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Paul E. Ceruzzi ( home page) has kindly granted permission to reproduce his book "Reckoners"on this web site ( www.ed-thelen.org ). A paper copy of the book was kindly loaned by Computer History Museum for this project.

Please recognize that optical character recognition is an imperfect operation, manual corrections are incomplete, and that differences exist between the original and this reproduction. My apologies - my OCR program does not adequately recognize special German characters.

Ed Thelen



Paul E. Ceruzzi

Library of Congress Cataloging in Publication Data

Ceruzzi, Paul E.

  (Contributions to the study of computer science, 
ISSN 0734-757X ; no. 1) 
  Bibliography: p. 
  Includes index. 
  1. Electronic digital computers-History. I. Title. 
II. Series. 
QA76.5.C4164   1983 621.3819'58'09   82-20980 
ISBN 0-313-23382-9 (lib. bdg.)

Copyright  1983 by Paul E. Ceruzzi

All rights reserved. No portion of this book may be
reproduced, by any process or technique, without the express
written consent of the publisher.

Library of Congress Catalog Card Number: 82-20980
ISBN: 0-313-23382-9
ISSN: 0734-757X

First published in 1983

Greenwood Press
A division of Congressional Information Service, Inc.
88 Post Road West
Westport, Connecticut 06881

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1


. Illustrations vii
. Tables ix
. Preface xi
1. Background 3
2. Computers in Germany 10
3. Bessie-The Automatic Sequence Controlled Calculator 43
4. Number, Please-Computers at Bell Labs 73
5. Faster, Faster: The ENIAC 104
6. To the First Generation 131
7. The Revolution? 149
. GLOSSARY A: Translations and Equivalents of German Terms 153
. GLOSSARY B: Technical Terms Used in the Text 155
. APPENDIX: Program Listings 159
. Selected Bibliography 167
. Index 177


Konrad Zuse and Helmut Shreyer at Work in Zuse's Parents' Apartment, Berlin 20
The Reconstructed Z3 at the German Museum, Munich 32
The IBM ASCC at Harvard 50
Complex Number Computer, One of the Three Terminals 90
The ENIAC 114

2.1 Graphical Representation of 2 (ab + cd) 12
2.2 Automatic Placement of Numbers 13
2.3 Sketch of the Basic Functional Elements of a General-Purpose Computer, c. 1936 15
2.4 Binary Memory Device 19
2.5 The Conditional Combinatoric 22
2.6 Mechanical Implementation of an "and" Statement 25
2.7 Basic Vacuum Tube Switching Circuit 27
2.8 Bistable Switching Circuit 27
2.9 Display and Keyboard of Z3 33
3.1 Sketch of a Decimal Wheel for the Mark I 53
4.1 Using Multiple Key Contacts to Encode Decimal Digits 82
4.2 Keyboard Layout of the Complex Number Computer 85
4.3 Block Diagram of the Complex Number Computer 88
5.1 Sketch of a Decade Counter 113
5.2 One of the ENIAC's Accumulators 115
5.3 Timing Pulses in the ENIAC 118


2.1 The Z3 34
3.1 The IBM ASCC 58
4.1 The Bell Labs Model I 86
4.2 Bell Labs Models II through V 95
5.1 The ENIAC 123
6.1 Types of Computer Architectures 141

Reckoners, Preface, page 0001


Human agents will be referred to as "operators" to distinguish them from
"computers" (machines).
-George Stibitz, 1945

The modern digital computer was invented between 1935 and 1945. That was the decade when the first machines that could be called true digital computers were put together. This book tells the story of that invention by looking at specific events of the 1930's and 1940's that show the computer taking its modern form.

Before 1935 there were machines that could perform calculations or otherwise manipulate information, but they were neither automatic nor general in capabilities. They were not computers. In the 1930's the word computer meant a human being who calculated with the aid of a calculating machine. After 1945 the word meant a machine which did that. From that time on computers have continued to evolve and improve, becoming dramatically cheaper and smaller, but their de- sign has not really changed. So the story of what happened in that ten-year period will reveal quite a bit of the entire history of the computer as it is known today.

I have chosen four projects from that era that best illustrate how the computer was invented. These are by no means all that happened, but they are representative of the kinds of activities going on.

The first is the set of electromechanical computers built in Germany by Konrad Zuse, who because of the war had no knowledge of similar activities in America and England. His independent line of work makes for an interesting and self- contained case study of just how one goes about building a computer from scratch.

