Digi-Comp II Instruction Manual - Evil Mad Scientist

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INSTRUCTIONMANUALDIGI-CDMP JI MECHANICALBINARYDIGITALCOMPUTERIt ' s more fun than you thinkwhen you think for fun

TABLE OF CONTENTSForeword.Chapter 1Chapter 2Chapter 3Chapter 4Chapter 5Chapter 6Chapter 7Chapter 8Chapter 9Chapter 10Chapter 11Chapter 12Chapter 13Chapter 14PAGE. , . 1About your DIGI-COMP II. . . . . . . . . . . . . . . . . . . . . 2Checking out your DIGI·COMP II . . . . . . . . . . . . . . . . . . . . . . . . . . . 5New Operations Check List. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Binary Counting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10Binary to Decimal Number Conversion . . . . . . . . . . . . . . . . . . . . . . . 11Arithmetic Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Count & Clear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Addition & Multiplication. . . . . . . . . . . . . . . . . . . . . . .16Subtraction & Division. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17Compiler Language . . . DIGI-TRAN . . . . . . . . . . . . . . . . . . . . . . . .18DIGI-TRAN Commands . . . . . . . . . . . . . . . . . . : . . . . . . . . . . . . . . 18The Accumulator Register. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Speeding up DIGI-COMP II Operation . . . . . . . . . . . . . . . . . . . . . . . . 20More About Binary Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21The Octal System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Binary to Decimal Conversion Using Octal. . . . . . . . . . . . . . . . . . . . . 22Decimal to Binary Using Octal. . . . . . . . . . . . . . .22The MQ (Multiplier Quotient) Register. . . .23and The DistributorThe Memory Register and Addition. . . . . . .25Rules of Binary Addition. . . . . . . . . 28Multiplication of Binary Numbers. . . . . . . . . . .29Multiplying and Shifting. . . . . . . . . . . . . . . . . . . .30Multiply-Add Operation . , . . . . . . . . . . . . . . . . .31Converting Decimal Binary Automatically. . . . . . . . . . . . . . . .31Complement Arithmetic and Subtraction. . . . . . . . . . . . . . . . . .33Negative Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36Division of Binary Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . ' . 040How to Handle Remainders. . . . . . . . . . . . . . . . . . . . .41Binary Fractions. . . . . . . . . . . . . . . . . . . . . . . . . . . .43Summary of Information Necessary . . . . . . . . . . . . . . . . . . . . . . . . . .46to Operate DIGI-COMP IISpecial Problems and Applications for DIGI-COMP II . . . . . . . . . . . . . 49. .49Computing Areas. . . . . . . . . . . . . . . . . . . . . . . . . . . .Calculating the Weight of Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49The Principle of Archimedes . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49Iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50Summing Infinite Series. . . . . . . . . . . . . . . . . . . . . . . . 51The Population Explosion. ; . . . . . . . . . . . . . . . . . . 53Area of a Circle. . . . . . . . . . . . . . . . . . . . . . . . . . .54Random Number Generation. . . . . . . . . . . . .55. . . . . .56Simulation. . . . . . . . . . . . . .An Accounting Problem. . . . . . . . . . . . . . . .57Ballistic Missile Calculations. . . . . . . . . . .58Programs for Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60How to Program Your DIGI-COMP II . . . . . . . . . . . . . . . . . . . . . . . . . 63Problems on a Commercial ElectronicDigital ComputerDifferences between "DIGI-TRAN and FORTRAN". . . . . . . . . . . . . . . 63

