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ELEMENTARY COMPUTER PROGRAMMING Lesson 1 Copyright 1990 Castle Oaks Computer Services Post Office Box 36082 Indianapolis, IN 46236-0082 COMPUTER ORGANIZATION Each model of computer usually differs from every other model in many of its details. However, all computers have the same general organization. This organization is shown in Figure I-1. +---------+ +<<<<<<| CONTROL |>>>>>>+ v +---------+ v v v ^ v v v v | v v +-------+ +--------+v +--------+ | INPUT |->| MEMORY |-->| OUTPUT | +-------+ +--------+v +--------+ | ^ v v | v +-----------------+ | ARITHMETIC UNIT | +-----------------+ Figure I-1 There are five major elements. They are: a. MEMORY - This may consist of several types of memories which may be programmed to transfer data and/or instruc- tions from one type (or part) of memory to another as required. The single headed arrows in the figure indicate the normal flow of information between the memory and the other elements, and the lines of multiple arrows indicate the flow of control signals from the control unit to the other units. b. CONTROL - This unit calls instructions from the memory, decodes them, and controls all other elements in order to perform the required actions. Note: The difference be- tween a computer and a calculator is that a computer is a calculator that can store its instructions in its own memory. c. ARITHMETIC UNIT - This unit performs the necessary arithmetical and data manipulation operations. d. INPUT(s) - This unit may be a console keyboard, floppy disk, hard disk, etc. There may be several of these. I-1 e. OUTPUT(s) - This unit may be a console screen, floppy disk, hard disk, printer, etc. There may be several of these. In most computers, the flow of data from input devices and to output devices is usually via the memory as shown in Figure I-1. A programmer working in a high level language, such as PASCAL, FORTRAN, BASIC, etc., need not know many of the details of the computer. However, the basic organization, as outlined above, is useful in organizing a problem for computer solution. In order to learn more about how computers operate, it is best to limit the discussion by presenting the details of only one model of computer. Once a person is familiar with the specifics of one particular model of computer, it is relatively easy to understand other models of computers, even more complex ones. Therefore, in this course, we will discuss a particular computer that is not very complex. The computer is called TRAC which is an acronym for TRAin- ing Computer. This computer does not exist in reality. However, we will use a simulation of this computer which runs on an IBM PC compatible computer. Using that simulator, we will execute TRAC programs as if they were running on a real TRAC. In the next les- son, we will cover the material you need to know to execute a TRAC program. In this lesson, we will cover the attributes of TRAC and how to program it in its own machine language. TRAC has the same general hardware configuration as other computers. Some of the specifics are shown in Figure I-2. +----------------------+ | CONTROL | +<<<<<| (P register is 4 |>>>>>>>>>>>>>+ v | decimal digits, I | v v +<| register is 7 digits |>>>>>>>>>+ v v v +----------------------+ v v v v v ^ v_ v v v v | / | v v_ v v | / | v / | v +----------------------+ __/ | v / | v | MEMORY |-->|Console| v __/ | v | 2000 decimal words | +-------+ v |Console|-->| Each word is 9 | +-------+ v +-------+ v | digits plus sign |-->|Printer|<+ v +----------------------+ +-------+ v | ^ v | | v v | v +----------------------+ +>| ARITHMETIC UNIT | |(Accumulator is 9 | | digits plus sign)| +----------------------+ Figure I-2 I-2 The specifics for each of the five categories of elements is as follows: a. MEMORY - The memory consists of 2000 words whose ad- dresses range from 0000 to 1999. Any other addresses, if used, will cause unpredictable results (including the possibility of "locking up" the PC). Each word is 9 decimal digits (plus sign) in length. A word may contain either a numeric value or an instruction. b. CONTROL - The control unit calls instructions from memory, decodes them, and controls all other elements to perform the required actions. The control unit contains a 4 decimal digit register called the P register which contains the memory address of the current instruction. The value in the P register is called the "location" of the instruction. Normally after each instruction is executed, the P register automatically increments by one. Therefore, consecutive instructions usually reside in consecutive memory locations. (In the discussion of the instruction repertoire, means for altering the sequence of instructions will be discussed.) The control unit also contains a 7 decimal digit register called the I register which contains the current instruction. The I register