The second is the Harvard Mark I, built by Professor Howard Aiken and first shown to the public in 1944. This machine was one of the first truly large-scale projects, and because it was well publicized it served notice to the world that the computer age had dawned.
Reckoners, Preface, page 0002

The third project is the series of relay computers built by George Stibitz of the Bell Telephone Laboratories between 1939 and 1946. These machines represented the best that could be done with electromechanical devices (telephone relays), and as such mark the end of that phase of invention and the beginning of another.

The final project is the ENIAC, the world's first working electronic numerical computer, using vacuum tubes for its computing elements, and operating at the speed of light. With its completion in late 1945 all of the pieces of the modern computer were present:
automatic control,
internal storage of information,
and very high speed.

What remained to be done after 1945 was to put those pieces together in a practical and coherent way. From the experience of building and using those machines there came a notion of what a computer ought to look like. The old definition of a computer gave way to the modern one: a machine capable of manipulating and storing many types of information at high speeds and in a general and flexible way. How this notion came about, and especially why the notion of storing the computer's program of instructions in the same internal memory as its data gained favor, are also examined.

This book has a dual purpose. The first is to recount the history of the computer, emphasizing the crucial decade between 1935 and 1945 but including earlier events and more recent trends as well. The second is to explain in simple terms the fundamentals of how those computers worked. Computing has certainly changed since 1945, but the basic concepts have not; I feel that it is easier to grasp these concepts as they were present in earlier, slower, and much simpler computers. I have included brief explanations of some of these concepts in the text of the book; a glossary at the end gives short definitions of many terms of modern computing jargon.

That the computer is having a profound effect on modern life is hardly at issue. Just how and why such a profound change in our society is happening because of computers can better be understood with a grasp of how this technology emerged.

I wish to thank the following persons and institutions for their help with the researching and writing of this book: the Society for Mathematics and Data Processing, Bonn; the Charles Babbage Institute, Minneapolis; the Linda Hall Library, Kansas City, Mo.; the Baker Library, Dartmouth College; and Professors Jerry Stannard, Walter Sedelow, and Forrest Berghom of the University of Kansas. Konrad Zuse, Helmut Schreyer, and George Stibitz supplied me with personal archival materials and criticized portions of the manuscript. I also wish to thank Bill Aspray, Gwen Bell, and Nancy Stern, who also read portions of the manuscript and gave me helpful advice. Any errors or statements of opinion are of course my own.

Reckoners, Background, page 0003


All the other wonderful inventions of the human brain sink pretty nearly into commonplaces contrasted with this awful mechanical miracle. Telephones, locomotives, cotton-gins, sewing-machines, Babbage calculators, Jacquard looms, perfecting presses, all mere toys, simplicities!
-Mark Twain, 1889

Computers have appeared so rapidly on the modern scene that it is hard to imagine that they have any history at all. Yet they do, and it is a most interesting history indeed. The computer has been around now for at least thirty years, maybe more. But there was a much longer period of activity before its invention when important preliminary steps were taken-a period of the computer's "pre- history." It is much more than just the story of specific machines and what they did, although that is at the center of this study. It is also a part of the history of mathematics and science-of the story of how mankind acquired a perception of quantities, and of the long, slow acquisition of the ability to code and manipulate quantities in symbolic form.

The history of computing, if not the history of the digital computer, could begin at the dawn of civilization, when people first sought to measure and keep track of surpluses of food, the management of which freed them from the anxiety of daily survival. The first mechanical aid to calculation was probably a device like the modern abacus, on which numerical quantities were represented by the positions of pebbles or beads on a slab. (The modern version, with its beads strung on wires, has been around at least a thousand years and is still in common use in many parts of the world.)

Or one could begin the history of the computer with Blaise Pascal, who in 1642 built a mechanical adding machine that performed addition automatically. (Like the abacus, it too survives-the cheap plastic totalizer sold in supermarkets to keep track of a grocery bill works the same way.)

Reckoners, Background, page 0004

But the computer is something more than just a sophisticated adding machine, even though at the heart of every computer is something like Pascal's automatic adder. The computer is a system of interconnected machines which operate together in a coherent way. Only one of those pieces actually does arithmetic. A computer not only calculates: it also remembers what it has just calculated, and it automatically knows what to do with the results of those calculations.

