroorical data, and of i nitiating a calculation.
Toronto Computer
program (noun) - a set of instructions, togethe r
wi th tape controls and numerical data, d esigned to solve a complete problem.
instruction number - the number associated with a
Transcode instruction in a Transcode program.
Numbering is consecutive.
routine - a set of instructions, usually a sub-set
of the instructions in a program, designedw
carry out a more elaborate function tha n is
provided by the instruction code.
coding (verb) - the translation of a sequence of
ari thmetical or logical operations into the
language of the instruction code.
number - a floating decimal number, which may ini tially be input to a Transcode s tor age
location or which may be generated a s the
result of obeying a Transcode instruction.
constant - a floating decimal number, which may
be input initially only into a Transcod e
storage location. A set of at most 21 available per program.
read - transfer data from the magnetic store to the
electronic store.
wri te - transfer data from the electronic s tor e
to the magnetic store.
interpretive routine - routine which translates a
program stored in pseudo-code into machi n e
code as each pseudo-instruction is obeyed.
compiling routine - a routine which, before the
computation is started, translates a program
written in pseudo-code into machine code and
arranges for all other necessary conversion
and organization to take place. Transco de
is a compiler-type routine.
APPENDIX V. TRANSCODE SUMMARY SHEET
NOTATION p, q, f, i, j, m, n, N are decimal digits.
xxxx is any permissible Transcode address,
including 0000.
o corresponds to the zero of the keyboard
on the tape punch, and must beplllcl1ed
wherever indicated.
aaa, bbb are X, Y, Z or C addresses.
X, Y, COOl to 021; Z 001 to 013.
ddd is an X, Y or Z address.
A, B, D are any of B lines 2, 3, •••• 6.
(aaa) exp refers to the exponent line 0 f
the address, only.
aaaA' bbbB, ddd D, are X, Y or Z addresses
modified by the respective B lines.
C addresses cannot be B modified.
(S) = contents of store location S
TAPE CONTROLS INST j j j
Reads in the following j
instructions, jjj :a 001,
002, •••• about 150.
FNTN Off
Reads in function tape to
function location 0 f f
(= 001, 002, ••• 015).
STOP
Stops tape reading.
ENTR
Causes pro g ram to be
translated and entered.
REEN
Causes translated program to be re-entered.
KOPY
Causes translated p r 0gram to be punched out.
Requires FNTNOOO.
OPERATIONAL INSTRUCTIONS
ADDN
SUBT
MULT
DIVD
aaaA
aaaA
aaaA
aaaA
~QRT aaaA
KOMP aaaA
ZERO dddO
bbbB
hbbB
bbbB
bbbB
0000
bbbB
0000
dddD
dddD
dddD
dddD
dddD
dddD
0000
OVER aaaA 0000 dddD
LOOP nnnO OOOA 0000
TRNS [iiiO 0000 0000
iiiO OOOA 0000
Transfer control to instruction iii.
Transfer control to instruction iii if
(A)~
iiiO 0000 dddO
READ mmmO OOOA dODO
WRTE mmmO OOOA dOOO
BSET (OOOA
tOOOA
JOTB OOOA
INCB OOOA
NEGB {OOOA
OOOA
nnnO
0000
0000
nnno
nnnO
0000
0000
bbbO
dddO
0000
0000
bbbO
o.
Transfer control to instruction iii if
(ddd) mantissa ~ o.
Read from drum mmm, modified by B line A, to
store d (:: X or Y.
Z only if originally Z).
Write from store d (~X,
Y or Z) to drum mmm,
modified by B line A.
nnn .... A.
(bbb) ex~-t A.
(A)..., ddo exp •
Add nnn to (Al.
Subtrac t nnn from (Al.
Subtract (bbb)exp' from
(A).
PRNT nnnN ommO dddO
CNST pqq ••• qt,nt) Reads in ~ 21 constan t ~n
pqq:. q!n'!Jof the form ±p.qq •• qXIO- •
"
NUMB pqq •• qtnt] Reads in ~ 21 number: nof
the form tP.qq •• qXIO- •
pqq •• qtn~ To be followed inmedia~e~
ly by a DRUM tape control.
ORUM omm
(aaaA)+ (bbbBH ddd D•
(aaaA)-(bbbB~ dddD'
(aaaA)X(bbbBr+ dddO.
(aaaA)+(bbbB~ dddD'
V(aaaA}-+ dddD'
\ (aaaA)' - (bbbBH dddD'
Place _10-10 ,000,
in dddO.
(aaaA>-+ dddD'
Prepare to cycle nnn
times under contro 1
of B line A.
Writes last set ofnumbers
to drum position omm ~OOl,
002, •• 064), divided into
two sets for B-modification.
- 31 -
FNTN 10ffO aaaA dddD
lOffO 0000 Zl40
HALT
VOID
COKE
QUIT
xxxx xxxx xxxx
xxxx xxxx xxxx
xxxx xxxx xxxx
xxxx xxxx xxxx
Print and/ or pu n c h nnn
consecutive numbers,
N numbers per pap e r
line, mm digits per
mantissa, start in g
wi th (ddd).
FNTN off {(aaaA) J
-tdddO·
For more general FNTN's.
Hal t operation of program.
No effect.
Refresh electronic store.
End of instruction list,
if obeyed, causes more
tape to be read.
- END -
WHO'S
WHO
IN
THE
COMPUTER
FIELD
(Supplement, information as of June 5, 1956)
This is Supplement No. 4 to the second edition
of the "Who's Who in the Computer'Field", published in the June 1955 issue of "Computers and Automation". The following issues contain other supplements: Supp. No.1, June 1955; Supp. No.2, Oct.
1955; Supp. No.3, June 1956, "The Computer Directory, 1956".
The purpose of this Who's Who is to give some
information about persons interested in one or mote
parts of the computer field. The source of this information is correspondence or completed Who's Who
forms received after May 3, 1956 and before June 3,
1956.
If your entry in the Who's Who in this or any
previous issue is incorrect, please send us the
correct information and we shall try to publish it
in an early issue.
