Converting Between Non-Decimal Bases?

Question

How can a number in an arbitrary base be converted to another random base - for example from 9.2E9B03 base 17 to base 5? I would prefer a generalized procedure avoiding an intermediary base 10 conversion - which I already know how to do.

Answer 1

You can use the same process you use for converting to/from base 10 but you will have to do arithmetic in another base. $17_{10}=32_5$, so $0.2E9B03_{17}=\frac{2\cdot 32^5+30\cdot 32^4+14\cdot 32^3+21\cdot 32^2+3}{32^6}_5$ Now multiply out the numerator and do long division in base $5$ to get the part right of the fraction point. For the whole numbers you do the same thing without the division.