Suppose your bank clerk gives you an arbitrary password such as hel34/hjal0@# and you cannot remember it without writing it to a paper. Dilemma: you never write passwords to paper. So you try to invent an encryption, one-to-one map, where you write only a key to a paper, only numbers, and leave the rest junk to your server. Of course, the password can consist of arbitrary things.

Implemention should work like

hel34/hjal0#@ ---- magic ----> 3442

and to other way:

3442 ---- server magic ---> hel34/hjal0#@

[Update] mvds has the correct idea, to change the base, how would you implement it?