A full entry consists of: name /title, organization, address / interests (the capital letters
"A,B,C,D,E,L,M,P,S" stand for main interests "Applications, Business, Construction, Design, Electronics, Logic, Mathematics, Programming, Sales",
respectively) / year of birth, college or last
school (background), year of entering the computer
field, occupation, other information (distinctions,
publications), etc. / code. In the code the digit
such as 6 denotes the year ('56) tvhen the information was received.
For the form of a Who's Who entry, see the
June issue.
The editors of "Computers and Automation" express their thanks to those in the following list
who made contributions towards the cost of preparing and printing the Who's Who.
~
Angstadt, Lloyd H / Consultant, 1225 Midland Ave,
Bronxville, N Y / AP / '96, Uni v of Penn, '24,
mgt consltnt, pub I "Impact of Computers" / 6
Bauer, Frances / Sr Mathn, Reeves Instrument Corp,
215 E 91 St, Net\, York 28, N. Y. / AMP / '23,
BrOll/D Univ, f50, mathn / 6
Bauer, Louis / Dir, Proj Cyclone, Reeveslnstrument
Corp, 215 ,East 91 St, NY 28, NY / AMP, operation elecnc analog compr ctr / '20, Brown Un~v,
'48, physicist / 6
Bauer, Walter F / Hd, Digi tal Compg Ctr, Ram 0wooldridge Corp, 5720 Arbor Vitae, Los Angeles,
Calif / ABDMP / '24, Univ of Michigan, '51, -/6
Bishop, John F / Gen Mgr, Beckman Instruments, Inc
2500 Fullerton Road, Fullerton Calif / ADEPS /
'24, Harvard Business School, U. of Calif, '51,
mgt / 6r
Boise E. B. / Chm, Sub Comm on Computer Tubes, J
Joint Electron Tube Engineering Council, 11 W.
42 St, New York 36, N.Y. / -, industry standardization / -,-,-,- / 6
Bonness, John J I Asst Mgr, Integrated Data P r 0cessg, North American Aviation, Intn'l Airport,
Los Angeles, Calif / ABP / '18, UCLA, '54, mgt/6t
Brisney, Gerald S / Sec Head, Minneapolis Hone ywell-Brown Instr Div, Wayne & Windrim Aven ues ,
Phila 44, Pa / A / '21, Virginia Poly Inst, '51,
elec engr / 6r
Brown, Arthur A / Staff Mbr, Arthur D Little, Inc,
30 Memorial Drive, Cambridge, Mass / AB / '13,
Princeton Univ, '55, operations res, Rho des
Scholar, author / 6
Brown, John / Asst lId Data Processg Group, Willow
Run Labs, Willow Run Air ort, Ypsilanti, Mich /
DE / '12, Univ of Md, '45, elecnc engr / 6r
Burris, Walter G / Dist Mgr, Remington Rand Univac,
Div, Sperry-Rand Corp, 2035 Franklin St, Oakland
12, Calif / ABPS / '07, -, '55, meth analys t /6r
Canning, Richard G / Partner, Canning, Sis son &
Assoc, 814 S Robertson Blvd, Los Angeles 35, Calif / A / '18, UCLA, '48, elecnc sys engr, author
"Elecnc Data Processing for Business & Industry
/6
Carr, J WIll / Asst Prof Math, University of Michigan, Ann Arbor, Mich / ADLMP / '23, Mass Ins t
of Techn, '48, mathn, pres A C M, 1956 / 6t
Carter, Gordon K / Engrg Analyst, General E
Co, Schenectady, N Y / AMP / '12, Univ of V i rginia, '45, engrg analysis & comptn / 6t
Chandler, Alan R / Res Engr, Mass Inst of Te c h n
Lincoln Lab, POBox 73, Lexington, Mass / ALP /
'30, Boston Univ, '54, res engr / 6t
Childress, J / Res Physicist, General CeramicsCoIp,
Keasbey, N J / AE, res, compr components / '30,
Louisiana State Univ, '51, physicist / 6
Codd, Edgar F / Hd, Data Processg Ctr, Computin g
Devices of Canada, Ltd, POBox 508, Ot taw a ,
Canada / ABLMPS, Operns Research / '23, Oxford,
'49, mathn / 6r
Coker, Frank B / Mgr Res & Devt, United Electrodynamics, Div United Geophysical Corp, 102C South
Marengo Ave, Pas adena, Cal if / CDE / '25, US C ,
'54, engr / 6t
Cook, C H / Group Engr, Glenn L Martin Co, Denver,
Colo / ABLMP / '25, State Univ of Iowa, Univ 0 f
Texas, -, mathn / 6t
Corkran, Davis H / Sales Engr, Electronic A s so c,
Inc, Long Branch, N J / AS / '20, Univ of Md,
'46, sales engr / 5r
(cont'd on page 34)
- 32 -
ENGINEERS
4RAlA announces
INERTIAL
NAVIGATION
delJelo/lment.pr(},?ram.for an adlJancedAir.Ebrce mIssile
Inertial Navigation offers the most advanced concept in guidance,
requiring no terrestrial source of energy or information, no earthbound direction Qnce the ultimate destination is selected. It offers
the most promising solution of the guidance problem for the longrange. missile.
Immediate openings
for Supervisory and
Staff positions as
well as for
Senior Engineers,
While the principles are simple, the realization involves advanced Engineers, and
creative engineering. ARM A's many successes in the creation of Associate Engineers,
precision instruments and systems for navigation and fire control, experienced in:
especially precision gyroscopic reference systems for all applications, fit it uniquely for a major role in this advanced area.
The height of imaginative resourcefulne!;ll and engineering skill
are required to create the degree of precision-hitherto unattained
- in the components essential to the guidance of advanced missile
systems-the gyros, accelerometers, and computer elements. Miniaturization must be coupled with extraordinary ability to provide
utmost accuracy under conditions of extreme velocities. temperatures, and accelerations.
There's significant scientific progress to be achieved at this leadership company and individual renown to be won, by engineers
associated with ARMA's Inertial Navigation Program. Many supplementary benefits make a career here1doubly attractive. ARM A
engineers are currently working a 48 hour week at premium rates
to meet a critical demand in the Defense Dept's missile program.
Moving allowances arranged.
