Quote from: azeteki on February 15, 2015, 09:33:32 AM

Hello e1ghtSpace;

Consider the very small and simple case of a 1-bit key.

Combinations are as follows:
0
1

Now go up to a 2-bit key. You have 2 possible combinations of a 1 bit key, and 2 possible combinations of the new bit.
00
01

10
11

3-bit: 4 possible combinations of the lower 2 bits, and 2 possible combinations of the new bit. 8 in total.
000
001
010
011

100
101
110
111

Every time you add an additional bit, you have all previous possibilities, multiplied by 2 (as the first, new, bit can be one of two possible values).

Therefore a 1 bit key has 2 possible values; a 2 bit key 2*2 = 4 possible values; a 3 bit key 2*2*2 = 8 possible values; and so on and so forth, until an N-bit key has 2^N possible values.

You can test this if you wish. Try counting from 0 to 31 in binary. See what you find.

Ah ok that makes more sense. Thanks for the explanation!