Editing Two's complement (section)

{{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. Two's complement uses the [[Most significant bit|binary digit with the ''greatest'' value]] as the ''sign'' to indicate whether the binary number is positive or negative; when the [[most significant bit]] is ''1'' the number is signed as negative and when the most significant bit is ''0'' the number is signed as positive. As a result, non-negative numbers are represented as themselves: 6 is 0110, zero is 0000, and −6 is 1010 (the result of applying the [[bitwise NOT]] operator to 6 and adding 1). However, while the number of binary bits is fixed throughout a computation it is otherwise arbitrary.

Unlike the [[ones' complement]] scheme, the two's complement scheme has only one representation for zero. Furthermore, arithmetic implementations can be used on signed as well as unsigned integers<ref>
{{cite book
 |first1=Alexandre |last1=Bergel
 |first2=Damien   |last2=Cassou
 |first3=Stéphane |last3=Ducasse
 |first4=Jannik | last4=Laval
 |year=2013
 |title=Deep into Pharo
 |page=337
 |url=http://files.pharo.org/books-pdfs/deep-into-pharo/2013-DeepIntoPharo-EN.pdf
}}
</ref>
and differ only in the integer overflow situations.