Salary - up to $15,000
(Commensurate with experience)
Send resume in confidence to:
Manager of Technical Personnel, Dept. 674
4RAlA
Systems Evaluation
Gyroscopics
Digital Computers
Accelerometers
Telemetry
Guidance Systems
Reliability
Stabilizing Devices
Servomechanisms
Automatic Controls
Thermodynamics
Environmental
Research
Weight Control
Transformers
Production
Test Equipment
Standards
Division of American Bosch Arma Corporation
Roosevelt Field, Garden City, Long Island, N. Y.
M*_______________________________________________________________
*__________________________________________________________________
APPLIED MATHEMATICIAN
to $11,500
in this stimulating
Missile Test Project
You will be challenged by the research and
theoretical studies involved in acquiring data
from high velocity missiles being, fired over the
world's longest test range. Ph.D. degree plus
several years' experience in work related to
.above, required.
Join a scientific team at top level in
this unprecedented work with one of
the nation's largest corporations.
I deal living and working conditions on
Florida's Central East Coast .
TO ARRANGE CONFIDENTIAL INTERVIEW
Send resume to Mr. H. C. LAUR, Dept. N-14G
Missile Test Project
P. O. Box 1226
Melbourne, Florida
(cont'd from page 32)
Computers and Automation
Q
Digricoli, Vincent J I Appld Science Rep, IBM, Boston, Mass I ALMP I '29, Columbia Univ, '51, appld
science rep I 6
Dodge, Eldon C I Mathl Analyst, Lockheed Missi 1 e
Sys Div, 7701 Woodley Ave, Van Nuys, Calif IMP,
operations res I '19, UCLA, '54, mathn I 6t
Donaldson, R D Jr I Asst Comptroller, Raytheon Mfg
Co, 138 River St, Waltham 54, Mass I BMP I '02,
Harvard Business, '51, asst comptroller I 6t
Doy Ie, James H I Genl Mgr, Elecnc Di v, Weber Ai rcraft Corp, 2820 Ontario St, Burbank, Cal i f I
ACDEL I '28, St Mary's College, '54, -, Aviation
Age Atvard I 6t
Hopkins, Richard T I Numerical Analyst, Gener a 1
Electric Co, 920 Western Ave, Lynn, Mass I ABP I
'25, Burdett College, '55, - I 6t
Horne, John B I Spec, Material Control Prgmg, Power
Trans Dept, General Elec Co, - I - I -, Univ 0 f
Texas, - I 6
Horne, William J I Elecnc Acctng Sys Dir, Un i te d
Shoe Machinery Corp, 140 Federal St, Bos ton 7 ,
Mass I ABP I '20, Boston College, '49, acctn t,
economist I 6t
Horrell, Maurice W. / Gen Mgr, Bendix Computer Div
Bendix Aviation Corp, 5630 Arbor Vitae St., Los
Angeles 45, Calif / -, computer design [ mfr /
'12, Kansas S.C., '50, mgnt, co-author "Basic
Electronics" / 6
Hunter, George T I Educatnl Coordntr, IBM Corp,590
Madison Ave, N Y 22, N Y I A, education I '18,
Univ of Wisconsin, '50, - I 6t
Eumarian, Charles I Sr Engr, General Mills Inc ,
Mech Div, 2003 E Hennepin Ave, St Paul, Minn I
D I '24, Univ of Minn, '52, mech des engrg I 6t
.E
Fink, J L I Mgr, Military & Spec Des, G en era 1
Electric Co, 1200 Western Ave, Lynn, Mass I
,
pOlver systems I '26, Univ of Kansas, '53, engr I
6t
5i
Geiser, K.R. I Chm, Comm on Computers, Radio Electronics elevision Mfr's Assn, 11 W42 St, New
York 36, N Y. I -, industry standardization I
----/6
Gindoff: David G. I Partner, Gindoff & Swartz,
5858 Wilshire Blvd, Los Angeles 36, Calif I AB I
'16, UCLA, 1952, sys consltnt, Past Pres LA
Chapter Sys Procedures Assoc, Instr. Acctg Sys/6
Greenwood, Ivan A, Jr I Assoc Hd, Res Dept. Geaeral
Precision Lab, Inc, 63 Bedford Rd, Pleasantville,
N Y I AD, editor, patents I '21, Case Inst. of
Techn, '42, physicist I 6
Gumas, George 1 Analvtical Engr, CDC Control Services, 400 SWarm inster Rd, Hatboro, Pa I D I
'24, Cooper Union, '50, engr I 6
l.!