consists of three parts as illustrated in Figure I-3. +-+-+-+-+-+-+-+ | | | | | | | | +-+-+-+-+-+-+-+ ^ ^ ^ ^ ^ ^ ^-^ ^-----^ ^ ^ ^ | | | T O A a p d g d c r o e d s e s Figure I-3 The first digit of the I register is called the "TAG" field and may contain any single decimal digit. Its use will be discussed under the subject "Index registers". For most instructions, this field will be blank or zero. The next two digits contain the operation code. This specifies the operation to be performed. Only certain operations are available. Each available operation will be discussed in the section on operations. Each operation requires an operand. That is, something to be operated on, to, or with. I-3 The last four digits of the I register contains the memory address of the operand. The operand field is also re- ferred to as the address field. It is usually the address of a memory location that contains a value to be operated on. In shift operations, this field gives the amount to shift rather than a memory address. In branch operations, this field gives an alternative memory location for chang- ing the sequence of instructions being performed. The address field will be explained more fully in the discus- sions of operations and index registers. c. ARITHMETIC UNIT - This unit consists of one 9 decimal digit (plus sign) register called the A register (or accumulator). It can perform the elementary operations of addition, subtraction, multiplication, and division. Other data manipulations can also be performed in the A register. These and the arithmetic operations will be discussed in the section on operations. d. INPUT - TRAC has only one input device. This device is the console keyboard and only numeric data may be entered. The specifics of the input data format will be discussed in the section on operations. e. OUTPUTS - TRAC has two output devices. One device is the console screen and the other is the printer. OPERATIONS For ALL instructions, the control unit fetches the contents of the memory location specified by the address field of the I register. On some operations, this value is needed but on others it is not needed. Since the given address (see note) is always accessed, it must always be a valid address. (Note: The address may be an effective address, see discussion of index registers.) The actions for each operation code is given in the following. For each operation, a two digit numeric operation code is given; and also, a two character mnemonic operation code is given in parenthe- ses. This is not required for machine language coding and can be ignored for the present. It will be referred to in Lessons 3 and 4. 00 (LD) LoaD the A register. This operation causes the operand (contents of the location specified by the address) to replace the contents of the A register. 01 (AD) ADd to the A register. Causes the operand to be added to the A register. The sum replaces the previous contents of the A register. (The programmer must use care to avoid causing an overflow. TRAC will permit an overflow but it will save only the least significant 9 digits and you will NOT get an error message.) I-4 02 (SU) SUbtract from the A register. Causes the operand to be subtracted from the A register. The difference replaces the previous contents of the A register. (The warning on over- flows applies to subtraction as well as addition.) 03 (ST) STore the contents of the A register. The contents of the A register is stored at the location specified by the address. The contents of the A register remain unchanged. 15 (MU) MUltiply the A register by the operand. The operand is the multiplier and the contents of the A register is the multi- plicand. The resulting product replaces the previous con- tents of the A register. Since the contents of the A regis- ter can not exceed 9 decimal digits, the sum of the digits in the multiplier and the multiplicand must not exceed 9. (e.g. If the multiplier is a 4 digit number, then the multi- plicand may not have more than 5 digits.) If this condition is not satisfied, an overflow will occur and no error mes- sage is given. An example program will be given later to demonstrate how to obtain a full 18 digit product from two 9 digit factors. 16 (DV) DiVide the A register by the operand. The operand is the divisor and the A register is the dividend. The quotient replaces the previous contents of the A register. Since this operation is division of one integer by another giving only the integral part of the quotient (no rounding), there can be no overflow as long as the divisor is non-zero. 24 (BN) Branch on Negative. The operand is the address itself. If the contents of the A register is negative, branch to the location specified by the operand to obtain the next in- struction. If the A register is zero or positive, obtain the next instruction from the next consecutive location. 