# Category: Binary arithmetic

Permute instruction
Permute (and Shuffle) instructions, part of bit manipulation as well as vector processing, copy unaltered contents from a source array to a destination array, where the indices are specified by a seco
Single-precision floating-point format
Single-precision floating-point format (sometimes called FP32 or float32) is a computer number format, usually occupying 32 bits in computer memory; it represents a wide dynamic range of numeric value
XOR swap algorithm
In computer programming, the exclusive or swap (sometimes shortened to XOR swap) is an algorithm that uses the exclusive or bitwise operation to swap the values of two variables without using the temp
Two's complement
Two's complement is a mathematical operation to reversibly convert a positive binary number into a negative binary number with equivalent (but negative) value, using the binary digit with the greatest
Excess-2048
No description available.
Cyclic redundancy check
A cyclic redundancy check (CRC) is an error-detecting code commonly used in digital networks and storage devices to detect accidental changes to digital data. Blocks of data entering these systems get
Excess-976
No description available.
Bit numbering
In computing, bit numbering is the convention used to identify the bit positions in a binary number.
Excess-16384
No description available.
Excess-256
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Excess-64
No description available.
Barrel shifter
A barrel shifter is a digital circuit that can shift a data word by a specified number of bits without the use of any sequential logic, only pure combinational logic, i.e. it inherently provides a bin
In digital circuits, an adder–subtractor is a circuit that is capable of adding or subtracting numbers (in particular, binary). Below is a circuit that adds or subtracts depending on a control signal.
Bit-length
Bit-length or bit width is the number of binary digits, called bits, necessary to represent an integer as a binary number. Formally, the bit-length of a natural number is a function, bitLength(n), of
A carry-save adder is a type of digital adder, used to efficiently compute the sum of three or more binary numbers. It differs from other digital adders in that it outputs two (or more) numbers, and t
Find first set
In computer software and hardware, find first set (ffs) or find first one is a bit operation that, given an unsigned machine word, designates the index or position of the least significant bit set to
Power of two
A power of two is a number of the form 2n where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent. In a context where only integers are c
Densely packed decimal
Densely packed decimal (DPD) is an efficient method for binary encoding decimal digits. The traditional system of binary encoding for decimal digits, known as binary-coded decimal (BCD), uses four bit
Binary Angular Measurement System
No description available.
Carry-less product
The carry-less product of two binary numbersis the result of carry-less multiplication of these numbers.This operation conceptually works like long multiplicationexcept for the fact that the carryis d
Division algorithm
A division algorithm is an algorithm which, given two integers N and D, computes their quotient and/or remainder, the result of Euclidean division. Some are applied by hand, while others are employed
The serial binary adder or bit-serial adder is a digital circuit that performs binary addition bit by bit. The serial full adder has three single-bit inputs for the numbers to be added and the carry i
Double-precision floating-point format
Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide dynamic range of numeric
Binary clock
A binary clock is a clock that displays the time of day in a binary format. Originally, such clocks showed each decimal digit of sexagesimal time as a binary value, but presently binary clocks also ex
Bit
The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. Th
Least significant bit
No description available.
Double dabble
In computer science, the double dabble algorithm is used to convert binary numbers into binary-coded decimal (BCD) notation. It is also known as the shift-and-add-3 algorithm, and can be implemented u
Excess-127
No description available.
Excess-3
Excess-3, 3-excess or 10-excess-3 binary code (often abbreviated as XS-3, 3XS or X3), shifted binary or Stibitz code (after George Stibitz, who built a relay-based adding machine in 1937) is a self-co
Linear-feedback shift register
In computing, a linear-feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state. The most commonly used linear function of single bits is exclusive
Excess-1024
No description available.
Biased representation (arithmetics)
No description available.
Bit manipulation
Bit manipulation is the act of algorithmically manipulating bits or other pieces of data shorter than a word. Computer programming tasks that require bit manipulation include low-level device control,
Excess-15
No description available.
The Adjust flag (AF) is a CPU flag in the FLAGS register of all x86-compatible CPUs, and the preceding 8080-family; it is also called the Auxiliary flag and the Auxiliary Carry flag (AC, though this m
Binary number
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" (one). The ba
1 + 2 + 4 + 8 + ⋯
In mathematics, 1 + 2 + 4 + 8 + ⋯ is the infinite series whose terms are the successive powers of two. As a geometric series, it is characterized by its first term, 1, and its common ratio, 2. As a se
Excess-128
No description available.
Byte
The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this
Binary angular measurement
The terms binary angular measurement (BAM) and binary angular measurement system (BAMS) refer to certain methodologies for representing and manipulating angles using binary (base 2) fixed-point arithm
Split octal
Syllabic octal and split octal are two similar notations for 8-bit and 16-bit octal numbers, respectively, used in some historical contexts.
Excess-32
No description available.
Finger binary
Finger binary is a system for counting and displaying binary numbers on the fingers of either or both hands. Each finger represents one binary digit or bit. This allows counting from zero to 31 using
Stibitz code
No description available.
XS-3 code
No description available.
Ones' complement
The ones' complement of a binary number is the value obtained by inverting all the bits in the binary representation of the number (swapping 0s and 1s). The name "ones' complement" (note this is posse
Sign bit
In computer science, the sign bit is a bit in a signed number representation that indicates the sign of a number. Although only signed numeric data types have a sign bit, it is invariably located in t
BIT predicate
In mathematics and computer science, the BIT predicate or Ackermann coding, sometimes written BIT(i, j), is a predicate that tests whether the jth bit of the number i is 1, when i is written in binary
A leading-one detector is an electronic circuit commonly found in central processing units and especially their arithmetic logic units (ALUs). It is used to detect whether the leading bit in a compute
Bitwise operations in C
In the C programming language, operations can be performed on a bit level using bitwise operators. Bitwise operations are contrasted by byte-level operations which characterize the bitwise operators'
In computer science, a mask or bitmask is data that is used for bitwise operations, particularly in a bit field. Using a mask, multiple bits in a byte, nibble, word, etc. can be set either on or off,
Gray code
The reflected binary code (RBC), also known as reflected binary (RB) or Gray code after Frank Gray, is an ordering of the binary numeral system such that two successive values differ in only one bit (
No description available.
