HP 42S/DM42: Base Programs

 HP 42S/DM42:   Base Programs

Unsigned NOT

The program UNOT applies a NOT to a binary integer (flips zeros to ones and ones to zeros) using unsigned binary integers.  The number of bits (size) is prompted.

HP 42S/DM42 Program UNOT

00  {40-Byte Prgm}

01  LBL "UNOT"

02  BINM

03  "BIN?"

04  PROMPT

05  STO 01

06  EXITALL

07  "SIZE?"

08  PROMPT

09  STO 02

10  2

11  X<>Y

12  Y↑X

13  RCL- 01

14  STO 02

15  1

16  -  

17  BINM

18  END

Examples:

Unsigned NOT of 10100, size 5:  1011  (01011)

Unsigned NOT of 10100, size 8:  11101011

Shift Left

Makes a binary integer shift left: a zero is added to the right side of the integer and "drops" off the left most digit.  The number of bits (size) is prompted.  The binary number is assumed to be non-negative. 

HP 42S/DM42 Program SL16

00  {35-Byte Prgm}

01  LBL "SL16"

02  BINM

03  "BIN?"

04  PROMPT

05  EXITALL

06  2

07  ×

08  "SIZE?"

09  PROMPT

10  2

11  X<>Y

12  Y↑X

13  MOD

14  BINM

15  END

Examples:

Shift Left:  10100, size 5:  1000   (01000)

Shift Left:  10100, size 8:  101000  (00101000)

Shift Right (Logical)

Makes a binary integer shift right: a zero is added to the left side of the integer and "drops" off the left most digit.  The binary number is assumed to be non-negative. A logical shift right divides an integer by 2 and taking the integer result.

HP 42S/DM42 Program SR16

00  {24-Byte Prgm}

01  LBL "SR16"

02  BINM

03  "BIN?"

04  PROMPT

05  EXITALL

06  2

07  ÷

08  IP

09  BINM

10  END

Examples:

Shift Right:  10100:  1010

Shift Right:  1010:  101

The next two programs deals with RGB and HEX codes for computer colors.

HP 42S/DM42 Program CLR→:   RBG to Hexadecimal Code

00  {51-Byte Prgm}

01  LBL "CLR→"

02  DECM

03  "RED?"

04  PROMPT

05  65536

06  BASE×

07  "GREEN?"

08  PROMPT

09  256

10  BASE×

11  BASE+

12  "BLUE?"

13  PROMPT

14  BASE+

15  HEXM

16  END

Example:

Red: 221, Green: 80, Blue 109

Result:  HEX Code:  DD506D

HP 42S/DM42 Program  →CLR:   Hexadecimal to RGB Code

00  {63-Byte Prgm}

01  LBL "→CLR"

02  HEXM

03  "HEX CODE?"

04  PROMPT

05  STO 00

06  DECM

07  65536

08  BASE÷

09  STOP   // Red

10  65536

11  BASE×

12  RCL 00

13  X<>Y

14  BASE-

15  STO 00

16  256

17  BASE÷

18  STOP   // Green

19  256

20  BASE×

21  RCL 00

22  X<>Y

23  BASE-

24  END

Example:  

HEX Code:  103E22

Result:  Red:  16, Green:  62,  Blue:  34

Eddie

All original content copyright, © 2011-2022.  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. 

HP 42S/DM42/Free 42: Advanced Boolean Functions

HP 42S/DM42/Free 42: Advanced Boolean Functions

Introduction

The programs NOTBIT, NAND, NOR, and IMPL are four advanced Boolean functions that work on Binary Numbers.  You designate a bit size, up to 35, on each of these functions.   There is no signed bit in these programs.  Results are stored in the Alpha Register while the decimal equivalent is stored in the X register. 

HP 42S/DM42/Free 42 Program:  NOTBIT

00 { 57-Byte Prgm }
01▸LBL "NOTBIT"
02 "BIT SIZE?"
03 PROMPT
04 STO 00
05 BINM
06 "BIN?"
07 PROMPT
08 STO 01
09 DECM
10 2
11 RCL 00
12 Y↑X
13 X<>Y
14 BASE-
15 1
16 BASE-
17 BINM
18 "NOT: "
19 ARCL ST X
20 AVIEW
21 EXITALL
22 .END.

Example:

NOT 11011, bit size:  8

Result: 
NOT:  11100100

HP 42S/DM42/Free 42 Program:  NAND

a NAND b = NOT ( a AND b )

00 { 67-Byte Prgm }
01▸LBL "NAND"
02 "BIT SIZE?"
03 PROMPT
04 STO 00
05 BINM
06 "BIN1?"
07 PROMPT
08 STO 01
09 "BIN2?"
10 PROMPT
11 STO 02
12 AND
13 DECM
14 2
15 RCL 00
16 Y↑X
17 X<>Y
18 BASE-
19 1
20 BASE-
21 BINM
22 "NAND: "
23 ARCL ST X
24 AVIEW
25 EXITALL
26 .END.

