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