Minimum variable size if the information are coded in non-binary system
One hexadecimal digit contains 4 binary digits. You can compute this as follows: $\log_2 16 = 4$. Alternatively, $2^4 = 16$. So the minimal memory element will contain 4 bits' worth of information.

This also works when the number of states is not a power of 2, but you have to be more flexible in your interpretation.