Two's complement

Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers,^[1] and more generally, fixed point binary values. As with the ones' complement and sign-magnitude systems, two's complement uses the most significant bit as the sign to indicate positive (0) or negative (1) numbers, and nonnegative numbers are given their unsigned representation (6 is 0110, zero is 0000); however, in two's complement, negative numbers are represented by taking the bit complement of their magnitude and then adding one (−6 is 1010). The number of bits in the representation may be increased by padding all additional high bits of negative or positive numbers with 1's or 0's, respectively, or decreased by removing additional leading 1's or 0's.

Unlike the ones' complement scheme, the two's complement scheme has only one representation for zero, with room for one extra negative number (the range of a 4-bit number is -8 to +7). Furthermore, the same arithmetic implementations can be used on signed as well as unsigned integers^[2] and differ only in the integer overflow situations, since the sum of representations of a positive number and its negative is 0 (with the carry bit set).