Signed numbers

The following section is optional. Most of the time when we deal with binary numbers and bit operations, we use unsigned numbers. However, it is interesting to examine how signed numbers are dealt with.

Signed numbers are typically stored using a method known as two’s complement. In two’s complement, the leftmost (most significant) bit is used as the sign bit. A 0 bit means the number is positive, and a 1 bit means the number is negative. Positive signed numbers are stored just like positive unsigned numbers. Negative signed numbers are stored as the inverse of the positive number, plus 1.

For example, here’s how we convert -5 to binary:

First we figure out the binary representation for 5: 0000 0101
Then we invert all of the bits: 1111 1010
Then we add 1: 1111 1011

Converting -76 to binary:

Positive 76 in binary: 0100 1100
Invert all the bits: 1011 0011
Add 1: 1011 0100

Why do we add 1? Consider the number 0. If a negative value was simply represented as the inverse of the positive number, 0 would have two representations: 0000 0000 (positive zero) and 1111 1111 (negative zero). By adding 1, 1111 1111 intentionally overflows and becomes 0000 0000. This prevents 0 from having two representations, and simplifies some of the internal logic needed to deal with negative numbers.

So, basically if you want to find the binary number of, for example, -100, what you have to do is get the binary number of 100, inverse the number (0 to 1, 1 to 0) and add 1. That's it!

yaya, i discussed with dony for half an hour, thank him for getting this explanation and set my mind clearer in this conversion.