Question

In an integer encoding of 8 bits 10101010 you have 0-255 possibilities.

In total 256 different possibilities as there are 8 1s and 0s. How many different possibilities would I get if I had 10 bits instead of 8?

How would I calculate that in PHP?

Answer 1

I assume you are thinking of binary rather than hexadecimal? Binary is base 2 (hence either 0 or 1s) where as Hexadecimal is base 16.

Assuming you are talking about binary:

• If you have 8 bits you have 2⁸ possibilities.
• If you have 9 bits you have 2⁹ possibilities.
• If you have 10 bits you have 2¹⁰ possibilities.

Etc…

You can therefore use the PHP pow function:

$possibilities = pow(2, 10);