Binary arithmetic

system that represents numeric values using two symbols; 0 or 1

The bit is the most basic unit of information in computing and digital communication. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represented as , but other representations such as true/false, yes/no, on/off, and +/− are also widely used.

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 reason it is the smallest addressable unit of memory in many computer architectures. To disambiguate arbitrarily sized bytes from the common 8-bit definition, network protocol documents such as the Internet Protocol () refer to an 8-bit byte as an octet.

Hexadecimal (hex for short) is a positional numeral system for representing a numeric value as base 16. For the most common convention, a digit is represented as "0" to "9" like for decimal and as a letter of the alphabet from "A" to "F" (either upper or lower case) for the digits with decimal value 10 to 15.

Octal is a numeral system for representing a numeric value as base 8. Generally, an octal digit is represented as "0" to "7" with the same value as for decimal but with each place a power of 8. For example:

digital circuit that performs addition of numbers

class of binary encodings of decimal numbers where each decimal digit is represented by a fixed number of bits, usually four or eight. Special bit patterns are sometimes used for a sign or for other indications

bit added to a binary string to ensure that the sum of the bit values is even or odd; used as an error detecting code

ordering of binary strings such that subsequent strings differ only in one bit

type of hash function used to detect errors in data storage or transmission

operation on binary numbers, and number representation based on this operation

computer operation that operates on values at the level of their individual bits

two raised to an integer power

mathematical function

any mathematical function with Boolean arguments and result

value obtained by inverting all the bits in the binary representation of the number

IEEE Standard for Floating-Point Arithmetic

bit position in a fixed-width binary number

computer format for representing real numbers

type of shift register in computing

64-bit computer number format

algorithm invented by Andrew D. Booth

bit position in a binary number

Simple algorithm to swap binary values

mathematical operation

data type

32-bit computer number format

clock that displays the time of day in a binary format

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-complementary binary-coded decimal (BCD) code and numeral system. It is a biased representation. Excess-3 code was used on some older computers as well as in cash registers and hand-held portable electronic calculators of the 1970s, among other uses.

infinite series

variant of the doubly linked list data structure used in computer programming

electronic circuit used to multiply binary numbers

16-bit computer number format

bit indicating the sign of a number

finger-counting system

digital circuit that implements a bit-shift operation

In electronics, a subtractor is a digital circuit that performs subtraction of numbers, and it can be designed using the same approach as that of an adder. The binary subtraction process is summarized below. As with an adder, in the general case of calculations on multi-bit numbers, three bits are involved in performing the subtraction for each bit of the difference: the minuend (X_{i}), subtrahend (Y_{i}), and a borrow in from the previous (less significant) bit order position (B_{i}). The outputs are the difference bit (D_{i}) and borrow bit B_{i+1}. The subtractor is best understood by cons

bit-level computer operation

operation of increasing the number of bits of a number while preserving the number's sign and value

128-bit computer number format

method for signed number representation

floating-point number format optimized for machine learning

algorithm for quotient and remainder of integer division

(also denoted \mathbb F_2, or \mathbb Z/2\mathbb Z) is the finite field with two elements.

shift operator in computer programming

convention to identify bit positions within a byte, word, or bit string

Binary/decimal adjustment flag bit in some computer processors

type of digital adder