Two's complement: Difference between revisions

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{{Short description|Mathematical operation on binary numbers, and a number representation based on this operation}}

'''Two's complement''' is the most common [[signed number representations|method of representing signed]] (positive, negative, and zero) [[Integer (computer science)|integers]] on computers,<ref>E.g. "Signed integers are two's complement binary values that can be used to represent both positive and negative integer values", Section 4.2.1 in ''Intel 64 and IA-32 Architectures Software Developer's Manual'', Volume 1: Basic Architecture, November 2006</ref> and more generally, [[Fixed-point arithmetic|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 asby taking the [[bit complement]] of their magnitude plusand then adding 1one (−6 is 1010). The number of bits in the representation may be increased by padding all additional high bits of positive or negative 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<ref>

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|series=Class notes for CS&nbsp;104

|publisher=Cornell University |department=Computer Science |place=Ithaca, New York

|url=httphttps://www.cs.cornell.edu/~tomf/notes/cps104/twoscomp.html |access-date=2014-06-22

}}</ref>