The Museum of HP Calculators

# HP-20S: Boolean Logic

Copyleft (C) 2003 Glen Kilpatrick

This program is supplied without representation or warranty of any kind. The author and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

## Description

The HP-20S is wonderful for offering base conversions to and from HEXadecimal, OCTal, and BINary. To quote from HP-20S Scientific Calculator Owner's Manual (Edition 6, Part Number 00020-90001, pages 47 and 49):

### Representation of Numbers

The internal representation of a number does not change when a number is converted to another base. When a number is converted from its decimal value to a different base, the integer part of the num- ber is represented as a 36-bit binary number.

In Hexadecimal, Octal, and Binary modes, numbers are displayed in 2's complement format. The left-most bit of the binary representation of a number is the sign bit. It is set to 1 for negative numbers.

### Range of Hexadecimal, Octal, and Binary Numbers

The 36-bit word size determines the range of numbers that can be represented in hexadecimal, octal, or binary base, and the range of decimal numbers that can be converted to other bases.

### Arithmetic Operations

All functions are active in all bases (except nonshifted functions on the top row keys).

All arithmetic operations in hexadecimal, octal, and binary base use 2's complement arithmetic. When a division produces a remainder, only the integer portion of the number is retained.

Alas, Boolean Logic isn't one of these. Thus I wrote these back in Autumn of 1994 for my own use.

## Notes

For AND / OR / XOR select base (HEXadecimal or OCTal; note the logic may be fine for BINary, but the programmatic uses of the number "2" preclude it as a base here), #1 INPUT #2, XEQ A / B / C; for NOT (1's complement), XEQ D or \R/S; for NOT (2's complement) \+/-.

## Example

```HEXadecimal:

1FFFF XEQ D               ---> FFFFE0000 (1's complement)
FFFFE0000 \R/S            ---> 1FFFF (returns original number)

1FFFF \+/-                ---> FFFFE0001 (2's complement)
FFFFE0001 \+/-            ---> 1FFFF (likewise)

dEAd INPUT bEEF XEQ B     ---> logical OR, FEEF

dEAd INPUT bEEF XEQ C     ---> logical XOR, 6042
6042 INPUT dEAd XEQ C     ---> logical XOR, bEEF (reverses prev. XOR)

OCTal:

123456701234 XEQ D        ---> 654321076543 (1's complement)
654321076543 \R/S         ---> 123456701234 (returns original number)

123456701234 \+/-         ---> 654321076544 (2's complement)
654321076544 \+/-         ---> 123456701234 (likewise)

157255 INPUT 137357 XEQ A ---> logical AND yields 117255

157255 INPUT 137357 XEQ B ---> logical OR, 177357

157255 INPUT 137357 XEQ C ---> logical XOR, 60102
60102 INPUT 157255 XEQ C  ---> logical XOR, 137357 (reverses prev. XOR)
```

## Program Listing

```Enter ... See
CLPRGM    00-
LBL D     01- 61 41 d
(         02- 33
+/-       03- 32
-         04- -
1         05- 1
)         06- 34
RTN       07- 61 26
LBL A     08- 61 41 A
XEQ 0     09- 41 0
LBL 4     10- 61 41 4
RCL 2     11- 22 2
X=0?      12- 61 43
GTO 3     13- 51 41 3
XEQ 8     14- 41 8
XEQ 9     15- 41 9
GTO 4     16- 51 41 4
LBL B     17- 61 41 b
XEQ 0     18- 41 0
LBL 5     19- 61 41 5
RCL 2     20- 22 2
X=0?      21- 61 43
GTO 3     22- 51 41 3
XEQ 8     23- 41 8
SWAP      24- 51 31
XEQ 9     25- 41 9
GTO 5     26- 51 41 5
LBL C     27- 61 41 C
XEQ 0     28- 41 0
LBL 6     29- 61 41 6
RCL 2     30- 22 2
X=0?      31- 61 43
GTO 3     32- 51 41 3
XEQ 8     33- 41 8
X\<=Y?    34- 61 42
GTO 7     35- 51 41 7
1         36- 1
XEQ 9     37- 41 9
GTO 6     38- 51 41 6
LBL 7     39- 61 41 7
0         40- 0
XEQ 9     41- 41 9
GTO 6     42- 51 41 6
LBL 0     43- 61 41 0
X\<=Y?    44- 61 42
SWAP      45- 51 31
STO 1     46- 21 1
SWAP      47- 51 31
STO 2     48- 21 2
1         49- 1
STO 0     50- 21 0
C         51- 71
STO 3     52- 21 3
RTN       53- 61 26
LBL 1     54- 61 41 1
(         55- 33
RCL 1     56- 22 1
-         57- 65
(         58- 33
\/        59- 45
2         60- 2
\*        61- 55
STO 1     62- 21 1
2         63- 2
)         64- 34
)         65- 34
RTN       66- 61 26
LBL 2     67- 61 41 2
(         68- 33
RCL 2     69- 22 2
-         70- 65
(         71- 33
\/        72- 45
2         73- 2
\*        74- 55
STO 2     75- 21 2
2         76- 2
)         77- 34
)         78- 34
RTN       79- 61 26
LBL 3     80- 61 41 3
C         81- 71
STO 0     82- 21 0
RCL 3     83- 22 3
RTN       84- 61 26
LBL 8     85- 61 41 8
XEQ 1     86- 41 1
INPUT     87- 31
XEQ 2     88- 41 2
X\<=Y?    89- 61 42
SWAP      90- 51 31
RTN       91- 61 26
LBL 9     92- 61 41 9
(         93- 33
\*        94- 55
RCL 0     95- 22 0
)         96- 34
STO+3     97- 21 75 3
2         98- 2
STO\*0    99- 21 55 0
SHOW      636F
```

## Resources Used

Registers 0 through 3 (the other six of ten registers, 4 through 9, are preserved unmodified for use in statistical calculations); LaBeLs A through D (E & F unused) and 0 through 9; program lines 00 through 99 (all program space).

## Acknowledgement

A grateful thanks go to Christof for the loan of an HP-20S (otherwise my photocopy of some hand-scrawled 3X5 index cards from 1993-4 might never have made sense).