Handy, Benjamin F Jr I Math Engr, Lockheed Missile
Sys Div, Van Nuys, Calif I AP I '23, Mass Ins t
of Techn, '49, prgmr I 6t
Hause, w.1 Chm, Comm on Automation, Radio Electronics Television Mfr's Assn, 11 W. 42 St, New York
36, N.Y. I -, industry standardization 1-,-,-,/ 6
Healy, Thomas L / -, Hq Air Res & Devt Comd, Det#l
Wright-Pat terson AFB, Ohio I ABCDELMP / -, 10 w a
State College, '54, Capt USAF I 6t
Heckert, Robert E I Res Engr, Hughes Aircraft Co,
Culver City, Califl EL I '23, Univ of Mich, USC,
'54, elecnc engr / 6
Heller, Jack I Res Assoc, NYU, Inst of Mathl Sc ience, AEC Compr Facility, 25 Waverly' Place, N YI
AMP I '22, -, '52, - I 6
IIi 11 , Harold Carl I LCdr, USN, Bureau of Personnel
U.S.N., Washington 25, D.C. I ALP, personnel /
'12, -, '55, machine operations / 6
IIi tchings, John LILt Col, tSA, Ret, Oak Harbor,
Southport, Florida I ABCDELMPS I '97, Yale West
Point, '25, owner sailing resort I 6t
Jones, Lawrence G I Advistory Engr Chg Dig Com p r
Group, Westinghouse Elec Corp, Friendship Airport,
0 f
Bal timore 27, Md I CDELP / '20, Mass Ins t
Techn, '46, engr I 6t
Kagan, Claude R I Compr Meth Planner, Western Elec
Co, Latvrence, Mass I ABLP I '24, Cornell, '55,
engr I 6t
Kennedy, Jerome D I Sales Engr, Elecnc Assoc, Inc,
Long Branch, N J I AS I '29, Uni v of III i n 0 is,
'53, sales engr, publ on operational amplifiers
in Jour of ACM I 5r
Kinne, Clifton B I Proj Engr, Computer Control Co,
NAMTC, Point Mugu, Calif / CDE I '21, Worcester
Tech, '50, engr I 6
Kunkel, Cobern C. I Tech Asst, Machine Sys Analysis Div, Bureau of Personnel, USN, Washington 25,
D.C. I A-~ ,r I '28, - 'S4, accnt I 6
1
Levy, S.L. I Sub Comm on Computer Diodes (SemiConductor) Joint Electron Tube Engineering Council, 11 W. 42 St, New York 36, N.Y. / t.., industry standardization / -,-,-,-,1 6
Lewis, Edt\'ard M I Assoc Res Engr, Willotv Run Labs,
Univ of Michigan, Willol\' Run Airport, Ypsilanti,
Mich I ALP I '23, Univ of Mich, '52, Hd D a t a
Processing Group I 6
Light, E Jerry I Patent Attorney, Monroe Calculating Machine Co, Elecnc Div, POBox 352, Morris
Plains, N J I -, patents, elecnc dig data p r 0cessing, informn handling I '25, George Washington Univ, Columbia, '50, patent attorney I 6
Lucas, John H I Chief Res Engr, Powers Samas Accounting Machines, Aurelia Rd, Croydon, Surrey,
England / BE / '11, Univ College, London, '50,
elec engr, author I 6t
Marsh, Charles J Jr I Dir of Sales, Elecnc Assoc,
Inc, Long Branch, N J / ABDS / '17, Chi I Ion
College, '47, sales exec / 5t
Mc'..eod, John II, Jr I Res Gp Engr, Convair, San
Diego, Calif. / ADS, information processing I
'II, -, '50, engr, Assoc. Ed. "Instruments 0Automation" / 6r
(cont'd on page 3R)
- 34 -
M A NUS
We are interested in articles, papers,reference
information, science fiction, and discussion relating to computers and automation. To be considered for any particular issue, the manurer~t
should be in our hands by the fifth of the preceding month.
Articles. We desire to publish articles that are
factual, useful, understandable, andin~sting
to many kinds of people engaged in one part or another of the field of computers and automation.
In this audience are many people t\lho h a\e expert
knowledge of SOlE part of too field, but wOO are laylEn in other parts of it. Consequently at~iter
should seek to explain his subject, and show its
context and significance. He should define unfamiliar terms, or use them in a 1vaythatmakes
their meaning unmistakable. He should identify
unfamiliar persons td th a few t\'ords. He shruld
use exnmples, details, comparisons, analogies,
etc., whenever they may help readers to understand a difficult point. He should give data
supporting his argument and evidence for his
assertions. We look particularly for articles
that explore ideas in the field of computers
and automation, and their applications and implications. An article may certainly be contr~
versial if the subject is discussed reason abl:l'
Ordinarily, the length should be 1000 to 4000
words. A suggestion for an article should be
submitted to us before too much work is done.
c
R
I
P
T
S
and which at the same time is a good story. 0rdinarily, the length should be 1000 to 400)t\Urds.
Discussion. We desire to print in "Forum" briff
discussions, arguments, announcements, netvs,
letters, descriptions of remarkable netv developments, etc., anything likely to be of substantial interest to computer people.
In many cases, we make small token
payments for articles, papers, and fiction, if
the author wishes to be paid. The rate is ordinarily ~¢ a word, the maximum is $20, and
both depend on length in words, whether printed before. whether article or paper, etc.
'~ayments.
- ENJl -
~*---------------------*------------------~*
DIGITAL
ENGINEERS
for Long-Range Programs
Airborne Control Applications
Challenging assignments
with opportunity to carry
your ideas through to final
hardware and operational
flight testing in:
Technical Papers. Many of the foregoing requbements for articles do not necessarily apply to
technical papers. Undefined technical terms,
unfamiliar assumptions, mathematics, circuit
diagrams, etc., may be entirely appropriate.
Topics interesting probably to only a few
people are acceptable.
•
•
•
•
•
Reference Information. We desire to print or mprint reference information: lists, roste~ abstracts, bibliographies, etc., of use to computer people. We are interested in m a kin g
arrangements for systematic publication from
time to time of such information, with other
people bes ides our own staff. Anyone who would
like to take the responsibility for a type of
reference information should write us.
Computer Organization
Logical Design
Advanced Circuit Design
Laboratory Development
Packaging and Reliability
Salary -
up to $12000
(Commensurate with experience)
Send resume in confidence to:
Manager of Technical Personnel
Dept. 674
Division of
American Bosch Arma Corporation
Roosevelt Field, Garden City
Long Island, N. Y.
Fiction. We desire to print or reprint fiction
which explores' scientific ideas and possibilities about computing machinery, robots, cybernetics, automation, etc., and their implica~
- 35 -
A Confidential Reporting Service
on the Use and Application of
Electronic Data Processing Equipment
By John Diebold & Associates, Inc., Management Consultants
Gives you
1. EQUIPMENT REPORTS
Up-to-date and detailed descriptions,
analyses and appraisals of available
equipment.
2. METHODS REPORTS
Documenting the specific uses of
ADP Equipment in various
Industries.
3. POLICY REPOR;rS
Analyses of important Issues of
particular Interest to management.
<
..
..
....................
~
'. ····mt\~u~~ ~tyn~\
4. NEWSLmERS
Management digests of current
Interest~-
5. ORIENTATION MATERIAL
Explaining the use _and _oper~~
principles of the equipment to
management.
..
---
6. SPECIAL REPORTS & INDEX
-
..
... .........
Cudahy Publishing Company
8141 NORTH CICERO AVENUE. CHICAGO 30
*----------------------------------------------------
--------------------------------~~-------------.
ROBOT
SHOW STOPPERS
Did you see our story
Magazine, March 19, pp
Bryant
magnetic
in L if e
173-176 ?
drums
From time to time you may nee d t 0
help organize a display in a business
show including some device that you
hope \'lill "STOP" every pers 0 n attending the show and make him notice
your display - a device which may
be called a "SHOW-STOPPER".