eee FOREWORDIr--- ·eHOW TO USE THIS INSTRUCTION MANUALThere are, of course, many ways to use the material in this manual with yourDIGI-COMP II. After you have assembled DIGI-COMP II we suggest the followingpossibilities for starting out. Note the binary-decimal conversion table on yourProgrammers Card.I. BEGINNERSA. Read through Ch pter 1.B. Learn how to INITIALIZE your DIGI-COMP II using the NEW OPERATIONSCheck List in Chapter 2, Page 5.C. Work out the five TESTS in Chapter 2, from Page 6 to Page 8.D. Learn how to read your DIGI-COMP II in binary and decimal numbers inChapter 3.E. Learn how to COUNT, CLEAR, ADD, MULTIPLY, SUBTRACT andDIVIDE from Chapter 4.F. Learn to understand the COMPILER Language codes in Chapter 4.G. Review the OPERATING INFORMATION given in Chapter 12.H. Try to do Problems 1, 2, 3, 4, 5, and 13 of Chapter 13.1. You will then no longer be a beginner and can go back and afterreviewing Chapters 3 and 4, study the operation in more detail fromChapters 5 through 10. This should help you do problems 6, 7, 8, 9, 10,11, 12, 14, and 15.J. If you haven't already done so, try our DIGI-COMP I, and learn moreabout computer machine organization, and logic.II. INTERMEDIATEA.B.C.D.E.Go through Chapters 1, 2, 3 and 4 thoroughly.Review the rules for binary addition of Chapter 7, Page 26.Review the OPERATING INFORMATION of Chapter 12.Try a few problems of Chapter 13, perhaps 1, 2,3,4,5, 6, 7 and 13.Review Chapters 5 through 11 and try doing the rest of the problems ofChapter 13.F. Review Chapter 14 on electronic computer FORTRAN Language.G. TRY our DIGI-COMP I with its Advanced Manual.III. ADVANCEDA. Simply go right through the Manual from Chapter 1 through 14. Dorelated problems of Chapter 13 as mentioned above.B. Try our DIGI-COMP I with its Advanced Manual and you will havefairly covered most of the basic theory of organization and operation ofDigital Computers.- 1-

CHAPTER 1ABOUT YOURDIGI-COMP IIDIGI-COMP II is an educational computer which actually works in a manner analogousto an electronic digital computer. It performs a surprising number ( but ofcourse not all ) of the operations performed by the electronic computer, but in avisible and mechanical manner rather than electronically.As an educational device the primary purpose of DIGI-COMP II is toshow how a computer works in binary arithmetic by mechanical simulation. Toexplain how a computer works, considerable attention must be devoted toan understanding of the binary number system. The operation of a computer, itslogical design and many other important underlying concepts may bemuch better explained and understood by the aid of this mechanical model. Chiefamong the benefits of this approach is that no understanding of electroniccircuitry is demanded.The various operations that DIGI-COMP II performs are executed in slowmotion as compared with an electronic machine. Where the electronic computerrequires only a few millionths of a second to complete an operation,DIGI-COMP II requires a few seconds to complete the same task. Thus,the speed of the electronic computer has been reduced by a factorof a million to one. This enables the person operating DIGI-COMP II to comprehendwhat is happening as it occurs.Further, the programming of DIGI-COMP II will be developed using computerlanguages similar to those in use in electronic computers. You mayrecognize words like FORTRAN or COBOL as languages used in manycomputers. Because DIGI-COMP II is a real binary digital computer itslanguages will be of the same type but, of course, specialized for it.As a climax to this Instruction Manual, in Chapter 14 you will be shownhow to convert your DIGI-COMP II language to the IBM Computer FORTRANlanguage so that if you should have available an IBM computer of themodels stated, you will actually be able to insert simple problems into it with nofurther help required!!!All of the computer language words used in this Manual are summarizedand defined at the end of this Manual, and on your programmers card.In DIGI-COMP II an electronic current impulse is simulated by arolling ball. The ball rolls down an inclined surface under the force of gravityin an exposed manner. Thus, gravity provides the source of power forDIGI-COMP II rather than an electrical power supply. In the course of itsjourney the ball is directed by guides ( which simulate the wireswhich guide electrons in the electronic computer) to the entry pointsof successive binary digital logic elements. The ball upon entering a logic element"questions" or "interrogates" it for its "state" and possibly changesits "state" in the process of going through it.1 - 2-IX-o

The logic elements in DIGI-COMP II simulate "FLIP-FLOP" circuits in an electroniccomputer. These elements are simply pivoted levers which have twopossible positions. In entering the element from the top the ball is directedto exit along one of two possible paths according to the present settingof the element. The path of the ball out of the element is determined by the setting of the element and reveals the setting of the element. Thisis the sense in which the ball "interrogates" or questions the elementas to its prior state. The "state", of course, refers to its leftor right setting.Thus, a single ball in its trip from the INPUT GUIDE at the top of the exposed surfaceto the COLLECTOR GUIDE at the bottom may take anyone of many possiblepaths, questioning and changing the settings or states of thelogic elements in the process. If the desired operation is only partially completedby the ba 11 when it reaches the bottom it will be automatically directedto "gate" or trigger a successor ball from the top. This successor will in turntravel down the surface by a different path and gate still another successorball if required, which will behave in like manner, etc., until theentire operation is complete. The machine will then shut itself off by directing the last ball to by-pass the gating mechanism.The operation of DIGI-COMP II can be entirely automatic or manual.With appropriate settings your DIGI-COMP II can be made to:1. Count out a specified number of balls.2. Count in binary arithmetic.3. Add.4. Multiply.5. Multiply and add.6. Obtain either the "l's" or "2's" complement.7. Subtract.8. Divide.9. Zero or clear.10. Overflow.11. Halt. IXMoreover, all of these operations may be performed either in a "MANUAL" or an"AUTOMATIC" mode. In the AUTOMATIC mode only a single pull of theSTART switch is required to complete any of the operations enumerated,but in the MANUAL mode the START switch must be pulled oncefor each machine cycle. Thus, the MANUAL mode permits afurther slowing down of the machine for demonstration purposes if desired.Your DIGI-COMP II operates in the Binary Number System. Youwill learn much about this important base two numbering system whileusing DIGI-COMP II. Indeed, the manner in which virtually all electronic computerswork is intimately related to this binary or base two system.- 3-

