(PC1211) Base Conversion

03242021, 03:44 PM
(This post was last modified: 03242021 03:47 PM by SlideRule.)
Post: #1




(PC1211) Base Conversion
An excerpt from Science and Engineering Sourcebook, pgs 2324:
Any Base to Any Base Conversion Description Converting numbers between different bases is frequently done by computer programmers, amthematicians, high school and college students. In particular, computer program development requires conversion between binary (2), octal (8), decimal (10) and hexadecimal (16) bases. Number tjeory problems may require conversion between these and other bases. Conversion between two arbitrary bases a and b is generally a two step procedure, converting first from base a to base 10 and then from base 10 to base b. The unique method presented here for positive integers uses the same algorithm for both conversions, thus saving on programming steps. To represent a number to base larger than 10, more than one place is necessary to represent one digit in that base. For example 17FE (base 16) would be entered or displayed as <01>, <07>, <15>, <14> or simply 1071514 (1=01, 2=02, …, A=10, B=11, C=12, D=13, E=14, F=15). In general, one place would be reserved per digit for bases 210, two places for bases 11100, etc. The program automatically interprets the entry or display depending on the base. The program has no inherent limitations on the magnitude of the base or the number to be converted. The only limiting factor is the computer's accuracy. For example the 10 digit accuracy of the Pocket Computer limits the input and output to 10 decimal places. A larger number would lead to error. PROGRAM LISTING 90: "Z"CLEAR : PAUSE "BASE CONVERSION" 100: INPUT "ARGUMENT?";C: F=C: G=110: GOTO 290 110: INPUT "OLD BASE?";D: F=D: G=120: GOTO 290 120: INPUT "NEW BASE?";E: F=E: G=130: GOTO 290 130: IF D<>10 GOTO 150 140: N=C: GOTO 170 150: U=D: GOSUB 280 160: S=C: Q=D: R=V: GOSUB 240 170: IF E<>10 GOTO 190 180: S=N: GOTO 210 190: U=E: GOSUB 280 200: S=N: Q=V: R=E: GOSUB 240 210: BEEP 1: USING "###########" 220: PAUSE C;" BASE";USING "####";D: PRINT USING "###########";"=";N;" BASE"; USING "####;E 230: PRINT USING "###########";"=";S;" BASE 10": GOTO 100 240: M=0: N=0: P=S 250: T=P: P=INT (P/R): N=N+INT ((TP*R)*Q^M+.5) 260: IF P=0 RETURN 270: M=M+1: GOTO 250 280: V=10^(1+INT LOG (U1)): RETURN 290: IF F=INT ABS F GOTO G 300: G=G10: BEEP 2: PAUSE "BAD INPUT": GOTO G INSTRUCTION Press Shift Z to start the program. Follow the prompts by entering the number to be converted (argument) the old and new base. You can optionally display the argument to base 10 after seeing the argument to the new base by pressing Enter after display of the result. For proper display, change the output format by adding additional "#" if one of the bases is larger than 999. EXAMPLE Convert 17C (base 16) to base 2. KEYIN DISPLAY REMARKS Shift Z BASE CONVERSION ARGUMENT? 17C(hex)=10712 10712 Ent OLD BASE? 16 Ent NEW BASE? Beeps when ready 2 Ent 10712 BASE 16 =101111100 BASE 2 Ent =380 BASE 10 Optional step Ent Prompt for a new case BEST! SlideRule 

03242021, 03:57 PM
Post: #2




RE: (PC1211) Base Conversion
(03242021 03:44 PM)SlideRule Wrote: An excerpt from Science and Engineering Sourcebook, pgs 2324: On some machines you can convert from base 2, 8 or 16 to base 10 by doing this: VAL("&B"+"11011011") VAL("&O"+"7413") VAL("&H"+"CF1A") and back PRINT BIN$(74) PRINT OCT$(912) PRINT HEX$(65521) Tom L Cui bono? 

03242021, 08:57 PM
Post: #3




RE: (PC1211) Base Conversion
Entering the Hex digits as 2 digit base10 pairs is an interesting way to get around the lack of string functions. I had considered an alternative of entering the digits as characters one by one and having 16 IF statements to convert them to their actual values, but this is much faster  at the cost of having to manually convert AF in your head when entering the numbers.
Thanks! 

03242021, 09:44 PM
Post: #4




RE: (PC1211) Base Conversion
(03242021 08:57 PM)pyedog Wrote: Entering the Hex digits as 2 digit base10 pairs is an interesting way to get around the lack of string functions. That was always the typical way to do it if you look at base conversion programs for the HP 65, 67, 15C, TI59, etc. Not surprising to see the tradition carried on here before decent string handling was available. 

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