hp41programs

Base Base Conversion for the HP-41

Overview

-2 programs are listed below:

-The first one only deals with ( positive ) integers and bases b < 101
If 10 < b < 101, each "digit" is represented by 2 decimal digits from the decimal point:
For instance N = 1A2EF ( base 16 ) must be keyed in 110021415 ( N = 107247 in decimal )

-The second program also deals with ( positive ) fractional arguments
If 10 < b < 101, each "digit" is represented by 2 decimal digits from the decimal point
If 100 < b < 1001, each "digit" is represented by 3 decimal digits from the decimal point ... and so on ...

For instance, in base 234, R = 5,233,001.122, is a number with 3 "digits" in its integer part ( 5 233 1 ) and 1 "digit" in its fractional part ( 122 )
( in decimal, R = 328303.5214 )

-Roundoff errors are often unavoidable for fractional numbers

Integer Arguments and b < 101

Data Registers: /
Flags: /
Subroutines: /

01 LBL "b-X"
02 10
03 X<Y?
04 X^2
05 STO T
06 CLX
07 STO M
08 SIGN
09 X<> Z
10 LBL 01
11 R^
12 ST/ Y

13 RDN
14 FRC
15 ST- L
16 R^
17 ST* Y
18 X<> T
19 ST* Y
20 X<> Z
21 ST* Z
22 X<>Y
23 ST+ M
24 X<> L

25 X#0?
26 GTO 01
27 X<> M
28 RTN
29 LBL "X-b"
30 SIGN
31 0
32 LASTX
33 R^
34 LBL 02
35 STO M
36 X<>Y

37 MOD
38 ST- M
39 X<> L
40 ST/ M
41 RCL M
42 X<>Y
43 R^
44 ST* L
45 X<> L
46 ST+ T
47 CLX
48 10

49 X<Y?
50 ST* X
51 ST* L
52 X<> L
53 RDN
54 X<>Y
55 X#0?
56 GTO 02
57 STO M
58 X<> Z
59 END

( 103 bytes / SIZE 000 )

1-Base b >>> Base 10 ( LBL "b-X" )

STACK	INPUTS	OUTPUTS
Y	N_b	b
X	b	N₁₀

2-Base 10 >>> Base b ( LBL "X-b" )

STACK	INPUTS	OUTPUTS
Y	N₁₀	b
X	b	N_b

Example1: Convert (1234)₇ to the decimal scale and then to the nonary scale

1234 ENTER^
7 XEQ "b-X" >>> 466
9 XEQ "X-b" ( or simply R/S ) >>> 567 whence (1234)₇ = 466 = (567)₉

Example2: Convert (16267)₁₂ to the decimal scale and then to the hexadecimal scale and the septenary scale.

   106020607 ENTER^
                 12 XEQ "b-X" >>> 31471
                                                         16   R/S yields 7101415     whence   (16267)₁₂ = 31471 = (7AEF)₁₆

-Similarly, 31471 ENTER^ 7 XEQ "X-b" gives 160516 whence (16267)₁₂ = (160516)₇

Fractional Arguments

Data Registers: /
Flags: /
Subroutines: /

-Line 72 = synthetic STO P

01 LBL "B-X"
02 CLA
03 ENTER^
04 DSE X
05 LOG
06 INT
07 1
08 +
09 STO N
10 X<> Z
11 ENTER^
12 LOG
13 RCL N
14 /
15   E2
16 +
17 INT
18   E2
19 -
20 R^

21 X<>Y
22 Y^X
23 STO Z
24 CLX
25 RCL N
26 ST* L
27 X<> L
28 10^X
29 /
30 LBL 01
31 ENTER^
32 INT
33 ST- Y
34 X<> Z
35 ST* Z
36 X<> Z
37 ST+ M
38 R^
39 ST/ T
40 RDN

41 CLX
42 RCL N
43 10^X
44 *
45 X#0?
46 GTO 01
47 X<> M
48 CLA
49 RTN
50 LBL "X-B"
51 CLA
52 ENTER^
53 DSE X
54 LOG
55 INT
56 1
57 +
58 STO N
59 STO O
60 CLX

61 RCL Z
62 LOG
63 RCL Y
64 LOG
65 /
66 INT
67 2
68 +
69 ST* O
70 CLX
71 11
72 STO P
73 RDN
74 LBL 02
75 RCL N
76 ST- O
77 RCL O
78 X<>Y
79 /
80 RCL Y

81 X<>Y
82 Y^X
83 RDN
84 X<> T
85 MOD
86 ST- Y
87 X<>Y
88 LASTX
89 /
90 RCL O
91 10^X
92 *
93 ST+ M
94 X<> Z
95 DSE P
96 GTO 02
97 RCL M
98 CLA
99 END

( 152 bytes / SIZE 000 )

1-Base B >>> Base 10 ( LBL "B-X" )

STACK	INPUTS	OUTPUTS
Y	N_b	b
X	b	N₁₀

2-Base 10 >>> Base B ( LBL "X-B" )

STACK	INPUTS	OUTPUTS
Y	N₁₀	b
X	b	N_b

Example1: Convert (12.34)₇ to the decimal scale and then to the nonary scale

12.34 ENTER^
7 XEQ "B-X" >>> 9.510204082
9 XEQ "X-B" ( or simply R/S ) >>> 10.45284032

whence (12.34)₇ = 9.510204082 = (10.45284032)₉

Example2: Convert (4,123.092,046)₁₂₈ to the decimal scale and then to the scale B = 41

   4,123.092,046 ENTER^
           128           XEQ "B-X" >>>   635.7215576
                                                                 41            R/S >>>   15,20.29,23,38

whence (4,123.092,046)₁₂₈ = 635.7215576 = (15,20.29,23,38)₄₁

References:

[1] Abramowitz and Stegun , "Handbook of Mathematical Functions" - Dover Publications - ISBN 0-486-61272-4
[2] Philippe Descamps & Jean-Jacques Dhenin , "Programmer HP-41" - PSI - ISBN 2-86595-056-5 ( in French )