I have reflected a little bit about the two programs. Both are valid and work - for all bases less than 10 ! It will fail for any base higher than 10, since it doesn't recognize other non-number characters. As such, I realize that the program needs to be limited to a maximum base number. According to the discussion with my son, they may have to work on a base-20 problem (about a tribe in Oceania that uses all their fingers to count, feet included), so I will have to create 2 subroutines to convert from 0 to i, to 0 to 19; and viceversa.
I will make the changes to the programs tomorrow.
Precisely today there is a thread in hpmuseum.org about base changes - limited to base 10 too, and in RPN. (Did I mention that the formulas can be used in RPN mode too?)