(41 or 42s) Hexadecimal / decimal conversions with no comparisons / branching

[arhtur]

I've looked for patterns in the past for processing directional key inputs and drawing mazes, and found that the hexadecimal / decimal conversion eluded me.

The problem is when converting either direction, there is a gap for ASCII characters: 0 to 9 are ASCII 49 to 58, but A to F are ASCII 65 to 70.

Well, by using the MOD function and a division, it is possible.

This will work on the HP 41, but also 42s/Free42/DM42 (with minor changes - INT becomes IP).

I first wrote the conversion from decimal to hexadecimal. For converting the number N, we do:

let X = N MOD 16
ASCII chr = INT( X / 10 ) * 7 + X + 48

We then divide N by 16 and repeat. We know how many times to execute a loop by doing LN( N ) / LN( 16 ).

To do the conversion, put the number on the stack and XEQ D2H. The result will be in the alpha register. There is only one GTO statement and one ISG statement. Of course, the number 0 cannot be converted due to the use of natural logarithm. 2's complement is not used in this implementation.

I initially had used the LOG function, but found that when converting 256, LOG(256) / LOG(16) = 2, but when doing INT( LOG(256) / LOG(16) ), I got 1 when using an IOS app of the HP 41CX. So I switched to using LN.

Code:

01 LBL “D2H”
02 CLA
03 STO 00
04 LN
05 16
06 LN
07 /
08 IP
09 1e3
10 /
11 STO 01
12 LBL 01
13 RCL 00
14 16
15 MOD
16 ENTER
17 ENTER
18 10
19 /
20 INT
21 7
22 x
23 +
24 48
25 +
26 XTOA
27 16
28 STO/ 00
29 -1
30 AROT
31 ISG 01
32 GTO 01
33 RTN

To convert from hexadecimal to decimal, put the hexadecimal number in the alpha register. The number of digits must be specified on the stack.

let X = ASCII value of the least significant digit.
then N = (X - 48) MOD 17 + INT ((X - 48) / 17) x 10

For characters 0 to 9, we get numbers 0 to 9. When we have characters A to F, the MOD function will give us 0 to 5 and when we do the integer divide by 17 and multiply by 10, we get numbers 10 to 15. Since the goal was to avoid any comparisons or branching, the number of digits has to be specified on the stack before doing XEQ H2D. There is only one GTO statement and one DSE statement. 0 can be converted when 1 digit is specified on the stack. 2's complement is not used in this implementation. Also, no checks are made for invalid characters.

Code:

01 LBL “H2D”
02 STO 01
03 0
04 STO 03
05 LBL 01
06 16
07 STOx 03
08 ATOX
09 48
10 -
11 STO 02
12 17
13 MOD
14 RCL 02
15 17
16 /
17 INT
18 10
19 x
20 +
21 STO+ 03
22 DSE 01
23 GTO 01
24 RCL 03
25 RTN