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# Two's complement

Two's complement is a mathematical operation on binary numbers, as well as a binary signed number representation based on this operation. [1]

64 relations: Absolute value, Adding machine, Addition, Additive inverse, Arithmetic overflow, Bill Gosper, Binary number, Bit, Bit array, Bitwise operation, Booth's multiplication algorithm, Branch (computer science), C (programming language), Carry flag, Carry-lookahead adder, CDC 6600, Computer, Continuous function, Convention (norm), Cyclic group, Data General Nova, Digital Equipment Corporation, Divergent series, Division algorithm, Electronic Delay Storage Automatic Calculator, Exclusive or, First Draft of a Report on the EDVAC, Group action, HAKMEM, IBM, IBM 700/7000 series, IBM System/360, John von Neumann, Least significant bit, Lexicographical order, Mathematical joke, Mechanical calculator, Method of complements, Metric space, MIT Computer Science and Artificial Intelligence Laboratory, Modular arithmetic, Most significant bit, Multiplication, Negative flag, Nibble, Offset binary, Ones' complement, Operation (mathematics), Overflow flag, P-adic number, ... Expand index (14 more) »

## Absolute value

In mathematics, the absolute value (or modulus) of a real number is the non-negative value of without regard to its sign.

An adding machine was a class of mechanical calculator, usually specialized for bookkeeping calculations.

Addition (often signified by the plus symbol "+") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.

In mathematics, the additive inverse of a number is the number that, when added to, yields zero.

## Arithmetic overflow

The term arithmetic overflow or simply overflow has the following meanings.

## Bill Gosper

Ralph William Gosper, Jr. (born 1943), known as Bill Gosper, is an American mathematician and programmer from Pennsauken Township, New Jersey.

## Binary number

In mathematics and digital electronics, a binary number is a number expressed in the binary numeral system, or base-2 numeral system, which represents numeric values using two different symbols: typically 0 (zero) and 1 (one).

## Bit

A bit is the basic unit of information in computing and digital communications.

## Bit array

A bit array (also known as bitmap, bitset, bit string, or bit vector) is an array data structure that compactly stores bits.

## Bitwise operation

In digital computer programming, a bitwise operation operates on one or more bit patterns or binary numerals at the level of their individual bits.

## Booth's multiplication algorithm

Booth's multiplication algorithm is a multiplication algorithm that multiplies two signed binary numbers in two's complement notation.

## Branch (computer science)

A computer program is, fundamentally, the use of instructions executed by a computer.

## C (programming language)

C (as in the letter ''c'') is a general-purpose, imperative computer programming language, supporting structured programming, lexical variable scope and recursion, while a static type system prevents many unintended operations.

## Carry flag

In computer processors the carry flag (usually indicated as the C flag) is a single bit in a system status (flag) register used to indicate when an arithmetic carry or borrow has been generated out of the most significant ALU bit position.

## CDC 6600

The CDC 6600 was the flagship mainframe supercomputer of the 6000 series of computer systems manufactured by Control Data Corporation.

## Computer

A computer is a general-purpose device that can be programmed to carry out a set of arithmetic or logical operations automatically.

## Continuous function

In mathematics, a continuous function is, roughly speaking, a function for which small changes in the input result in small changes in the output.

## Convention (norm)

A convention is a set of agreed, stipulated, or generally accepted standards, norms, social norms, or criteria, often taking the form of a custom.

## Cyclic group

In algebra, a cyclic group is a group that is generated by a single element.

## Data General Nova

The Data General Nova was a popular 16-bit minicomputer built by the American company Data General starting in 1969.

## Digital Equipment Corporation

Digital Equipment Corporation, also known as DEC and using the trademark Digital, was a major American company in the computer industry from the 1960s to the 1990s.

## Divergent series

In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit.

## Division algorithm

A division algorithm is an algorithm which, given two integers N and D, computes their quotient and/or remainder, the result of division.

## Electronic Delay Storage Automatic Calculator

Electronic Delay Storage Automatic Calculator (EDSAC) was an early British computer.

## Exclusive or

Exclusive disjunction or exclusive or is a logical operation that outputs true only when both inputs differ (one is true, the other is false).

## First Draft of a Report on the EDVAC

The First Draft of a Report on the EDVAC (commonly shortened to First Draft) was an incomplete 101-page document written by John von Neumann and distributed on June 30, 1945 by Herman Goldstine, security officer on the classified ENIAC project.

## Group action

In mathematics, a symmetry group is an abstraction used to describe the symmetries of an object.

## HAKMEM

HAKMEM, alternatively known as AI Memo 239, is a February 1972 "memo" (technical report) of the MIT AI Lab containing a wide variety of hacks, including useful and clever algorithms for mathematical computation, some number theory and schematic diagrams for hardware — in Guy L. Steele's words, "a bizarre and eclectic potpourri of technical trivia".

