Binary representation of numbers

First lets see how binary numbers are created. For positive numbers,

0 == 0000 0000 1 == 0 + 1 == 0000 0001 2 == 1 + 1 == 0000 0010 3 == 2 + 1 == 0000 0011 4 == 3 + 1 == 0000 0100 The other way around, 2 == 3 - 1, 1 == 2 - 1, and 0 == 1 - 1.

Now we come to -1. That's obviously 0 - 1. However, there's nothing to subtract from 0. So they came up with the special notation of all ones: 1111 1111. So -1 == 1111 1111. Let's continue this way for negative numbers: -2 == -1 - 1 == 1111 1110 -3 == -2 - 1 == 1111 1101 -4 == -3 - 1 == 1111 1100