Question

In the binary number system which is used in computer operations, there are only two digits allowed: 0 and 1. If eight binary digits are used, how many different binary numbers can be formed?

Answer 1

`2^8=256`

Explanation:

For each digit, there are 2 possibilities: 0, 1.

If we have a 1-digit number, the number of possibilities is 2.

If we have a 2-digit number, the number of possibilities is `2xx2=2^2=4`.

If we have a 3-digit number, the number of possibilities is `2xx2xx2=2^3=8`.

And so on.

An 8-digit number, therefore, has `2^8=256` possibilities