Educational Software Cooperative 4

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ELEMENTARY COMPUTER PROGRAMMING Lesson 2 Copyright 1990 Castle Oaks Computer Services Post Office Box 36082 Indianapolis, IN 46236-0082 TRAC, the hypothetical computer introduced in lesson 1, can be simulated on an IBM PC compatible computer. (In fact, it can be simulated on any MS-DOS computer even if it is not fully IBM PC compatible.) Therefore, it is possible to execute TRAC programs in order to gain a familiarity with coding in machine language. In this lesson, the information needed to actually execute a TRAC program will be given. First, the problem must be coded according to the rules of the language and the format given in Lesson 1. After coding the problem on paper, then it must be entered into a disk file on the computer. This package does not provide the software necessary to do this, but you may use any suitable text editor or word processor in non-document mode. At Castle Oaks we usually use WORDSTAR (TM MicroPro International Corporation) in non-document mode, but there are several shareware text editors that would also be adequate. Any file name can be used for your file, but we recommend that the name have an extension of 'OBJ'. The files that you run with TRAC are called 'object' files and therefore it is desirable to identify them as such. In the following lessons we will discuss another type of file. The general command line format for running TRAC is: TRAC [object file] [trace file] The parameters in brackets are optional. If the first parameter is omitted, the program will prompt you for a file descriptor of the object file to be run. This file descriptor may include a drive letter and subdirectories, if required. If the second parameter is also omitted from the command line, the program will ask if you want the program traced; and, if so, will ask if you want it traced on the screen or to a file. If to a file, you will also be prompted for a file name. If the object file and the trace file are both given on the command line, the program will start to execute without any queries. The purpose of tracing a program is to trouble shoot it in case it does not function correctly. It is a good idea to trace the exercises so you can analyze what is happening at each step in order to gain a fuller understanding of the process. When trac- ing a program, each instruction is displayed in the following format: II-1 LLLL T OO AAAA SVVVVVVVVV SAAAAAAAAA Where LLLL is the location of the instruction; T is the TAG; OO is the operation code; AAAA is the effective address of the operand; SVVVVVVVVV is the value of the operand; and SAAAAAAAAA is the current value in the accumulator. Note that the resulting value of an operation does not appear in the accumulator until the following line is printed. If you trace your program on the screen, it may print too fast for you to analyze. You may pause the display at any time by pressing ^S (control-S) or you may send the screen display to the printer by pressing ^P (control-P) before starting your program. If you send it to a file, later you may either view it on the screen or you can send it to the printer. It is suggested that when you name a trace file that you give it an extension of 'LST' which will help you identify it as a file to list. Figure II-1 is the source code of a simple program to illustrate the execution and tracing of a program. This program reads in two numbers, finds their sum and difference and prints out the numbers, and the results to the screen. ----------------------------------------------------------------- 0010 400100 Read X, Y into 100 and 101 0011 000100 Load X 0012 010101 Add Y 0013 030102 Store sum at 102 0014 410100 Print 100, 101, 102, (also 103 and 104) 0015 000100 Load X 0016 020101 Subtract Y 0017 030102 Store difference at 102 0018 410100 Print 100, 101, 102, (also 103 and 104) 0019 500000 Halt 9999 000010 Start program at 10 Figure II-1 ----------------------------------------------------------------- Figure II-2 shows what appears on the screen when this program is executed. II-2 ----------------------------------------------------------------- A:\TRAC TRAining Computer (TRAC) Version 1.0 Copyright 1990 CASTLE OAKS COMPUTER SERVICES Post Office Box 36082 Indianapolis, IN 46236-0082 What is the name of your object code file? FIGII-1.OBJ Do you want to trace the program? (Y or N) Y Do you want to trace it on screen (S) or on file (F)? S 10 0 40 100 0 0 ? 