## IBM

International Business Machines Corporation (commonly referred to as IBM) is an American multinational technology and consulting corporation, with headquarters in Armonk, New York.

## IBM 700/7000 series

The IBM 700/7000 series is a series of large-scale (mainframe) computer systems that were made by IBM through the 1950s and early 1960s.

## IBM System/360

The IBM System/360 (S/360) was a mainframe computer system family announced by IBM on April 7, 1964, and delivered between 1965 and 1978.

## John von Neumann

John von Neumann (Hungarian: Neumann János,; December 28, 1903 – February 8, 1957) was a Hungarian-American pure and applied mathematician, physicist, inventor, polymath, and polyglot.

## Least significant bit

In computing, the least significant bit (LSB) is the bit position in a binary integer giving the units value, that is, determining whether the number is even or odd.

## Lexicographical order

In mathematics, the lexicographic or lexicographical order (also known as lexical order, dictionary order, alphabetical order or lexicographic(al) product) is a generalization of the way the alphabetical order of words is based on the alphabetical order of their component letters.

## Mathematical joke

A mathematical joke is a form of humor which relies on aspects of mathematics or a stereotype of mathematicians to derive humor.

## Mechanical calculator

A mechanical calculator, or calculating machine, was a mechanical device used to perform automatically the basic operations of arithmetic.

## Method of complements

In mathematics and computing, the method of complements is a technique used to subtract one number from another using only addition of positive numbers.

## Metric space

In mathematics, a metric space is a set for which distances between all members of the set are defined.

## MIT Computer Science and Artificial Intelligence Laboratory

MIT Computer Science and Artificial Intelligence Laboratory (CSAIL) is a research laboratory at the Massachusetts Institute of Technology formed by the 2003 merger of the Laboratory for Computer Science and the Artificial Intelligence Laboratory.

## Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus.

## Most significant bit

In computing, the most significant bit (MSB, also called the high-order bit) is the bit position in a binary number having the greatest value.

## Multiplication

Multiplication (often denoted by the cross symbol "×", by a point "·" or by the absence of symbol) is one of the four elementary, mathematical operations of arithmetic; with the others being addition, subtraction and division.

## Negative flag

In a computer processor the negative flag or sign flag is a single bit in a system status (flag) register used to indicate whether the result of the last mathematical operation resulted in a value whose most significant bit was set.

## Nibble

In computing, a nibble (often nybble or even nyble to match the vowels of byte) is a four-bit aggregation, or half an octet.

## Offset binary

Offset binary, also referred to as excess-K, is a digital coding scheme where all-zero corresponds to the minimal negative value and all-one to the maximal positive value.

## Ones' complement

The ones' complement of a binary number is defined as the value obtained by inverting all the bits in the binary representation of the number (swapping 0s for 1s and vice versa).

## Operation (mathematics)

The general operation as explained on this page should not be confused with the more specific operators on vector spaces.

## Overflow flag

In computer processors, the overflow flag (sometimes called V flag) is usually a single bit in a system status register used to indicate when an arithmetic overflow has occurred in an operation, indicating that the signed two's-complement result would not fit in the number of bits used for the operation (the ALU width).

In mathematics the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a way different from the extension of the rational number system to the real and complex number systems.

## PDP-11

The PDP-11 is a series of 16-bit minicomputers sold by Digital Equipment Corporation (DEC) from 1970 into the 1990s, one of a succession of products in the PDP series.

## PDP-6

The PDP-6 (Programmed Data Processor-6) was a computer model developed by Digital Equipment Corporation (DEC) in 1963.

## PDP-8

The 12-bit PDP-8, produced by Digital Equipment Corporation (DEC), is the first successful commercial minicomputer.

In mathematical numeral systems, the radix or base is the number of unique digits, including zero, used to represent numbers in a positional numeral system.

## Relational operator

In computer science, a relational operator is a programming language construct or operator that tests or defines some kind of relation between two entities.

## Russian State University for the Humanities

The Russian State University for the Humanities (RSUH, RGGU; translit. Rossijskij gosudarstvennyj gumanitarnyj universitet, RGGU), is a university in Moscow, Russia with over 14,000 students.

## Sign bit

In computer science, the sign bit is a bit in a signed number representation that indicates the sign of a number.

## Signed number representations

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

## Signed zero

Signed zero is zero with an associated sign.

## Status register

A status register, flag register, or condition code register is a collection of status flag bits for a processor.

## Subtraction

Subtraction is a mathematical operation that represents the operation of removing objects from a collection.

## Zero flag

The Zero Flag is a single bit flag that is a central feature on most conventional CPU architectures (including x86, ARM, PDP-11, 68000 and numerous others).

## 0 (number)

0 (zero; BrE: or AmE) is both a number and the numerical digit used to represent that number in numerals.

## 1 + 2 + 4 + 8 + ⋯

In mathematics, 1 + 2 + 4 + 8 + … is the infinite series whose terms are the successive powers of two.

## References

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