enINPUT GUIDEMULTIPLY - - - - - - - -DISTRIBUTORMQ OR MULTIPUEIV'\.,\QUOTIENT REGISTER /02. ,(CONTAINS 100,/ \FOR MULTIPLY ORI011 FOR DIVIDE). 1\ \ I. I02I I.lo II 0I. I03II (Q. O. I§)l II '1.\)COUNT!' ""\)03 \ 01--'1"---- / /M11lI",'I . \::' I"CLEAR DrL ":' 'CF1 , ,ACCUMULATORREGISTER(CONTAINS 0000000)JY M2 00l- - - -A1'WEI\.O·,,,, ·) I T1 " / -A20J II ol. M3"-.II\":5 Dr -1I'O!'A3 :4:T2I\)"- O' T' -LT31"-.0I A4,l -1-:J(.-:0'\ ! ' T4MEMORY REGISTER(CONTAINS 1101)I A5 \y IT5A61 1 2: IT6IOVERFLOW - Idb\-h! I --- COMPLEMENT :2NOT:E :"""""""" REGISTERS ARE READ FROM BOTTOM TOTOP TO CORRESPOND TO READING THEBINARY NUMBER FROM LEFT TO RIGHT. '(Iraul I::II-- ·ICOLLECTOR GUIDE- 4-START

CHAPTER 2CHECKING OUT YOURDIGI-COMP IINow that you have assembled DIGI-COMP II let us identify its basic parts andtest them to be sure they operate properly.Figure 1 shows the top of the computer and identifies the three binarynumber "registers" by name. They are the "ACCUMULATOR"REGISTER, the "M-Q" REGISTER and the "MEMORY" REGISTER.These three registers are each comprised of a number of logic elements. One ofthe functions of these registers is to hold or "remember" binarynumbers used in calculations. All of the arithmetic performedby the computer occurs in either the ACCUMULATOR or theM-Q REGISTER. The MEMORY REGISTER "remembers" a number but thisnumber is not changed during the course of calculation.Each of these registers is comprised of binary "logic elements". A register may contain a number having as many binary digits, or "bits",as the REGISTER has logic elements. Specifically, theACCUMULATOR may contain any 7 bit number; the M-Q REGISTER any 3 bitnumber; and the MEMORY REGISTER any 4 bit number. Binary numbers will beexplained in more detail later by actually operating DIGI-COMP II andnoting what they represent.Before describing the use of the three REGISTERS, let us first check them out tosee if they are working properly.As with an electronic computer, if the machine is to know what we wantit to do, all of the switches must be set correctly. This is called"initializing" the computer. To help you remember how to do it, the followingcheck list has been developed. Also, the outline of each "switch"or "flip-flop" in its correct normal position has been printedon the face of your DIGI-COMP II.At the beginning of a new operation you will be instructed to, "INITIALIZE" thecomputer.This means to follow the instructions given in the "New OperationCheck List" below performing all the steps that need to be performed. Ifthe elements to be reset are already in their correct position then no changeneed be made, of course.NEW OPERATIONS CHECK LIST1. Be sure that Tl, T2, T3, T4, TS and T6 are to the left.2.3.4.Be sure that CFl is to the left and that CF2 is to the right.Set flip-flops Dl, D2, D3, in the DISTRIBUTOR to the right as shown in Figure LSet all the Control Switches to their "normal positions" according tothe following table ( Figure 1 also shows the control switches in theirnormal positions ).Normal Positions of Control Switches5.Switch NameSettingMULTIPLYCLEARCOUNTCOMPLE