123456789 876543210 11 0 0 100 123456789 0 12 0 1 101 876543210 123456789 13 0 3 102 0 999999999 14 0 41 100 123456789 0 123456789 876543210 999999999 0 0 15 0 0 100 123456789 999999999 16 0 2 101 876543210 123456789 17 0 3 102 999999999 -753086421 18 0 41 100 123456789 -753086421 123456789 876543210 -753086421 0 0 19 0 50 0 0 -753086421 Figure II-2 ----------------------------------------------------------------- If the program is run with the object file named on the command line and with no tracing, the resultant screen display will be as shown in Figure II-3. ----------------------------------------------------------------- A:\TRAC FIGII-1.OBJ TRAining Computer (TRAC) Version 1.0 Copyright 1990 CASTLE OAKS COMPUTER SERVICES Post Office Box 36082 Indianapolis, IN 46236-0082 Do you want to trace the program? (Y or N) N ? 123456789 876543210 123456789 876543210 999999999 0 0 123456789 876543210 -753086421 0 0 Figure II-3 ----------------------------------------------------------------- Note: Locations 103 and 104 print zero because zero was entered into them implicitly during the read. Note also that TRAC first clears all memory locations to zero before loading and executing the program. Do not count on other computers doing this. II-3 Note that in Figure II-2 the trace printout and the program were both intermixed on the screen. This may be desirable or it may be undesirable. If you do not want them together, you can send the trace printout to a file and view it later; or you may send your program output to the printer while tracing on the screen. The remainder of this lesson will be devoted to showing some other examples. The coding and tracing of these examples also will be given. The following Figure gives a flow chart for finding the factorial of a number. A factorial is the product of all integers up to and including the given number. Thus factorial 3 is 1*2*3=6; factorial 4 is 1*2*3*4=24; etc. ----------------------------------------------------------------- | v --------- / Read N /<------------------+ --------- | | | v | / \ <= +------+ | <N:0>----->| STOP | | \ / +------+ | +------------------+ | > ^ | Note: N>12 is | v | | not allowed | / \ | | since the result | / \ >= | | would exceed the | - - <N:13 >---------+ | capacity of the | \ / | A register. | \./ | +------------------+ | < | v | +-------+ | | F = 1 | | | K = 2 | | +-------+ | | | v | +-------+ / \ > ------------ | | F=F*K |-><K:N>----->/ Print N,F /--+ | K=K+1 | \ / ------------ +-------+ | ^ | <= +--------+ Figure II-4 ----------------------------------------------------------------- Figure II-5 gives the coding for the flow chart of Figure II-4. Note: In a flow chart, a diamond shaped box is used to indicate a decision point. An expression such as K:N in a diamond means to compare K and N (usually by subtraction) and then taking the appropriate path based on the symbols shown. II-4 ----------------------------------------------------------------- 0010 401901 Read value for N 0011 001901 Load N into A 0012 240016 If negative go to stop 0013 250016 If zero go to stop 0014 021801 Subtract 13 0015 240017 If negative skip around stop 0016 500000 Stop 0017 001802 Load 1 0018 031902 Store at F 0019 001803 Load 2 0020 031804 Store at K 0021 021901 Subtract N 0022 240026 Jump, if negative, to update F 0023 250026 Jump, if zero, to update F 0024 411901 Print 0025 260010 Branch back to beginning 0026 001902 Load F 0027 151804 Multiply by K 0028 031902 Store at F 0029 001804 Load K 0030 011802 Add 1 0031 031804 Store at K 0032 260021 Branch to test if done 1801 13 Constant 13 1802 1 Constant 1 1803 2 Constant 2 9999 000010 End of code Figure II-5 ----------------------------------------------------------------- There are a few features of this program that should be noted. Almost any location can be picked to receive the value of N. In this case, 1901 was chosen. Constants can go almost anyplace. In this case, 1801, 1802, and 