Two's complement: Difference between revisions - Wikipedia

Tag: Reverted

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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. 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 11101010 (~6 + 1). Note that 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>

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== Procedure ==

The following is the procedure for obtaining the two's complement of a given ''negative'' number in binary digits:

* Step 1: starting with the absolute binary representation of the number, with the leading bit being a sign bit;<ref>{{cite web|url=https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/DM3_TwosComplement_BP_9_22_14.pdf|title=Two’s Complement|website=University of Rochester Academic Success Center}}</ref>

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|+ Some special numbers to note

!Decimal

!Binary (8-bit)

|-

|align="right"| 127 ||0111 1111