In addition to publishing the magazine "COMPUTERS AND AUTOMATION", we
have for s i '\ years been developi ng
and constructing "ROBOT SHOW-STO PPERS". small robot machines th a t
respond to their environmen t a n d
behave by themselves.
lwo of them
are:
RELAY MOE: A machine that will play
the game Ti t-Tat-Toe tv!th a human
being. and either win or draw all
the time, or (depending 0 nth e
setting of a st'l1itch) will sometimes lose. so as to make the game
more interesting for the hum an
being (lvas at the I.R.E. Show, in
Guardian Eleetric's exhibiti see
picture in Life Magazine)i
SQUEE: An electronic robot squirrel that will hunt for a "nut"
indicated by a person in the
audience, pick it up in his
"hands", take the nut to his
"nest", there leave it and then.
hunt for more nuts (see picture
in Life Magazine);
Besides these we have other small
robots finished or under development.
These machines may be rented for
shows under certain conditions; also, modifications of the small robots to fit a particular purp 0 se
are often possible.
To: Uerkeley Enterprises Inc.,
815 Washington St.. IU66
Nett'tonville 60, Mass.
for semi·permanent storage of data in digital
computers or for use as delay lines
• Designed to purchaser's requirements
• Drum runout .00010" T.I.R. or less
• Air bearings or super-precision ball bearings
• Belt drive or integral motor drive
• Speeds to 100,000 RPM
• Capacities to 5,000,000 bits or more
• Vertical or horizontal housing
• Head mounting surfaces to suit
Please send us more informa ti 0 n
about your ROBOT SHOW STOPPERS. The
advertising appli_cation we have in
• High density magnetic oxide or electroplated
magnetic alloy coating
mind is : _ _ _ _ _ _ _ _ _ _ _ __
From:
(Organization)
(Address)
(Filled in by: Name, Title, Date)
Complete Information On Request- write:
BRYANT GAGE and SPINDLE DIVISION
P. O. Box 620-K, Springfield, Vermont, U.S.A.
DIVISION
- 37 -
OF BRYANT CHUCKING GRINDER CO.
Computers and Automation
(cont'd from page 34)
Miller, Gerald E / Dir. Machine Sys Analysis DiV,
Bureau of Personnel, USN, Washington 25, D.C. /
A I '19, US Naval Academy, Stanford U. '55
naval officer I 6
'
,
Miller, J P I Math Lecturer, Univ Mathematical Lab,
Cambridge, Corn Exchange St, Cambridge, Mass I
MP / '06, Trinity College, '28, uni v lecture r ,
Index Mathematical Tables, author, etc I 6
Mills, H. Jefferson, Jr I Mgnt Consltnt, Booz,
Allen :-, Hamilton, 1625 Eye St, N lV., Washington
25, D.C. I ABP I '26, Yale, '55, Mgnt consl tntl
6
Moss, James L I Trng G Educn, Machine Sys. Analysis Div, Bureau of Naval Personnel, USN, Washington 25, D.C. / A, personnel G training / '25
US Naval Acade~, Stanford U., '55, Lt, USN I (-
Walley, B. / West Coast Chm, Sub Comm. on Computer Tubes, Joint Electron Tube Engineering Council, 11 W. 42 St, New York 36, N.Y. I -, indust~y standardization I -,-,-,- I 6
Weiss, Eric A / Chrmn, Compr Comm, Sun Oil Co,I608
Walnut St, Phila, Pa I AB I '17, Lehigh Un iv,
'53, elec engr I 6t
tfuipple, Paul W/ Sr Sys. Analyst, Bureau of Naval Personnel, U.S.N., Washington 25, D.C. I A I
'15, Williamette Univ, American Univ, 855, sys/
~nalyst
Q
O'Connor, William H / Res Assoc, Willow Run Labs,
Univ of Michigan, Willow Run Airport, Ypsilanti,
Mich / ADE I '26, Univ of Mich, '55, elecnc erq:/6
Olander, William 0 / -, General Ceramics Cor p ,
Keasbey, N J I ACES I '24, Newark ColI e g e of
Engrs, '52, - / 6
O'Toole, John B I Proj Engr, Digital Compr Lab,
Philco Corp, 4700 Wissahickon Ave, Phila 44, Pa I
Uvi I '27, Univ of Pittsburgh, '55, logical des/6
I 6
Wilkins, J Ernest Jr / Div Dir, Nuclear Devt Cor p
of America, 5 Netv St, White Plains, N Y I MP I
'23, -, '51, mathn / 6t
Wilson, Verne H. I Computer Engr, Monroe Calculating Machine Co, E. Hanover Ave., Morris Plains,
N.J. / DLP I '30, Univ of Michigan, '51, logician / 6
Worley, Charles W/ Aplns Engr, Elecnc AssocCompn
Ctr, POBox 582, Princeton, N J / A / '25, ano
State Univ, '54, aplns engr, publns
Yeager, Robert LII Sales Engr, Elecnc Assoc lnc,
Long Branch, N J I AS / '28, The Johns Hopkins
Univ, '56, sales engr
END
Peck, Leslie G I Dir, Compg Lab, Arthur D Little,
Inc, 30 Memorial Drive, Cambridge, Mass I ABLMP/
'22, NYU, '50, consltnt, author various publns/6
*------------------- *-------------------
Ramo, Simon / Exec VP, Ramo-Wooldridge Corp, 5730
Arbor Vitae St, Los Angeles, Calif / -, general
/ '13, Calif Inst of Teehn, '40, engrg exec / 6t
FORUM
Schallerer, J W/ -, General Ceramics Corp, Kea&e~
N J I ADELS / '28, Amer TV, '52, elecnc engr I 6
Smdth, Phil I Consultant, Logistics Research, Inc,
141 S Pacific Ave, Redondo Beach, Calif / - I -,
EASTERN JOINT COMPUTER CONFERENCE,
DECEMBER, 1956, NEW YORK
Strong, John D / Aplns Engr, Elecnc Assoc CompnCtr,
POBox 582, Princeton, N J / ADE I '22, Univof
Calif, '52, elecnc engr, publns I 5r
Strong, Peter F / Staff Mbr, Arthur D Little, Inc,
30 Memorial Drive, Cambridge, Mass / ACDLMP /
'26# Harvard Univ, '48, operns res, des Mark IV/6
Swift, Charles J / Dsgn Specialist, General Dynamics Corp, 3700 Pacific Hpvay, San Diego, Calif
I MP I '18, Univ. of Penna, '51, dsgn / 6t
The 1956 Eastern Joint Computer Conference
has been set for Dec. 10, 11 and 12 at the Hotel
New Yorker in New York City. This year's annual meeting, jointly sponsored by the Institute
of Radio Engineers, American Institute of Electrical Engineers and the Assoc i a t ion for
Computing Machinery, will have as its theme,
"New Developments in Computers."