1803 were used for constants. F could have been stored almost anyplace; but looking ahead, it was noted that it was to be printed along with N. Therefore, at print time they need to be in consecutive locations. Since N is already in 1901 and 1902 was not used, it is logical to assign 1902 for F. At location 0021 we have the beginning of a loop. Since location 0021 can be entered two ways, once from 0020 and later from 0032, we must be careful about what is in the accumulator at the begin- ning of this loop. Normally we would load the accumulator at the beginning of the loop. But by careful planning we see that we can have K already in the accumulator when we enter from either direction. This saves the load instruction. Figure II-6 shows what would appear on the screen if the program is traced and the values 3 and 13 are entered for N. II-5 A:\TRAC FIGII-5 TRAining Computer (TRAC) Version 1.0 Copyright 1990 CASTLE OAKS COMPUTER SERVICES Post Office Box 36082 Indianapolis, IN 46236-0082 Do you want to trace the program? (Y or N) y Do you want to trace it on screen (S) or on file (F)? s 10 0 40 1901 0 0 ? 3 11 0 0 1901 3 1 12 0 24 16 500000 3 13 0 25 16 500000 3 14 0 2 1801 13 3 15 0 24 17 1802 -10 17 0 0 1802 1 -10 18 0 3 1902 2 1 19 0 0 1803 2 1 20 0 3 1804 3 2 21 0 2 1901 3 2 22 0 24 26 1902 -1 26 0 0 1902 1 -1 27 0 15 1804 2 1 28 0 3 1902 1 2 29 0 0 1804 2 2 30 0 1 1802 1 2 31 0 3 1804 2 3 32 0 26 21 21901 3 21 0 2 1901 3 3 22 0 24 26 1902 0 23 0 25 26 1902 0 26 0 0 1902 2 0 27 0 15 1804 3 2 28 0 3 1902 2 6 29 0 0 1804 3 6 30 0 1 1802 1 3 31 0 3 1804 3 4 32 0 26 21 21901 4 21 0 2 1901 3 4 22 0 24 26 1902 1 23 0 25 26 1902 1 24 0 41 1901 3 1 3 6 0 0 0 25 0 26 10 401901 1 10 0 40 1901 3 1 ? 13 11 0 0 1901 13 1 12 0 24 16 500000 13 13 0 25 16 500000 13 14 0 2 1801 13 13 15 0 24 17 1802 0 16 0 50 0 0 0 Figure II-6 II-6 Another simple problem is shown in Figure II-7. In this program we will raise a number, X, to any positive power, N. We cannot do a negative power since that would result in a fraction. Therefore, we will use a negative N to terminate execution of the program. ----------------------------------------------------------------- | v ----------- / Read N,X /<-----------------+ ----------- | | | v | +-------+ | | F = 1 | | | K = N | | +-------+ | +------->| | | v | +-------+ > / \ = -------------- | | F=F*X |<-<K:0>--->/ Print N,X,F /--+ | K=K-1 | \ / -------------- +-------+ | < | v +------+ | STOP | +------+ Figure II-7 ----------------------------------------------------------------- The coding is shown in Figure II-8. ----------------------------------------------------------------- 1001 400011 Read N, X into 11, 12 1002 001501 Load A with a 1 1003 030013 Store F at 13 1004 000011 Load N into A 1005 031502 Store at K 1006 241017 Jump to stop instruction 1007 251015 Jump to print 1008 000013 Load F 1009 150012 Multiply by X 1010 030013 Store at F 1011 001502 Load K 1012 021501 Subtract 1 1013 031502 Store at K 1014 261006 Go back to start of loop 1015 410011 Print N, X, F 1016 261001 Jump to beginning of program 1017 500000 Stop the program 1501 1 Constant 1 9999 001001 End of code Figure II-8 ----------------------------------------------------------------- II-7 Figure II-9 shows some sample results of the program as they would appear on the screen. ----------------------------------------------------------------- A:\>TRAC FIGII-8.OBJ TRAining Computer (TRAC) Version 1.0 Copyright 1990 CASTLE OAKS COMPUTER SERVICES Post Office Box 36082 Indianapolis, IN 46236-0082 Do you want to trace the program? (Y or N) n ? 10 2 10 2 1024 0 0 ? 10 4 10 4 1048576 0 0 ? 