25 (BZ) Branch on Zero. The operand is the address itself. If the contents of the A register is zero, branch to the location specified by the operand to obtain the next instruction. If the A register is non-zero, obtain the next instruction from the next consecutive location. 26 (BU) Branch Unconditionally. The operand is the address itself. Branch to the location specified by the operand to obtain the next instruction. 36 (SR) Shift Right. The operand is the value of the effective address. Shift the contents of the A register right the number of decimal places specified by the address. Digits shifted out of the right end of the A register are lost. The positions vacated at the left end of the A register are filled with zeroes. The sign of the A register is pre- served. Although right shifts of more than 9 places are permissible, they have no utility. I-5 37 (SL) Shift Left. The operand is the value of the effective address. Shift the contents of the A register left the number of decimal places specified by the address. Digits shifted out of the left end of the A register are lost. The positions vacated at the right end of the A register are filled with zeroes. 40 (RD) ReaD input data. This operation allows five values to be read from the console keyboard into five consecutive memory locations. The first value is read into the location speci- fied by the address field; the next four are read into the next four consecutive locations. The address must not exceed 1995. When the program encounters the read command, the console will display a '?' followed by a space and will wait for the manual entry of up to five values. The format for entering data values is almost free-form. Values are entered as whole numbers (preceded by a '-', if negative) and separated from each other by one or more spaces. Each value must not exceed 11 digits, including sign and spaces. The entering of values is terminated by pressing the "ENTER" key. You must enter at least one value, even if zero. 41 (PC) Print to Console. This operation causes up to five values to be displayed on the console screen. The five values are output from five consecutive memory locations beginning with the memory location specified by the effective address. The effective address cannot exceed 1995. 42 (PP) Print to printer. This operation is identical to the previ- ous print command but the output is sent to the printer. 50 (HT) HalT. This operation stops the execution of the program. ALL programs should be terminated with a halt command. The address has no meaning but it still must be a valid address. (Note: Any operation other than those given will give an error message, set the op code to 99, and continue.) INDEX REGISTERS TRAC has nine index registers. These registers are numbered 1 through 9 and are actually memory locations 0001 through 0009. If you use any of these as index registers, you normally would avoid their use for instructions or constants. The purpose of an index register is to provide a simple method of modifying an instruction. An index register is used by placing its number in the TAG field of the instruction to be modified. When the TAG field is non-zero, the contents of the specified index register is added to the address of the instruction to give a new address called the effective address. The effective address must always be a valid machine address. Thus, if index register 2 contains the value, 3, the instruction: +-+-+-+-+-+-+-+ |2|0|1|1|0|0|4| +-+-+-+-+-+-+-+ I-6 would cause the contents of the memory location 1007 (1004 plus 3) to be added to the A register. Or, in the case of the following shift operation: +-+-+-+-+-+-+-+ |2|3|6|0|0|0|1| +-+-+-+-+-+-+-+ the contents of the A register would be shifted right 4 (1 plus 3) places. EXAMPLE Convert an octal number (base 8) to decimal. The flow chart of Figure I-4 provides a method for converting an octal number to decimal. For those not familiar with numbers in bases other than 10, the following explanation is given. Suppose the number, 637 is given and it is identified as being in base 8. The position of a digit in the number specifies that that digit is to be multiplied by a power of the base (in this case 8) in order to give its actual value. In the example, the number represents 6 * 64 + 3 * 8 + 7. In decimal this would calculate to be 415. Note that no digit of the number can be as great as the base. Therefore, to convert a number from base 8, we must isolate each digit of the number, multi- ply it by the appropriate power of 8 and then sum the individual products. In the method illustrated, we first enter the octal number that is to be converted. Then we test to see if it is zero. If it is we stop the program. Next we determine if the number is positive or negative. If it is negative, we must temporarily make it positive for the conversion. Later we will change it back. Next we set an index register to 1 (this is