Swiss Micros DM16L: Advanced Boolean and Factorial (up to 20)
Introduction
The program listing, for the Swiss Micros DM16L and Hewlett Packard HP 16C, will assign the following functions to the labels:
A: NAND: nand(x, y) = not(x and y)
B: NOR: nor(x, y) = not(x or y)
C: XNOR: xnor(x, y) = (not x and not y) or (x and y)
D: Implication: y → x = (not y) or x
E: Factorial: x! (x is a positive integer up to 20, 64 word size
NAND, NOR, NXOR, and Implication are advanced Boolean functions. You can check out program code for the HP Prime here:
http://edspi31415.blogspot.com/2020/03/hp-prime-advanced-boolean-functions.html
Program - DM16L/HP 16C
// NAND
001 43,22,A LBL A
002 42,20 AND
003 42,30 NOT
004 43,21 RTN
// NOR
005 43,22,b LBL B
006 42,40 OR
007 42,30 NOT
008 43,21 RTN
// XNOR
009 43,22,C LBL C
010 44,1 STO 1
011 42,30 NOT
012 34 x<>y
013 44,2 STO 2
014 42,30 NOT
015 42,20 AND
016 45,1 RCL 1
017 45,2 RCL 2
018 42,20 AND
019 42,40 OR
020 43,21 RTN
// Implication
021 43,22,d LBL D
022 34 x<>y
023 42,30 NOT
024 42,40 OR
025 43,21 RTN
// Factorial
026 43,22,E LBL E
027 44,32 STO I
028 1 1
029 44,1 STO 1
030 43,22,1 LBL 1
031 45,1 RCL 1
032 45,32 RCL I
033 20 ×
034 44,1 STO 1
035 43,23 DSZ
036 22,1 GTO 1
037 45,1 RCL 1
038 43,21 RTN
Examples
Let:
R1 = 1011 0001
R2 = 1100 1100
Set up: 2-16-0000 (2's complement, 16 bits)
RCL 2, RCL 1, GSB A NAND(R2, R1): 0111 1111*
RCL 2, RCL 1, GSB B NOR(R2, R1): 0000 0010*
RCL 2, RCL 1, GSB C XNOR(R2, R1): 1000 0010*
RCL 2, RCL 1, GSB D R2 → R1: 1100 1110*
* only the last eight bits
Set word size to 64:
0 [ f ] [ STO ] (WSIZE)
5 GSB E 5! = 120
9 GSB E 9! = 362880*
* if the word size is insufficient, it will not show 362880 but a weird result as an overflow
12 GSB E (64 word size)
12! = 4 79001600
Window 1: 4
Window 0: 79001600
20 GSB E
20! = 243 29020081 76640000
Window 2: 243
Window 1: 29020081
Window 0: 76640000
Source for the Advanced Boolean Functions:
John W. Harris and Horst Stocker. Handbook of Mathematics and Computation Science Springer: New York, NY. 2006. ISBN 978-0-387-94746-4
Eddie
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