On Mon, 6 Apr 2015, Jon Purdy wrote:

Could you offer a specific use case? When I need to convert a number
to its representation in some base, it’s because I’m displaying or
serialising it. A base is a notation (or a variant of a notation) and
it seems sensible to represent such notations with characters.

E.g. you can use it to pack a tuple of small integers space efficiently into a larger integer type. E.g. you can pack 3 integers from the range 0..4 into 7 bits using a base-5 representation, but you would need 9 bits if you reserve three bits for every small integer.

Using the positional representation you can also convert between tupled and linear indexes of an array with equal extents in all dimensions (i.e. a hypercube).

Both examples also work with mixed-base representations.