Base 4 math

I need to create a custom data type that will only hold numbers in base 4 (unsigned) that will roll over properly and restricted to a number of bits such that if 0 is interpreted as 'A' (0 = 'A', 00 = "AA", 000 = "AAA")and the number it holds is 0 it will print out 'A'
I will need to know how to edit it so that a slightly different data type will print out "AA" exc...

how do i do this in C?

struct mytype { int foob : 4 };