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ABC - Computer
An Atanasoff - Berry - Computer Simulation

With a simulation program for the PC

as of Nov 26, 2014

Recent changes

Table of Contents

BACKGROUND:


First Electronic Computer (speed for scientific problems)
There were about six serious efforts in the ten year period (1935-1945) to use machinery to aid in solving scientific oriented computing. Here is a Mini History of the efforts.

The above mini-history history does not include commercial data processing problems, such as inventory, billing, payroll, ..., which were being handled by a group of companies, including the famous International Business Machines ( IBM ).

- - - - - - - - - - - - - - - - - - -

There is a viable claim that the "First Electronic Computer" (as in computing machine)

  • was conceived and designed by John V. Atanasoff
  • and constructed by Clifford Berry
  • at and funded by Iowa State College.
    • It also used the first "dynamic memory" - the principles used in your computer today, invented by Atanasoff.
    • First use of binary arithmetic, used in your computer today
    • First actually constructed parallel machine. (Babbage designed parallel into his second design for his polynomial evaluator (difference engine), but did not complete construction.
    • First SIMD ( Single Instruction Multiple Data ) machine. The pivot values determine whether add, subtract, shift right - will be performed on all data elements of the two vectors in the ABC memory drums.


First Scientific Problem on Electronic Computer
The "ABC" was an equation solving machine, constructed to find the variables of up to 29 simultaneous equations, and was successfully tested in 1942. It could not run Windows ;-)) nor do most other current computery things such as play games.

However - it was a "giant leap" in the quest for solving simultaneous linear equations.

Here is a simultaneous linear equation
        
x + 2y + 3z = 39
x + 3y + 2z = 34
3x + 2y + z = 26
Many high school students learn to "solve" this size problem, and by extension, larger number of equations with larger number of unknowns.
BUT It quickly becomes apparent that solving larger numbers of equations and unknows becomes very time consuming and error prone :-((

Level of Computational Effort in solving Simultaneous Equations
John Gustafson gives this approximation for the number of operations to solve n equations with n unknowns.
"For people who use operation counts to measure complexity, the solution of a linear system with n unknowns is
           (2/3) n^3 + 2 n^2
where a multiply and an add are each counted as one floating-point operation. There are also order n terms, usually ignored. You cannot avoid doing n divides somewhere along the way, for example."

number of
variables
(equations)
Approx.
operation
counts
3 36
5 133
10 866
20 6,133
29 17,942
    
click to enlarge
Many of us have enough trouble doing thirty six 5 digit multiplies (practical data precision) and adds with out a blunder :-((

More information on the First Electronic Computer

Documentation Needed
  • ABC Machine Operator's Manual - likely never written for the original machine - WWII called
    My (Ed Thelen's) start of an 'Operator's Manual'
    Charles Shorb's start of User Manual / Guide for the ABC in PDF.
    Probably useful to me to help tie things together. Should include
    • data (input card) preparation,
    • handling intermediate decks/arced_paper ?
    • Would the operator be responsible for selecting pivot points
    • Gauss-Jordan, or just use Gauss, or ??
    • preparation of final (report) from data from the machine
    (This Data Flow diagram (Feb 8, 2010) is based on John Gustafson's "ABC Instructions"
    - and needs checking by ABC folks)
    Operator's Panel, annotated

    image from Charles Shorb
    annotations from "http://www.scl.ameslab.gov/Projects/ABC/may98/May98.html" now defunct

  • Maintenance and Trouble Shooting Manual - likely never written for original machine - WWII called
    • I probably won't write one either ;-))
    • A place for documents and comments by the reconstructors ??
    • ?John Gustafson? mentioned using repeating ( ?5x5? ) problems to assure rather complete testing
    • ?Voltage margin testing
  • Acceptance Tests - likely never written for the original machine - WWII called
    • A complete simulation should pass these
    • Input test cases, and expected results for each,
    • probably no discussion of results/hour, uptime, ... ;-))
    • John Gustafson suggests simulating the worrysome data punching errors to estimating the largest practical array size -