for counting places) then we isolate the first (high order) digit and save it where the answer is developed. We then start a loop in which we multiply the partial answer by 8, isolate a digit, and add it to the partial result. The index is incremented and if it is less than 9, the loop is repeated. Otherwise, the sign is restored to the input value and the result and the answer are displayed. I-7 | v ---------- +----------->/ Read X / | --------- | | | v | / \ Equal +------+ | <X:0>------>| HALT | | \./ +------+ | | Not equal | v | +--------+ > / \ < +--------+ | | S = +1 |<---<X:0>--->| S = -1 | | +--------+ \./ | X = -X | | | +--------+ | v v | +------------------------+ | | I = 1 | | | Shift X right 8 places | | | Store result at Y | | +------------------------+ | | | v | +------------------------+ | | Y = Y * 8 | | +->| Shift X left I places | | | | Shift right 8 places | | | | Add to Y | | | +------------------------+ | | | | | v | | +-----------+ | | | I = I + 1 | | | +-----------+ | | | | | v | | < / \ | +------------<I:9> | \./ | | >= | v | +-----------+ | | X = S * X | | | Y = S * Y | | +-----------+ | | | v | -------------- +----------/ Display X,Y / -------------- Figure I-4 I-8 The code in Figure I-5 gives one way that the flow chart could be coded in TRAC. Some variations of this code are possible and may even be better. The example uses all the operations except divide and print to printer. Here are some additional features of the code that should be noted. The last line of a program must contain 9999 in the location field and the address of the first instruction of the program must appear in the address field. Columns 1 through 4 are to contain the location of an instruction (or constant). Column 5 must be blank. Columns 6 through 15 are used for entering a constant or an instruc- tion. These columns are used differently for constants than they are for instructions. Constants may be placed anyplace within these columns (no embedded blanks). Instructions must also leave columns 6, 7, and 8 blank. The tag field is column 9, columns 10 and 11 are for the operation code, and columns 12 through 15 are used for the operand field. Column 16 should be blank. Columns 17 through 80 may be used for comments. You are encouraged to include comments since it is very difficult to understand machine code without comments. These comments are ignored by TRAC. I-9 L O A O P D C E D R R 0010 401000 Put X into 1000 (Sets 1001 - 1004 to zero) 0011 001000 Load accumulator with X 0012 250048 If X is zero jump to halt instruction 0013 240017 If X is negative, skip next 3 instructions 0014 001501 Load +1 0015 031502 Store at S (sign) 0016 260022 Branch unconditionally around next 5 0017 001503 Load -1 0018 031502 Store at S 0019 001500 Load zero 0020 021000 Subtract X (This makes a negative X positive) 0021 031000 Store back at X 0022 001501 Load 1 0023 030002 I=1 using index register 2 0024 001000 Load X 0025 360008 Shift it right 8 0026 031001 Store at Y 0027 001001 Load Y (Note this is the start of a loop) 0028 151504 Multiply by 8 0029 031001 Store at Y 0030 001000 Load X 0031 2370000 Shift left by I (Contents of register 2) 0032 360008 Shift right 8 (This isolates an octal digit) 0033 011001 Add previous Y 0034 031001 Store back at Y 0035 000002 Load I 0036 011501 Add 1 0037 030002 Store at I 0038 021505 Subtract 9 to see if done 0039 240027 If negative repeat loop 0040 001000 Load X 0041 151502 Multiply by sign 0042 031000 Store at X 0043 001001 Load Y 0044 151502 Multiply by sign 0045 031001 Store at Y 0046 411000 Print X, Y 0047 260010 Branch back to start 0048 500000 Halt 1500 0 Zero 1501 1 One 1503 -1 Negative one 1504 8 Eight 1505 9 Nine 9999 10 End of code and starting location Figure I-5 I-10 The following flow chart is exercise 1. In this exercise, you are to read five values from your keyboard, sum them using an index register in a loop and then display the sum. The program will keep prompting you for values until you enter a zero in the first posi- tion. Code this problem now and enter it into a file. After com- pleting lesson 2 you should try running the program to see if it functions correctly. | v -------------------------------- +-->/ Read X(0),X(1),X(2),X(3),X(4) / | -------------------------------- | | | v | / \ | / \ = +------+ | <X(0):>--->| STOP | | \ 0/ +------+ | \./ | | Not = | v | +-------+ | | I = 0 | | | S = 0 | | +-------+ | | | v | +---------------+ | | S = S + A(I) |<--+ | +---------------+ | | | | | v | | +-----------+ | | | I = I + 1 | | | +-----------+ | | | | | v | | / \ < | | <I:5>---------+ | \./ | | >= | v | ---------- +--------------/ Print S / ---------- Exercise I-1 Note: When an expression such as I:4 appears inside a diamond, this means that I and 4 are to be compared (usually by finding I-4) and then testing and branching according to the conditions shown on the flow chart. I-11