HP-67 Base Conversion from HP Key Notes

[Karl-Ludwig Butte]

Dear All,

in HP Key Notes Vol. 3 No. 2 p. 13 there was a base conversion routine for the HP-67/97 written by Cass R. Lewart (Holmdel, New Jersey). In the following issue (Vol. 3 No. 3 p. 11) Bob Edelen corrected a missing program step in this routine.

The program works perfectly and even can convert directly from one non-decimal base to another non-decimal base (e.g. from base 2 to base 8) just by entering:

number
ENTER
original base
ENTER
new base
Function key A

The program listing is as follows:

001 *LBL A
002 STO 0
003 Roll Down
004 Enter
005 GSB 3
006 GSB 0
007 RCL 0
008 GSB 3
009 RCL 0
010 *LBL 0
011 STO 1
012 Roll Down
013 STO 2
014 Roll Down
015 STO 3
016 0
017 STO 4
018 1
019 STO 5
020 *LBL 1
021 RCL 3
022 X=0?
023 GTO 2
024 RCL 1
025 /
026 ENTER
027 INT
028 STO 3
029 -
030 RCL 1
031 x
032 RCL 5
033 x
034 INT
035 ST+4
036 RCL 2
037 STx5
038 GTO 1
039 *LBL 2
040 RCL 4
041 RTN
042 *LBL 3
043 1
044 -
045 LOG
046 INT
047 1
048 +
049 10^x
050 RTN

Alas, the original Key Notes article has not a tiny clue of how this routine works. And although I can see all the program steps I cannot reverse engineer the program to find out the algorithm which is behind this clever routine. I already did a Google search for base conversion algorithms but I only found descriptions for converting base X to base 10 and base 10 to base X. Most of them use string operations to seperate single digits.

So my question is: Can anyone of you math gurus of this forum please explain the algorithm of this base conversion routine to me?

Any hint will be very much appreciated.

Thank you very much in advance.

Best regards

Karl