Unger, Louis WI Field Rep, Wiancko Engineering Co,
255 N Halstead Ave, Pasadena, Calif I - I -, -, -/6t
Utman, R E / Mgr Data Processing, Southern Calif
Div, Stanford Res Inst, 820 Mission St, S Pasadena, Calif I ABC DEUviPS, training, adminstrn /
'26, Pomona College, '51, sr elecnc sys engr /6
In addition to an extensive program of
technical papers, the meeting will dis pia y
exhibits by many manufacturers in the computing field. Registration fee at the Conferenoe
is $5 for members of any of the three sponsoring societies, $8 for non-members. Advanc e
registration, arranged to save regis tran t s
time and effort over registration at the Conference, is $4 for members, $7 for non-members.
All registrants !vill receive a free copy of the
Proceedings of the Computer Conference.
-, -, - I 6
Voelker, Stephen A / Mgr, Devt Engrg Sales, Elecnc
Assoc Inc, Long Branch, N J / S / '22, Cornell
Univ, '50, engr / 5
- 38 -
PATENTS
(cant'd from page 22)
P U 8 LIe A T ION S
P 34: LINEAR PROGRAMMING AND COMPUTERS. Reprint of two articles by Chandler Davis, in
July and Augus t 1955 "Computers and Automation".
A clear, well-written introduction to linea r
programming, with emphasis on the ideas.
•••• $1.20
P 2E: THE COMPUTER DIRECTORY, 1956. 104 pagesj
370 organization entries, 700 entries of Products and Services in the Computer Field, 220
entries of automatic computers,. e te.; ow~ l3O,ooo
words of condensed factual information about
the computer fieldi the June 1956 issue of
'Computers and Automation"
•••• $6.00
P 32: SYMBOLIC LOGIC, by LEWIS CARROLL. Reprint of "Symbolic Logic, Part. I, Elementary,"
4th edition, 1897, 240 pages, by Lewis Carroll
(C. L. Dodgson). Contains Lewis Carroll's inimitable and entertaining problems in symbolic
logic, his method of solution (now partly out
of date), and his sketches of Parts II and III,
which he never wrote since he died in 1898.
•••• $2.50
P 25:
MINDS.
like:
NUMBLES -- NUMBER PUZZLES FOR NIMBLE
Report. Contains collection of puzzles
TRY H A V E and T R A I N
FUN your WIT S
_TWVAS WASE
ENTNS
WYE = VIF
+ THE S E
In fact, you can also: 90893 85202 44393
29081 (Solve for the digits -- each letter
stands for just one digit 0 to 9).
All are new numbles, additions, multiplica tions, etc.j some easy, some hard. Each with
two messages, one open, one hidden. Hints for
solution. Good exercises in logical reasoning.
• ••• $1.00
Eugene Richard Shenk, Bergenfield, N. J.,
and Hajime James Kiski, Net\' York, N.Y. /
Radio Corp. of America, Del. / A reversible
electronic code translator circuit ar~ange
mente
2,744,959 / Johannes Anton Greefkes, Frank de
Jager, and Piet van Tilburg, Eindhoven,
Netherlands / Hartford National Bank and
Trust Co., Hartford, Conn. / A transmitter
for emitting in time-multiplex pulse code
modulation signals.
2,744,960 / Johannes Anton Greefkes and Piet
van Tilburg, Eindhoven, Netherlands / Hartford National Bank and Trust Co., Hartford,
Conn. / A time-multiplex pulse-code modulation signal transmission system.
2,744,961 / Johannes Josephus Alphonsus Peek,
Eindhoven, Netherlands / Hartford National
Bank and Trust Co., Hartford, Conn. / A
receiver for the simultaneous reception of
an incoming signal constituted by two distinct carriers having a predetermined frequency displacement.
2,745,004 / Yeo Pay Yu, Passaic, N. J. / Allen
B. Du Mont Lab., Inc., Clifton, N.J. / A
variable pulse delay circuit.
2,745,006 / Jeffrey C. Chu, Naperville, a nd
David H. Jacobsohn, Chicago, Ill. / An electric impulse binary counter.
2,745,024 / Robert G. Quick, West CalID\'ell,
N.J. / A sensitive time delay relay.
2,745,063 / Frank de Jager, Eindhoven, Netherlands / Hartford National Bank and Trust Co.,
Hartford, Conn. / A pulse code modulator.
2,745,064 / Christopher Edmund Gervase Bailey,
Bromma, Sweden, and David Harker Paul, Loughborough, England / Hartford National Bank
and Trust Co., Hartford, Conn. / A pulse code
modulation system.
2,745,095 / James V. Stoddard, St. Josephs,
N. Y. / A radiant energy control system for
missile guidance.
I enclose $
in full payment. (Add
10¢ per item to cover cost of handling and
mailing.) (If in good condition, returnable
in seven days for full refund.) My name and
address are attached.
May 15, 1956: 2,745,288 / Henry Konet, HOOokus,
and Charles E. Hurlburt, Teaneck, N. J. / A
servo sys tem.
2,745,599 / William Woods-Hill, Letchworth,
and David T. Davis, Wandsworth Common, London,
England / International Business Machines
Corp., New York, N.Y. / An electronic registering device for electronically s tor i n g
values in accordance with a chosen radix.
2,745,600 / Richard Y. Miner and Quentin J.
Evans, New York, and Clifford F. Abt, Long
Island City, N. Y. / American Bosch Arma
Corp., N.Y. / An electromechanical computing
apparatus.
2,745, 959 / Alfred R. Kilbey, Albuquerque, N.