3 1234 3 1234 879080904 0 0 ? -1 A:\> Figure II-9 ----------------------------------------------------------------- In this program there is no simple way to determine that the answer will exceed the capacity of the A register. Therefore there is a possibility of having an overflow. That happened in the case of raising 1234 to the 3rd power. The correct answer is 1879080904. Each of the example programs are included in the package. The ones associated with this lesson are FIGII-1.OBJ, FIGII-5.OBJ, and FIGII-8.OBJ. You should run each of these and experiment with various inputs, tracing, etc. before trying one of your own programs. When you are comfortable with how to execute and trace a program then you might experiment with the above programs such as chang- ing from printing to the screen to printing to the printer. You should try executing your Exercise I-1 now. Then you should code and execute exercise II-1. The flow chart for this exercise appears on the next page. In this program, you are to enter 10 values (done in two reads and the second read should use locations that immediately follow those of the first read.) The program will do a "minimum-in- pass" sort and the sorted array is printed. It will be necessary to use two index registers. II-8 | v -------------------------------- / Read A(0),A(1),A(2),A(3),A(4) / -------------------------------- | v -------------------------------- / Read A(5),A(6),A(7),A(8),A(9) / -------------------------------- | v +-----+ | J=0 | +-----+ | v +---------+ | S=A(J) |<-------------+ | I=J+1 | | +---------+ | | | v | / \ | / \ >= | +----><A(I) >------+ | | \ :S/ | | | \ / | | | | < | | | v | | | +---------+ | | | | T=S | | | | | S=A(I) | | | +-------+ | | A(I)=T | | | | STOP | | +---------+ | | +-------+ | | | | ^ | v | | | | +-------+ | | ------------------------- | | I=I+1 |<----+ | / Print / | +-------+ | /A(5),A(6),A(7),A(8),A(9)/ | | | ------------------------- | v | ^ | / \ | | | < / \ | ------------------------- +-----<I:10 > | / Print / \ / | /A(0),A(1),A(2),A(3),A(4)/ \./ | ------------------------- | >= | ^ v < | | +-------+ +-------+ / \ >= | | A(J)=S|->| J=J+1 |-><J:9>-----------+ +-------+ +-------+ \./ Exercise II-1 II-9 Here (Figure II-10) is a method of multiplying two 9-digit numbers to obtain an 18-digit product as promised earlier. The factors are each divided into three 3-digit groups. Then individual products are found and summed with proper attention to overflow digits. See the comments for more detail. Try tracing this program (on disk as DOUBLMPY.OBJ) using the factors 999888777 and 666555444. These factors will help illustrate the isolation of the groups and how the product is reassembled. Note that if the lower part of the product has leading zeroes, TRAC does not print them. A shorter program for doing this multiply could probably be devised but this method was chosen because of its symmetry. If it is known that the product will contain fewer than 18 digits, the program could be modified so fewer steps would be required. 0010 401000 Read A and B 0050 151503 Times Z 0011 001000 Load A 0051 031507 V*Z --> T 0012 360006 Isolate high 3 0052 001506 Load W 0013 031501 Store as X 0053 151502 Times Y 0014 001000 Load A 0054 011507 Plus V*Z 0015 370003 Isolate 0055 011003 Plus LOWER 0016 360006 middle 3 0056 031003 V*Z+W*Y+???000 0017 031502 Store as Y 0057 001506 Load W 0018 001000 Load A 0058 151503 Times Z 0019 370006 Isolate 0059 031507 W*Z --> T 0020 360006 low 3 0060 360003 Isolate high 3 0021 031503 Store as Z 0061 011003 Plus LOWER 0022 001001 Load B 0062 031003 Save at LOWER 0023 360006 Isolate high 3 0063 360006 Isolate carry 0024 031504 Store as U 0064 031508 Save at CARRY 0025 001001 Load B 0065 001003 Load LOWER 0026 370003 Isolate 0066 370003 Shift off carry 0027 360006 middle 3 0067 031003 Save at LOWER 0028 031505 Store as V 0068 001507 Load W*Z 0029 001001 Load B 0069 370006 Isolate 0030 370006 Isolate 0070 360006 low 3 0031 360006 low 3 0071 011003 Plus LOWER 0032 031506 Store as W 0072 031003 Save at LOWER 0033 151501 Times X 0073 001504 Load U 0034 031507 X*W --> T 0074 151502 Times Y 0035 001505 Load V 0075 031507 U*Y --> T 0036 151502 Times Y 0076 001505 Load V 0037 011507 Plus X*W 0077 151501 Times X 0038 031507 X*W+V*Y --> T 0078 011507 Plus U*Y 0039 001504 Load U 0079 011002 Plus UPPER 0040 151503 Times Z 0080 011508 Plus CARRY 0041 011507 Plus X*W+V*Y 0081 031002 Save at UPPER 0042 031507 X*W+V*Y+U*Z --> T 0082 001504 Load U 0043 360003 Isolate high 3 or 4 0083 151501 Times X 0044 031002 Save in UPPER 0084 370003 Position U*X 0045 001507 Load X*W+V*Y+U*Z 0085 011002 Plus UPPER 0046 370006 Isolate 0086 031002 Save at UPPER 0047 360003 low 3 0087 411000 Print A,B,Product 0048 031003 Save in LOWER 0088 500000 Halt 0049 001505 Load V 9999 000010 Figure II-10 II-10