And numbers are not the only kind of information a computer can handle. Letters and words can be coded into numbers and thus made grist for the computer's mill; the same holds true for photographs, drawings, maps, graphs: any information which can be symbolically represented. A computer is a machine which is capable of physically representing coded information (numbers, words, or whatever) and which is further capable of manipulating those values in any combination or sequence one desires. Numerical calculation is of course one form of symbol manipulation, but it is by no means the only one.

By this definition, the history of the computer really begins sometime after 1935, when machines with such general and automatic capabilities first appeared. It is that emergent period of their history-beginning around 1935 and ending about ten years later-that this book examines.

The invention of the computer was the result of a convergence of a number of different social, technical, and mathematical traditions.1 Some of those traditions are external: the increasing need by governments for statistical information, for example, brought on in the United States by political developments such as the Progressive Era and the New Deal. Other traditions are more internal to the computer: they are literally present as components of the machine itself.

The tradition of mechanizing arithmetic has already been mentioned: its legacy may be found in the "central processor" of any modern computer. The tradition of building devices that control a sequence of mechanical motions can be traced back to medieval cathedral clocks, where mechanical cams directed an elaborate sequence of movements at the striking of every hour. (The cuckoo clock is a much simplified version; one of the most elaborate examples is the cathedral clock at Strasbourg, France.) An electronic version of that mechanism, too, is present in a modern computer.

A computer directs a sequence of activities, senses what it has already done, and modifies its future course of action accordingly. That kind of intelligence has its roots in medieval devices such as windmills which automatically adjusted the pitch of their vanes to adapt to the prevailing winds.2 Another example of such a device is the fly-ball speed governor that James Watt attached to his steam engine, turning that machine into a reliable source of steady power.

Finally, there is a long tradition of techniques that record information; certainly the invention of writing itself, and of printing with movable type in the 15th century in Europe are part of it. The idea of using holes punched in pieces of cardboard to represent and manipulate data was first successfully employed by Herman Hollerith for the 1890 United States Census. (Punched cards had earlier been used in the silk weaving industry to control the pattern made by a loom, but that belongs more to the tradition of automatic control than to that of data storage.) Punched cards are still the backbone of modern data storage, although much faster electronic devices are used in a computer's main store. More modern storage techniques have appeared which may displace the punched card entirely; for example, the use of bar-codes to identify items in a supermarket.

Reckoners, Background, page 0005

Each of those traditions forms a separate block that goes to make up a computer. They are revealed whenever a computer is described by a block diagram that groups its functions together. But each tradition developed separately from the others, with a few exceptions-until the 1930's, when they merged and continued on as one.

Despite the general capabilities of computers, their immediate ancestors were machines that performed arithmetic. But their enormous impact on modem life is due less to their numerical abilities than to their ability to sort and handle large amounts of data, and to their ability to direct their actions intelligently. Nevertheless they bear the legacy of their "calculating" ancestry. The word itself reveals that legacy: before 1935 a "computer" often meant a human being who evaluated algebraic expressions with the aid of a calculating machine. That person (who was often a woman-the job of "computing" was thought of much like typing) would be given a mathematical expression-say a formula that evaluated the solution of a differential equation-plus the numerical values that were plugged into that formula. Depending on the "computer's" prior mathematical training, the instructions given to him or her to evaluate the expression would be more or less detailed.

These workers had the use of mechanical calculators which performed addition, subtraction, multiplication, and division to an accuracy of eight to ten decimal digits. (These machines are still in common use, as are adding machines that only add or subtract.) The calculators were driven by turning a crank or by a small electric motor, but all arithmetic done in them was mechanical. The person had one other important aid to computation: a pencil and sheets of paper, on which intermediate results were written down for use later on. With only a few exceptions, the mechanical calculators could not store intermediate results.

Taken together, the person, the calculator, the pencil and "scratch" paper, and the list of instructions formed a system which could solve a wide range of numerical problems, as long as the solutions to those problems could be specified as a series of elementary steps. That human and mechanical system was precisely what the first digital computers replaced.3

By 1945 the definition of the word computer had changed to reflect this invention: a computer was no longer a human being but a machine that solved computing problems. The definition of calculator remained unchanged: a device which could perform the four ordinary arithmetic operations, working with no more than two numbers at a time. (The modern definitions are in the same spirit but a little different; see Glossary B.)

