Question

How many bits, unsigned integer, are required to represent

a: 100states

b: 10000stated

c;100000stated

Answer 1

Number of bits, unsigned integer, are required to represent n states = floor(log2(n)) + 1

a:
Answer = floor(log2(n)) + 1
       = floor(log2(100)) + 1
       = floor(6.643856189774724) + 1
       = 6 + 1
       = 7 bits


b:
Answer = floor(log2(n)) + 1
       = floor(log2(10000)) + 1
       = floor(13.287712379549449) + 1
       = 13 + 1
       = 14 bits


c:
Answer = floor(log2(n)) + 1
       = floor(log2(100000)) + 1
       = floor(16.609640474436812) + 1
       = 16 + 1
       = 17 bits