Excess-1023
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Excess-16383
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Hertz encoding
No description available.
Excess-weighted code
No description available.
Binary multiplier
A binary multiplier is an electronic circuit used in digital electronics, such as a computer, to multiply two binary numbers. A variety of computer arithmetic techniques can be used to implement a dig
Excess-25
No description available.
IEEE 754
The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). Th
In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of 16. Unlike the decimal system r
Excess-11
No description available.
Microsoft Binary Format
In computing, Microsoft Binary Format (MBF) is a format for floating-point numbers which was used in Microsoft's BASIC language products, including MBASIC, GW-BASIC and QuickBASIC prior to version 4.0
Arithmetic shift
In computer programming, an arithmetic shift is a shift operator, sometimes termed a signed shift (though it is not restricted to signed operands). The two basic types are the arithmetic left shift an
Boolean function
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). Alternative names are switching function, use
Most significant bit
No description available.
Half-carry flag
A half-carry flag (also known as an auxiliary flag or decimal adjust flag) is a condition flag bit in the status register of many CPU families, such as the Intel 8080, Zilog Z80, the x86, and the Atme
In computing, quadruple precision (or quad precision) is a binary floating point–based computer number format that occupies 16 bytes (128 bits) with precision at least twice the 53-bit double precisio
Negative and non-negative in binary
No description available.
Octuple-precision floating-point format
In computing, octuple precision is a binary floating-point-based computer number format that occupies 32 bytes (256 bits) in computer memory. This 256-bit octuple precision is for applications requiri
Parity bit
A parity bit, or check bit, is a bit added to a string of binary code. Parity bits are a simple form of error detecting code. Parity bits are generally applied to the smallest units of a communication
Moser–de Bruijn sequence
In number theory, the Moser–de Bruijn sequence is an integer sequence named after Leo Moser and Nicolaas Govert de Bruijn, consisting of the sums of distinct powers of 4, or equivalently the numbers w
Excess-6
No description available.
Binary digit
No description available.
Logical shift
In computer science, a logical shift is a bitwise operation that shifts all the bits of its operand. The two base variants are the logical left shift and the logical right shift. This is further modul
Octal
The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7, that is to say 10octal represents eight and 100octal represents sixty-four. However, English, like
Excess-500
No description available.
Booth's multiplication algorithm
Booth's multiplication algorithm is a multiplication algorithm that multiplies two signed binary numbers in two's complement notation. The algorithm was invented by Andrew Donald Booth in 1950 while d
Subtractor
In electronics, a subtractor – a digital circuit that performs subtraction of numbers – can be designed using the same approach as that of an adder. The binary subtraction process is summarized below.
Binary logarithm
In mathematics, the binary logarithm (log2 n) is the power to which the number 2 must be raised to obtain the value n. That is, for any real number x, For example, the binary logarithm of 1 is 0, the
Chen–Ho encoding
Chen–Ho encoding is a memory-efficient alternate system of binary encoding for decimal digits. The traditional system of binary encoding for decimal digits, known as binary-coded decimal (BCD), uses f
Binary degree
No description available.
Binary-coded decimal
In computing and electronic systems, binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each digit is represented by a fixed number of bits, usually four or eight. Some
No description available.
An adder, or summer, is a digital circuit that performs addition of numbers. In many computers and other kinds of processors adders are used in the arithmetic logic units (ALUs). They are also used in
Bfloat16 floating-point format
The bfloat16 (Brain Floating Point) floating-point format is a computer number format occupying 16 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating rad
Offset binary
Offset binary, also referred to as excess-K, excess-N, excess-e, excess code or biased representation, is a method for signed number representation where a signed number n is represented by the bit pa
Half-precision floating-point format
In computing, half precision (sometimes called FP16) is a binary floating-point computer number format that occupies 16 bits (two bytes in modern computers) in computer memory. It is intended for stor
Excess-129
No description available.
Excess-250
No description available.
Fibbinary number
In mathematics, the fibbinary numbers are the numbers whose binary representation does not contain two consecutive ones. That is, they are sums of distinct and non-consecutive powers of two.
GF(2)
GF(2) (also denoted , Z/2Z or ) is the finite field of two elements (GF is the initialism of Galois field, another name for finite fields). Notations Z2 and may be encountered although they can be con
An XOR linked list is a type of data structure used in computer programming. It takes advantage of the bitwise XOR operation to decrease storage requirements for doubly linked lists.
Redundant binary representation
A redundant binary representation (RBR) is a numeral system that uses more bits than needed to represent a single binary digit so that most numbers have several representations. An RBR is unlike usual
Division by two
In mathematics, division by two or halving has also been called mediation or dimidiation. The treatment of this as a different operation from multiplication and division by other numbers goes back to
Excess-123
No description available.
Fixed-point arithmetic
In computing, fixed-point is a method of representing fractional (non-integer) numbers by storing a fixed number of digits of their fractional part. Dollar amounts, for example, are often stored with
Excess-512
No description available.
Sign extension
Sign extension (abbreviated as sext) is the operation, in computer arithmetic, of increasing the number of bits of a binary number while preserving the number's sign (positive/negative) and value. Thi
Bitwise operation
In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits. It is a fast and simple action,