Dear Aaron,
I am not quite sure whether I understand your question correctly. I suppose that when you say
The number 23 COULD be 2:3, but it could Also be 23, two digits or one
digit.
you mean that in base 25, you could have a digit that corresponds to 23 units, so if you type that into Mathematica it cannot know whether it is the single "digit" corresponding to 23 units. If that is your problem, and I a not sure whether it is, then Mathematica solves that trivially. It attaches letters to the higher digits. For example if in base 11 you need another digit (beyond the digits 0-9 for the decimal system), Mathematica calls that "a" so the digits that you need are just letters. Given that there is only a finite number of letters, this does cause a problem for bases which are large. For the small ones it works quite effortlessly:
BaseForm[25^^afdda52, 16]
Converts the number afdda52 (given in to base 25) to base 16. The digits in base 25 are:
0,1,2,3,4,5,6,7,8,9,a,b,c,d,e,f,g,h,i,j,k,l,m,n,o.
This is why
25^^p
gives an error, whereas
25^^o
works just fine. So the "digit" 23 corresponds to m.
BaseForm[25^^m,10]
evaluates, as expected, to 22.
I am not sure whether this helps, but I just wanted to give it a shot.
Cheers,
Marco