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# Two's complement

Two's complement is a mathematical operation on binary numbers, best known for its role in computing as a method of signed number representation. [1]

65 relations: Absolute value, Adding machine, Addition, Additive inverse, Bill Gosper, Binary number, Bit, Bit array, Bit numbering, Bitwise operation, Booth's multiplication algorithm, Branch (computer science), C (programming language), Carry flag, Carry-lookahead adder, CDC 6600, Computing, 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, Integer overflow, John von Neumann, Lexicographical order, LINC, Mathematical joke, Mechanical calculator, Method of complements, Metric space, MIT Computer Science and Artificial Intelligence Laboratory, Modular arithmetic, Multiplication, Negative flag, Nibble, Offset binary, Ones' complement, Operation (mathematics), Overflow flag, P-adic number, ... Expand index (15 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 basic operations of arithmetic; the others are subtraction, multiplication and division.

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

## Bill Gosper

Ralph William Gosper Jr. (born April 26, 1943), known as Bill Gosper, is an American mathematician and programmer.

## Binary number

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

## Bit

The bit (a portmanteau of binary digit) is a basic unit of information used in computing and digital communications.

## Bit array

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

## Bit numbering

In computing, bit numbering (or sometimes bit endianness) is the convention used to identify the bit positions in a binary number or a container for such a value.

## 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 branch is an instruction in a computer program that can cause a computer to begin executing a different instruction sequence and thus deviate from its default behavior of executing instructions in order.

## 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 of the 6000 series of mainframe computer systems manufactured by Control Data Corporation.

## Computing

Computing is any goal-oriented activity requiring, benefiting from, or creating computers.

## Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily 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 or monogenous group is a group that is generated by a single element.

## Data General Nova

The Data General Nova is a series of 16-bit minicomputers released by the American company Data General.

## 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 1950s 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

The electronic delay storage automatic calculator (EDSAC) was an early British computer.

## Exclusive or

Exclusive or or exclusive disjunction is a logical operation that outputs true only when 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) is 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, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.

## 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

The International Business Machines Corporation (IBM) is an American multinational technology company headquartered in Armonk, New York, United States, with operations in over 170 countries.

## 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) is a family of mainframe computer systems that was announced by IBM on April 7, 1964, and delivered between 1965 and 1978.

## Integer overflow

In computer programming, an integer overflow occurs when an arithmetic operation attempts to create a numeric value that is outside of the range that can be represented with a given number of bits – either larger than the maximum or lower than the minimum representable value.

## John von Neumann

John von Neumann (Neumann János Lajos,; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, and polymath.

## 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 words are alphabetically ordered based on the alphabetical order of their component letters.

## LINC

The LINC (Laboratory INstrument Computer) is a 12-bit, 2048-word transistorized computer.

## 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, is 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 institute 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 (plural moduli).

## Multiplication

Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") 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 in which the most significant bit was set.

## Nibble

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

## Offset binary

Offset binary, also referred to as excess-K, excess-N, excess code or biased representation, 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)

In mathematics, an operation is a calculation from zero or more input values (called operands) to an output value.

## Overflow flag

In computer processors, the overflow flag (sometime 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 different way from the extension of the rational number system to the real and complex number systems.

## PDP-1

The PDP-1 (Programmed Data Processor-1) is the first computer in Digital Equipment Corporation's PDP series and was first produced in 1959.

## 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 PDP-8 was a 12-bit minicomputer produced by Digital Equipment Corporation (DEC).

## Python (programming language)

Python is an interpreted high-level programming language for general-purpose programming.

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), 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.

## Status register

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

## Subtraction

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

## UNIVAC 1100/2200 series

The UNIVAC 1100/2200 series is a series of compatible 36-bit computer systems, beginning with the UNIVAC 1107 in 1962, initially made by Sperry Rand.

## 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, 6502, and numerous others).

## 1 + 2 + 4 + 8 + ⋯

In mathematics, is the infinite series whose terms are the successive powers of two.

## References

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