Originally Posted by

**Wikipedia**
The two's complement of a binary number is defined as the value obtained by subtracting the number from a large power of two (specifically, from 2N for an N-bit two's complement). The two's complement of the number then behaves like the negative of the original number in most arithmetic, and it can coexist with positive numbers in a natural way.

A two's-complement system or two's-complement arithmetic is a system in which negative numbers are represented by the two's complement of the absolute value;[1] this system is the most common method of representing signed integers on computers.[2] In such a system, a number is negated (converted from positive to negative or vice versa) by computing its two's complement. An N-bit two's-complement numeral system can represent every integer in the range −2N-1 to +2N-1-1.

The two's-complement system has the advantage of not requiring that the addition and subtraction circuitry examine the signs of the operands to determine whether to add or subtract. This property makes the system both simpler to implement and capable of easily handling higher precision arithmetic. Also, zero has only a single representation, obviating the subtleties associated with negative zero, which exists in ones'-complement systems.