Reckoners, Background, page 0006

After 1945 the evolution of computing technology followed a single line to the present. With the end of the Second World War the many computer projects that were in progress around the world became known and were publicized to varying degrees. Conference reports and other written descriptions of the first computers became templates for computer designs thereafter.4 The ideas and writings of one man, John von Neumann, were especially influential, so much so that even today computers are said to have a "von Neumann type" architecture.

So after 1945 there was a more common understanding of the nature of this new invention, what it could do, and what overall structure ("architecture") it should have. There was still little agreement on what its components should be, especially for its memory, but by 1950 it was clear that a computer had to be made of high-speed electronic components (such as vacuum tubes), and it should be organized into functional units that performed the operations of storage, arithmetic, input, and output. Since 1950 those decisions have not changed, even though the components that make up a computer have. So the analogy of a person working with a desk calculator and some scratch paper still holds true, although everything has gotten much more complicated at every stage.

In the following chapters I have chosen four case studies of computer projects undertaken between 1935 and 1945 which I feel best illustrate the emergence of the new technology. These case studies by no means exhaust the subject, but the details encountered represent the major issues well.

The first project examined was one of the first to be completed. It was surprisingly not in England, where Charles Babbage had proposed building an Analytical Engine a century before, nor was it in the United States, where sophisticated calculating and punched card equipment was being extensively used, but rather in Germany, where the story may be said to have really begun. Konrad Zuse, an engineering student at the Technical College in Berlin, began looking for ways to ease the drudgery of calculations required for his coursework--drudgery which the slide rule and the desk calculator could not relieve. Zuse was not well versed in the calculating-machines technology of his day (which may have been a blessing), but by the end of the war in 1945 he had not only designed and built several working automatic computing machines, but he had also laid the foundations for a theory of computing that would independently emerge in America and Britain a decade later. Zuse's electromechanical devices were the first that could be programmed to do sequences of calculations, so they will be examined first.

In America, a similar idea occurred to a Harvard physics instructor named Howard Aiken, who had faced long and tedious calculations for his graduate thesis. The result was a computing machine that used the components of standard punched card equipment that the IBM Corporation had developed. Aiken's "Mark I" was the first large computing device to be made public (in 1944), and as such its name is appropriate-it marks the beginning of the computer age, despite the fact that it used mechanical components and a design that soon would become obsolete.

The third example is the work of Dr. George Stibitz and his colleagues at the Bell Telephone Laboratories in New York, where a series of computers was built out of telephone relays, as were Zuse's machines. These machines, too, would soon become obsolete, but their design and the programming done on them contributed much to the mainstream that followed.

Reckoners, Background, page 0007

Finally I look at the ENIAC: the first computer that could carry out, automatically, sequences of arithmetic operations at electronic speeds. It was completed in late 1945, and from that time onward the age not only of computing but also of high-speed electronic computing had begun.

For each of the machines examined in the next four chapters I hope to establish the following data:
  1. how the machine was conceived, designed, and constructed;
  2. how it was programmed and operated; and
  3. to what practical use, if any, it was put.
(Actually, for all the experimental computers of that day the design specifications were never really "frozen" for long. Someone was always improving and modifying them. I have tried to establish those vital statistics for the machines when they first began solving mathematical problems.)

Where it has been feasible, and in the Appendix, I have included sample programs. The reader who is unfamiliar with modern computer programming may follow these samples; the terms and details of each one are defined and explained as they are introduced. Several early programs have also been rewritten for a pocket programmable calculator, for the reader who wishes to get a better feel for just what the prehistoric computers could do.

The public dedication of the ENIAC in 1946 marked the dawn of the electronic computer age; actually it was more like the herald of the dawn. The ten years from 1935 to 1945 saw the convergence of various traditions to make the computer; the ten years following that saw both a continuation of the projects begun during the war, and an intensive study of the theory of computing itself not so much how to build a computer as how one ought to build a computer. This activity was made visible as conferences, reports, memorandums, lectures, and short courses in computing that were held throughout America and Europe. John von Neumann was one central figure; others who contributed to this phase of activity were D. R. Hartree, Alan Turing, and Maurice Wilkes in England; Howard Aiken and George Stibitz in America; and Konrad Zuse, Eduard Stiefel, and Alwin Walther in continental Europe, to mention only a few.

What they accomplished can be summed up in a few words: the computer, as before, was seen as a device that did sequences of calculations automatically, but more than that, it was seen as not being restricted to numerical operations. Problems such as sorting and retrieving non-numeric information would be just as appropriate and in fact, from a theoretical standpoint, even more fundamental to computing than numerical problems.