Simulation Goal:
  • Use a PC and open source code to emulate and display most of the functionality of the ABC [ Computer }
    • Except the card "punch", card reader, and decimal conversion machinery
      - I/O is visible as decimal and binary.
      - Intermediate results, equation coefficients, are stored in PC memory not physical media.
    • Making the internal states and operations visible
    • Atanasoff used a variation of Gaussian Elimination, using kind of a "microcoded" division to form the correct ratios to permit coefficient elimination.
      (Determine the values of the variables.)
    • Showing the progress of the elimination of the variables in the succeeding stored equations.
  • I am using FREEBASIC with the "FBIDE" developer's interface, because I can paint an arbitrary pixel with an arbitrary color !! You would be surprised how few languages permit you do that. It gets compiled to machine code and runs fast :-))
  • Shows the Gaussian selection of equation pairs to load into the ABC, and a pivot point, for Gaussian elimination. You don't have to be a matrix whiz :-))
    - This provides a better reconstruction of operator activities. (The actual equation input, processing, and output are rather automatic after selection.)
  • Provide a section "Why are people interested in solving simultaneous equations?" Like why bother?
  • Provide the code and show the source of the compiler to help assure potential users that there are no virus present. The user can examine, compile, and run the source code.
    Posssibly provide a JAVASCRIPT version for safe running on your PC -
  • Just plain have fun ;-))

Graphical User's Interface
  • (Monitor must be at least 1280x1024, Tested on a PC running Windows XP)
    PLEASE NOTE & REMEMBER: click mouse on "EXIT" (middle of top line) or type "q" to quit the program.
    ABC-0V2-Sim10-03-21.exe - .exe file for images below - click to download and run (on a PC) - 106 KBytes
    ABC-0V2-Sim10-03-21.bas - source file for images below - 47 KBytes
  • This Graphical User Interface is at Alpha 1.0 release, Bit fields rotated 90 degrees from 0.1 release, card reading/writing vectors added.

    Images of monitor are about 150 KBytes

    Atanasoff used terminology similar to the desk calculators of the era because current terminology hadn't been developed yet - although he was the ?first? to use the now universal word "memory".
    • "Keyboard" (KA) is the equation being compared in this cycle, shifted in processing
    • "Counter" (CA) is the equation being modified for the elimination, modified
    - Carries, being of some interest, are also painted
  • The equations in the GUI (above) are selectable as "3x3, Integer", "5x5, Random", and "9x9, Random" with dynamic display of the bits, numeric changes and various eliminations of unknowns.

    The remark of "Atanasoff technique" refers to the method not requiring a formal multiply and the only divide is a shift right one bit, greatly simplifying the machine.


    3x3 done

    9x9 half

    9x9 done
  • Movies of the simulated ABC doing 15 seconds of a 9 unknown set of equations
    - ABC Speed, 1 rotation per second - .wmv file, 1.5 MBytes
    - Your Computer Speed, fast speed - .wmv file, 1.5 MBytes
    • I'm trying to make the display sexy, attractive, sparkle, ...
      "If I look at this, I can drive my convertible on the beach, and the girls will flock about"
      - you know those ads ;-))
    • As best I can figure, most folks know of simultaneous equations only as a topic to torment high school "math" students.
    • If folks have some clue why solving equations of more than say three unknowns, they might give a hoot. Solving for just one unknown is usually puzzling enough !! ;-))
    • Why would some guy in Iowa ( or anywhere for that matter ) want to solve for up to 29 unknowns?
      So your GPS receiver solves 4 simultaneous equations each second, GPS is magic anyway -
    • Your comments on the above are solicited - Send e-mail or (510) 742-1146

Pages from the Burks & Burks book - the best published technical reference
Six vital pages from
"The First Electronic Computer: The Atanasoff Story" (above)
are being made available courtesy of Alice R. Burks - each about 150 K Bytes

from cover

Page 25

Page 26

Page 27

Page 28

Page 29
Here is the basic scheme
Page 11

Page 12
and the vector elimination scheme
Page 269

From the school of hard knocks
  1. The algorithm on page 269 (above) has been simplified too much -
    There needs to be a check for the pivot CA being zero after the arithmetic, if zero, stop, go to next pivot.

  2. Many simple examples of integer simultaneous equations with known integer solutions give wildly incorrect results with Atanosoff's ratioing - unless scaled up by factors of say 10000.
    This link provides examples with exact and non-exact answers as run under Atanosoff rules.

  3. A further problem, somewhat alleviated by more scaling, is where the coefficients differ by several orders of magnitude. a small coefficient not on the pivot can get shifted right to become zero very early in the ratioing cycle - introducing further inaccuracies. It is easy to imagine that Atanosoff selected the large fixed point capability - 50 binary bits or about 15 decimal places to help fight the above problems.

  4. You may begin to appreciate floating point computations which (usually) eliminate the scaling problems noted above. We are so spoiled, and can work so much faster, and confidently, with much less concern about various overflows and underflows. I am so thankful -


If you have comments or suggestions, Send e-mail to Ed Thelen