Mexico, and George E. Tucker, Waltham, Mass. /
Raytheon Mfg. Co., Newton, Mass. / A trigger
cireui to.
2,745,963 / Alwin Hahnel, Little Silver, N.J./
A frequency multiplier.
2,745,972 / Jules Sandock, Hyattsville, Md./
Raytheon Manufacturing Co., Waltham, Mass. /
An electronic position and motion conorol system.
-END-
-END-
--------------MAIL THIS COUPON--------------or a copy of it
Edmund C. Berkeley and Associates,
815 Washington St., R 166
Newtonville 60, Mass.
Please send me publications circled and your
announcement of publications:
P2E
P25
P32
P34
- 39 -
COMPUTERS ANn <\(TTOMATION
RACK COPIES
REFERENCE INFORMATION: (with notes
fegarding latest issues containing same)
Organizations:
Roster of Organizations in the Computer Field (June, 1956)
Roster of Computing Services (June
1956)
Roster of Consulting Services (June
1956)
Computing Machinery and Automation:
TYpes of Automatic Computing Machinery (Dec ~ 1955)
Roster of Automatic Computers (June,
1956)
Outstanding Examples of Automation
(July 1954)
Commercial Automatic Computers (Dec.
1954)
TYpes of Components of Automatic Computing Machinery (March 1955)
Products and Services in the Computer
Field:
Products and Services for Sale or
Rent (June 1956)
Classes of Products and Services
(June 1956)
Words and Terms:
Glossary of Terms and EXpressions in
the Computer Field (Jan. 1956)
Information and Publications:
Books and Other Publications (many
issues)
New Patents (nearly every issue)
Roster of Magazines (Dec. 1955)
Titles and Abstracts of Papers Given
at Meetings (many issues)
People:
Who's Who in the Computer Field
(June, 1955, and later issues)
BACK COPY PRICES: If available, $1.25
each, except June 1955, $4.00, and
June 1956 $6.00 (the June issue is
the Computer Directory issue).
l
-------Mail this Request-----or a copy of It
To:
Berkeley Enterprises
815 Washington St., R166
Newtonville 60, Mass.
Please send me the following back
copies
I
I
I
I
II
I enclose $ _ _ _ in full payment.:
My name:
My address: ___________ :
Model ~I~ Digital Magnetic Tape Handler
The Ultimate in Digital Tape Handlers for High-Speed
Computers, Electronic Business Machines, Industrial
Control and Other EDP Applications.
-Regardless of cost, many features are exclusive with Potter
Speed and ease of operation;-Up to 75"/ sec in a variety of
dual speed combinations, with 3 msec starts and stops.
Tape widths from %" to 1 %" are accommodated. Automatic
threading, fast rewind, end-of-tape sensing, and front panel
or remote control provide unmatched flexibility and ease
of operation.
Standard 19" Rack Mounting-Hinged front panel provides
quick access to mechanical parts and plug-in electronic
components. Transparent dust cover protects tape and moving
parts without hindering visual observation of tape track.
Auxiliary Equipment-A complete line of digital data-handling
accessories is available, including record-playback heads
(Model 6400) in numerous channel number and tape width
combinations. Record-playback amplifiers can be furnished as
individual plug-in units (Models 52, 53) or in complete systems
(Model 920) for return-to-zero or non-return-to-zero recording.
Shift registers, high speed printers and other data-handling
components are available separately or in integrated systems
for solving specific data-processing problems.
WRITE FOR INFORMATIVE BULLETIN .•• and feel free to consult Potter
engineers on your data-handling problems. No obligation,
of course.
-----------------------------1
I
I
1
I
I
r
I
I
I
I
- 40 -
Just off press'
COMPUTERS
Their Operation
and Applications
by EDMUND C. BERKELEY
President, Berkeley Enterprises, Inc.
and LAWRENCE WAINWRIGHT
Consultant
c o
N
T
E
N
T
s
1. MACHINES THAT HANDLE INFORMATION
Computers; Types of Automatic Cbmputers
2. AUTOMATIC DIGITAL COMPUTING MACHINES
The Automatic Digital Computer
Storing Information and the Memory Unit
Calculating and the Arithmetic Unit
Programming and the Control Unit
The Input and Output Units
Reliability - Checking and Maintenance
The Advantages and Disadvantages of an Automatic Digital
Computer
A Checklist of Characteristics of an Automatic Digital Computer
366 pages
$8.00
Published May 24, 1956, by
Reinhold Publishing Corp., New York
Order your copy now from
Berkeley Enterprises, publishers of
"Computers and Automation"
815 Washington St., R166
Newtonville 60, Mass.
----------Mail this request or a copy of it----------Berkeley Enterprises, Inc.
815 Washington St., R l6~
Newtonville 60, Mass.
Please send me P 41: "Computers -- Their Operation and Applications" by Berkeley and Wainwright. I
enclose $8.00. (Returnable in seven days for full
refund if not satisfactory).
Name ______________________________________________
Address __________________________________________
3. AUTOMATIC ANALOG COMPUTING MACHINES
The Analog Principle and Its Use
The Essential Elements
A Simple Computer
Analog and Digital Computers Compared
Examples of Analog Computer Units
Examples of Analog Computers
Functional Considerations
Error Control
System and Supply Considerations
Future Prospects
4. OTHER TYPES OF AUTOMATIC COMPUTING MACHINES
Types of Automatic Computing Machines that are not Digital
Computers
The Components of Automatic Computing Machines
5. MINIATURE COMPUTERS, AND THEIR USE IN TRAINING
Training for Automatic Computers
Simon - Its History and Main Features
Simon - Numbers, Operations and Programming
How Simon is Constructed'
6. SOME LARGE-SCALE AUTOMATIC DIGITAL COMPUTERS
Univac
IBM Type 701, 702 and 705
ERA Type 1103
7. APPLICATIONS OF AUTOMATIC COMPUTING MACHINES
Whose Work Can Automatic Computers Do?
What People Will Buy Automatic Computers?