Example:

110011 NAND 111100, bit size: 8

Result:
NAND:  11001111

HP 42S/DM42/Free 42 Program:  NOR

a NOR b = NOT ( a OR b )

00 { 64-Byte Prgm }
01▸LBL "NOR"
02 "BIT SIZE"
03 PROMPT
04 STO 00
05 BINM
06 "BIN1?"
07 PROMPT
08 STO 01
09 "BIN2?"
10 PROMPT
11 STO 02
12 OR
13 DECM
14 2
15 RCL 00
16 Y↑X
17 X<>Y
18 BASE-
19 1
20 BASE-
21 BINM
22 "NOR: "
23 ARCL ST X
24 AVIEW
25 EXITALL
26 .END.

Example:

110011 NOR 111100, bit size: 8

Result:
NOR:  11000000

HP 42S/DM42/Free 42 Program:  IMPL

IMPL (Implication):  a → b = (NOT a) OR b

00 { 66-Byte Prgm }
01▸LBL "IMPL"
02 "BIT SIZE?"
03 PROMPT
04 STO 00
05 BINM
06 "BIN1?"
07 PROMPT
08 STO 01
09 DECM
10 2
11 RCL 00
12 Y↑X
13 X<>Y
14 BASE-
15 1
16 BASE-
17 BINM
18 "BIN2?"
19 PROMPT
20 STO 02
21 OR
22 "A→B: "
23 ARCL ST X
24 AVIEW
25 EXITALL
26 .END.

Example:

110011 IMPL 111100, bit size: 8

Result:
IMPL:  11111100

You can download the raw files here: 
https://drive.google.com/open?id=19u8tPcX4_-o0lwvjUc0KO4-WSmhnxpwe

Source:

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, © 2011-2020.  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.

HP Prime: Advanced Boolean Functions

Advanced Boolean Functions

This is a collection of advanced Boolean functions and how you can do this on a scientific calculator that has base conversions and Boolean functions (and, or, not).   One thing to keep in mind is that Boolean functions on a scientific calculator assume that you are working with a set bit size.

Order of Operations:  Parenthesis, NOT, AND, OR

For the examples below, I am going to work with only 8 bit size binary integers, and display the last 8 bits (rightmost 8 digits in Binary numbers).   For all examples, let (in base 2):

A = 1100 1010
B = 1110 0011

Like the Boolean functions and, or, and not, these functions work on each bit (0s and 1s) of the binary form of the number.

Integer Types on the HP Prime

On the HP Prime, the integer type is used for Boolean function calculations.  Symbolize integer types by preceding it by a hashtag # and designated a letter at the end of the integer:  b for binary, o for octal, d for decimal, and h for hexadecimal.

Example:  #11010b  represents the binary number 11010.

You can specify the bit size, from 1 to 64, by attaching a colon and bit size in between the integer and it's indicator.

Example:  #11010:8b represents the 11010 in an 8-bit format.  You can specify the default size in the Home Settings.

NAND (Not And)

The function NAND is also known as the Shaffer function.

nand(A, B) = not(A and B)

nand(1100 1010, 1110 0011) = not(1100 1010 and 1110 0011) = 0011 1101

Truth Table - NAND
0 nand 0 = 1
0 nand 1 = 1
1 nand 0 = 1
1 nand 1 = 0

HP Prime Program:  NAND

EXPORT NAND(a,b)
BEGIN
// not and Boolean Function
RETURN  NOT (a AND b);
END;

Syntax:  NAND(a,b)

NOR (Not Or)

The function NOR is also known as the Peirce function.

nor(A, B) = not(A or B)

nor(1100 1010, 1110 0011) = not(1100 1010 or 1110 0011) = 0001 0100

Truth Table - NOR
0 nor 0 = 1
0 nor 1 = 0
1 nor 0 = 0
1 nor 1 = 0

HP Prime Program:  NOR

EXPORT NOR(a,b)
BEGIN
// not or Boolean Function
RETURN  NOT (a  OR  b);
END;

Syntax:  NOR(a,b)

XOR (Exclusive Or)

Note:  some calculators will have the XOR function

xor(A, B) = (A or B) and (not A or not B)

xor(1100 1010, 1110 0011)
= (1100 1010 or 1110 0011) and (not 1100 1010 or not 1110 0011)
= 0010 1001

Truth Table - XOR
0 xor 0 = 0
0 xor 1 = 1
1 xor 0 = 1
1 xor 1 = 0

Equivalence (←→), XNOR

A ←→ B = (not A and not B) or (A and B)

1100 1010 ←→ 1110 0011
= 1100 1010 xnor 1110 0011
= (not 1100 1010 and not 1110 0011) or (1100 1010 and 1110 0011)
= 1101 0110

Truth Table - ←→, xnor 
0 xnor 0 = 1
0 xnor 1 = 0
1 xnor 0 = 0
1 xnor 1 = 1

HP Prime Program XNOR

EXPORT XNOR(a,b)
BEGIN
// equivalence, XNOR
RETURN (NOT a AND NOT b) or (a AND b);
END;

Syntax:  XNOR(a, b)

Implication (→)

A → B = (not A) or B

1100 1010 → 1110 0011
= (not 1100 1010) or 1110 0011
= 1111 0111

Truth Table -  Implication, →
0 → 0 = 1
0 → 1 = 1
1 → 0 = 0
1 → 1 = 1

HP Prime Program:  IMPL

EXPORT IMPL(a,b)
BEGIN
// implication
RETURN (NOT a) or b;
END;

Source:

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, © 2011-2020.  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.