Second, the realized that the instructions that told a computer what to do at each step of a computation should be kept internally in its memory alongside the data for that computation. Both would be kept in a memory giving access to any data or instructions at as high a speed as possible. This criterion allowed the execution of steps at speeds that matched those of the arithmetic unit of the machine, but it also allowed for more than that. The data and the instructions were stored alongside one another because they were not really different entities, an it would be artificial to keep them separate. An understanding of that startling fact, when implemented, made the computer not just a machine that "computed" but one which also "reckoned"--it made decisions and learned from its previous experiences. It became a machine could think, at least in a way that many human beings had defined thinking.

Reckoners, Background, page 0008

It was the adoption and recognition of this stored-program concept that would make the computer's impact on society so strong in later years. That recognition was slow in coming- the principle is even today not full understood. How it emerged, and how it was eventually incorporated into the design of computers after 1950, is the subject of Chapter 6. As with the other chapters, I discuss the stored-program concept and its implications in layman's terms.

In presenting the history of the digital computer in the years of its birth I have several goals in mind. One goal concerns the state of the art today. The fact that computers have such an impact on daily life today should lead us to understand more of their nature and what gives them their power. But for someone unfamiliar with the engineering and mathematical concepts, that task can be difficult, if not impossible. Looking at the history of the computer offers a way out of that bind. The men and women whom we shall encounter on the following pages knew nothing of "computer science" when they began their work--such a science did not exist then. They created computer science, out of their diverse backgrounds and from their experiences in trying to build machines which later generations would call "milestones." By retracing some of their steps, we can learn something of the foundations of modern computer science, for it was then that the foundation was laid.

Another goal, closely related, is to try and get a fresh outlook on the computing world today. It is a crazy world: a mixture of wild speculation, careful theoretical research, technological breakthroughs every few months, fortunes made (or lost) overnight. We frequently hear that these machines are smarter than we are, and sooner or later they will "take over" (whatever that means). Can a computer really think? Indeed, does it even make sense to ask a question like that? And with twenty-five dollar computer games that speak, with computer programs that make accurate medical diagnoses (and with others that only pretend to be psychoanalysts), it is hard to find a good vantage point from which to survey the field and get an overall view.

By looking not at those computer programs that dazzle us today, but rather at simpler ones that did more routine problems on the earliest machines, we can get such a view. We shall be examining the computer before it got so complex that, in Alan Turing's memorable words, "I suppose, when it gets to that stage, we shan't know how it does it."5

Today we often hear the command that we must learn about computers if we want to keep up with the pace of modern society. We hear further that computers are bringing us a technological Utopia (at last!), but if we do not learn about them, all we can do is forlornly press our noses against the window looking in; we may never enter. I have always felt uncomfortable with that scenario--I do not like to be coerced into doing something I otherwise might never have thought of doing. Nor do I feel that learning about computers is absolutely necessary to manage in the world today. Humans can get by without them, just as many live comfortable lives without telephones or automobiles. Why not learn about computers because they are inherently interesting, and because it is fun to see what makes them tick? They are, after all, "only" creations of ordinary human beings. And learning about them can tell us something about how we tick, as well. And that should not threaten or intimidate anyone.

Reckoners, Background, page 0009


  1. Thomas M. Smith, "Some Perspectives on the Early History of Computers," in Perspectives on the Computer Revolution, ed. Zenon W. Pylyshyn (Englewood Cliffs, N.J.: Prentice-Hall, 1970), pp. 7-15.

  2. Otto Mayr, The Origins of Feedback Control (Cambridge, Mass.: MIT Press, 1970).

  3. George R. Stibitz, "Relay Computers," Report 171.18, U.S. National Defense Research Committee, Applied Mathematics Panel, Feb. 1945, p. 2.

  4. See, for example, Arthur Burks, Herman Goldstine, and John von Neumann, "Preliminary Report on the Design of an Automatic Computing Machine," in John von Neumann, Collected Works, vol. 5 (New York: Macmillan, 1963), pp. 34-79; there were also several conferences held at Philadelphia, Harvard, and Cambridge, England, just after the dedication of the ENIAC.

  5. Sara Turing, Alan Turing (Cambridge, England: W. Heffer and Sons, 1956), p. 98.

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