Question

Prove or disprove: The number of bits required to express the n^th Fibonacci number in binary is Θ(n).

Answer 1

N    F(N)      0.694*N
1      0         1       
2      1         1
3      1         1
4      2         2
5      3         2
6      5         3
7      8         4
8     13         4

As per the table above, nth Fibonacci number has about 0.694*n bits in the binary representation.

Hence, the statement that the number of bits required to express the n^th Fibonacci number in binary is Θ(n).