Signed Number Representations

In computing, signed number representations are required to encode negative numbers in binary number systems.

In mathematics, negative numbers in any base are represented by prefixing them with a − sign. However, in computer hardware, numbers are represented in bit vectors only without extra symbols. The four best-known methods of extending the binary numeral system to represent signed numbers are: sign-and-magnitude, ones' complement, two's complement, and excess-K. Some of the alternative methods use implicit instead of explicit signs, such as negative binary, using the base −2. Corresponding methods can be devised for other bases, whether positive, negative, fractional, or other elaborations on such themes. In practice the representation most generally used in current computing devices is two's complement, although there is no definitive criterion by which any of the representations is universally superior.