Bases that are powers of 2 are easy to compute with because you can deal with collections of binary bits: base 2 is 1 bit (numbers 0-1), base 4 is 2 bits (numbers 0-3), base 8 is 3 bits (numbers 0-7), and base 16 is 4 bits (numbers 0-15). Base 4 would actually be fine, but you only get 2 bits to play with, so it's not so common.