Sunday, April 18, 2021

Swiss Micros DM16L: Advanced Boolean and Factorial (up to 20)

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


All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


No comments:

Post a Comment

Retro Review and Comparison: TI-82 Advanced

 Retro Review and Comparison: TI-82 Advanced I can officially say that I have a French calculator.   Quick Facts: Models:  TI-82 Advanced Co...