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Sign and Magnitude

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 minus sign ("−"). However, in computer hardware, numbers are represented only as sequences of bits, 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 offset binary. 

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Four useful rules

  • 1-There are two ways to represent zero, 00000000 (0) and 10000000 (−0).
  • 2-Addition and subtraction require different behavior depending on the sign bit, whereas one's complement can ignore the sign bit and just do an end-around carry, and two's complement can ignore the sign bit and depend on the overflow behavior.
  • 3-Comparison also require inspecting the sign bit, whereas in two's complement, one can simply subtract the two numbers, and check if the outcome is positive or negative.
  • 4-The minimum negative number is −127 instead of −128 in the case of two's complement.