The Attitudes of Prospective Buyers Towards Automatic Computing
Machines
Applications of Automatic Computing Machines in Business
Military Applications of Analog Computers
Applications of Automatic Computing Machines in Other Fields
Recognizing Areas Where Automatic Computing Machines May
Apply
8. MISCELLANEOUS
References - Books and Other Sources of Information
Roster of Organizations Making Automatic Computers
Roster of Automatic Computing Services
Glossary of Terms and Expressions
ADVERTISING IN ~~COMPUTERS AND AUTOMATION"
:,
Memorandum fr()m' Berkel ey Enterpris'c's, Inc.
Publisher of CO~]PIJTERS. A'NO AUTO:\1ATION
815 Washin,gton St., Newtonville 60~". ~1ass.
,
1. What is "COMPUTERS AND AUTOMATION"? It is
a monthly magazine containing ~rticles, p~pers,
and reference information related to computing
machinery, robots, automatic control, cybernetics, automation, etc. One important piece of
reference information published is the "Ros t e r,
of Organizations in the Field of Computers and
Automation". the basic subscription rate is
$5.50 a year in the Uni ted States.' Sin g 1 'e
copies are $1.25, except June, 1955, "The Computer Directory" (164 pages, $ 4.00). For the
titles of articles and papers in recent issues
of the magazine, see the "Back Copies" page in
this issue.
2. What is the circulation? The circulation
includes 2300, subscribers (as of June 10): over
300 purchasers of ind'i vidual back copies; and
an estimated 3000 nonsubscribing readers. The
logical readers of COMPUTERS AND AUTOMATION
are people concerned wi th the field of computers
and automation. These include a great number
of people Ivho will make recommendations to their
organizations about purchasing computing machinery, similar machinery, and comp,onent s,
and whose decisioris may involve very substantial figures. The print order for the May
issue wa~ 2700 copies. The overrun is'largely
held for eventual sale as back copies, and in
the case of several issues the over ru n has
been exhausted through such sale.
,
copy that may be put under the ph ot 00 f f s e t
.:, camera wi thout further preparation. Unscreened
photographic prints and any other copy requirmg
addi tional preparation for photooffset s hou I d '
, be furnishe
!'l m
1
6
11
16
21
zen ."
m- rrI
~p :u
l!
~ ~ ~
0- ....
2
7
12
17
22
3
8
13
18
23
5 26 '1l 28 29 30 51 52 53 54 55 76 n 78 79 80 101 102 103 104 105 126 127 128 129 YJO
10 31 32 33 34 35 56 57 58 59 60 81 82 83 84 85 106 107 108 109 110 131 131. 133 134 133
15 36 37 38 39 40 61 62 63 64 65 86 87 88 89 90 111 112 113 114 115 136 137 138 139 140
20 41 42 43 44 45 66 67 68 69 70 91 92 93,9<4 95 116 117 118119 120 141 142 143 1« 145
2-4 25 46 J,7 48 49 50 71 72 73 74 75 96 97 98 99 100 121 122 123 124 125 146 147 148 1,(9 150
4
9
1.4
19
REMARKS:
-<
111111111111111 ; ~;~ :
1_ _ _ _ _ _ _ _ _ _ _ _ _ -
-
-
;
J ________ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- ---
Be sure the
rotary stepping switches
YOU use have this
"free-floating" pawl
Automatic Electric Rotary Stepping Switches
•Insure bind-free operation
Look at the pawl in the small illustration above. Automatic
Electric's Type 44 and 45 rotary stepping switches can't
bind. Automatic Electric has eliminated the old-style pawl
stop block that jammed the pawl and caused binding.
Instead, Automatic Electric uses a unique ufree-floating"
pawl, and a set of stopping teeth on the end of the armature. These teeth engage the ratchet wheel smoothly,
without jarring or jamming. They stop the wiper assembly positively, and position it exactly right on the
bank contacts.
Automatic Electric offers many exclusive advantages
over older type rotary stepping switches:
• Pawl breakage is eliminated
AUTOMATIC
• He-adjustment of armature stroke is never required
• T~ere's no possibility of pawl binding, even at very
low temperatures
• There's no possibility of double-stepping or overthrow
No wonder more and more design engineers are choosing Automatic Electric rotary stepping switches!
Plan now to use the Automatic Electric Type 44 or
Type 45 rotary stepping switch in your products.
For complete information, write for Circular 1698.
Address Automatic Electric Sales Corporation, 1033 West
Van Buren Street (HAymarket 1-4300), Chicago 7, Ill.
In Canada: Automatic Electric Sales (Canada) Ltd.,
Toronto. Offices in principal cities.
ELECTRIC
choose from this complete line of
NOW YOU CAN CHOOSE from eighteen sta ndard pulse transformers in four major
construction styles, all in quantity production at Sprague. The standard transformers
covered in the table below offer a complete range of characteristics for computer circuits,
blocking oscillator circuits, memory array driving circui ts, etc.
Thes.e hermetically sealed units will meet such stringent military specifications as
MIL-T-27, and operate at temperatures up to 85°C. Special designs are available for high
acceleration and high ambient temperature operation. In addition, the electrical counterparts of each transformer can be obtained in lower cost housings designed for typical
commercial environment requirements.
Complete information on this high-reliability pulse transformer line is provided in
Engineering Bulletin 502A, available on letterhead request to the Technical Literature
Section, Sprague Electric Company, 377 Marshall Street, North Adams; Massachusetts.
ELECTRICAL CHARACTERISTICS OF SPRAGUE PULSE TRANSFORMERS
Type
No.
Sprague, on request, will
provide you with complete
application engineering service for optimum results in the
use of pulse transformers.
Turn.
Ratio
Pul •• Width Rise Time
Po lecond.
Po second.
Repetition
Ra'.
0.1
0.04
200 I'H
51'H
0.Q7
0.03
200 I'H
2Ol'H
0.07
0.03
1251'H
121'H
0.07
0.03
16Ol'H
151'H
1 to 4
0.22
18 mH
1 to 7
0.25
55 mH
2.4
0.2
Typical
Applications
Used in digital
computer
circuitry for
impedance
matching and interstage coupling.
Pulses are of
sine wave type.
2.8 mH
SPRAGUE®~
Expor' lor the Americas: Sprague Electric International tiel., Nort'" Adams, Mon.
HPB-950B
Leakage
Inductance
CABLE: SPREXINT
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