Given N bits, how many integers can be represented in binary?

Question

Suppose you have 14 bits. How do you determine how many integers can be represented in binary from those 14 bits?

Is it simply just 2^n? So 2^14 = 16384?

Please

Answer 1

Yes, it's that easy as 2^n.

A bit can have 2 distinct values: 0 and 1.

If you have 2 bits, than you have 4 distinct values: 00, 01, 10, 11. The list goes on.

Combinatorics has the simple counting formula

N = n_1 ⋅ n_2 ⋅ ... ⋅ n_k

Since n_1 = n_2 = n_k = 2 you can reduce the formula to

N = 2 ^ k