Why are negative numbers stored as 2’s complement?

When doing addition/subtraction on binary numbers in other representations we need to apply different logics (circuits) to perform addition and subtraction. In 2s-complement representation, we represent a positive number as it is and negative number by its corresponding 2s-complement, so we can use the same circuit to perform addition and subtraction.

For example: to add 6+3 using 5 bit 2s-complement representation,

00110

+

00011

——–

01001

To subtract 6-3, rewrite as 6+ (-3):

00110

+

11101 (2s-complement of 3)

——-

00011