A computer has 2^32 addressable memory locations, each able to hold one byte

Question

a) What is the largest unsigned integer expressed in base 2 that could be fit into this amount of memory? Please express answer as a power of 2.

b) What is the largest unsigned integer expressed in unary that could be fit into this amount of memory? Please express answer as a power of 2.

c) What is the ratio of the maximum binary value to the maximum unary value?

Answer 1

The $35$ comes from the fact that you have 8 bits per location.

a) $2^{2^{35}}-1$

b) $2^{35}$

c) $2^{2^{35}-35}-2^{-35}$