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# Power of two

In mathematics, a power of two is a number of the form where is an integer, i.e. the result of exponentiation with number two as the base and integer as the exponent. [1]

139 relations: Ackermann function, Advanced Encryption Standard, Base (exponentiation), Binary number, Binary operation, Binary prefix, Binary relation, Binomial coefficient, Bit, Byte, C (programming language), C Sharp (programming language), C++, Cardinality, Classless Inter-Domain Routing, Color, Color depth, Computer monitor, Computer science, Conway chained arrow notation, Cross-polytope, Data Encryption Standard, Data type, Decimal, Disk storage, Divisor, Double exponential function, Double-precision floating-point format, Dyadic rational, Euclid's Elements, Exa-, Exabyte, Exbibyte, Exponentiation, Fermat number, Finite field, Fraction (mathematics), Fundamental theorem of arithmetic, Geometric progression, Gibibyte, Giga-, Gigabyte, Googol, Gould's sequence, Hypercube, Hyperoperation, Inchworm (song), Integer, Integer (computer science), International System of Units, ... Expand index (89 more) »

## Ackermann function

In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive.

The Advanced Encryption Standard (AES), also known by its original name Rijndael, is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001.

## Base (exponentiation)

In exponentiation, the base is the number b in an expression of the form bn.

## 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).

## Binary operation

In mathematics, a binary operation on a set is a calculation that combines two elements of the set (called operands) to produce another element of the set.

## Binary prefix

A binary prefix is a unit prefix for multiples of units in data processing, data transmission, and digital information, notably the bit and the byte, to indicate multiplication by a power of 2.

## Binary relation

In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

## Binomial coefficient

In mathematics, any of the positive integers that occurs as a coefficient in the binomial theorem is a binomial coefficient.

## Bit

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

## Byte

The byte is a unit of digital information that most commonly consists of eight bits, representing a binary number.

## 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.

## C Sharp (programming language)

C# (/si: ʃɑːrp/) is a multi-paradigm programming language encompassing strong typing, imperative, declarative, functional, generic, object-oriented (class-based), and component-oriented programming disciplines.

## C++

C++ ("see plus plus") is a general-purpose programming language.

## Cardinality

In mathematics, the cardinality of a set is a measure of the "number of elements of the set".

## Classless Inter-Domain Routing

Classless Inter-Domain Routing (CIDR) is a method for allocating IP addresses and IP routing.

## Color

Color (American English) or colour (Commonwealth English) is the characteristic of human visual perception described through color categories, with names such as red, orange, yellow, green, blue, or purple.

## Color depth

Color depth or colour depth (see spelling differences), also known as bit depth, is either the number of bits used to indicate the color of a single pixel, in a bitmapped image or video frame buffer, or the number of bits used for each color component of a single pixel.

## Computer monitor

A computer monitor is an output device which displays information in pictorial form.

## Computer science

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.

## Conway chained arrow notation

Conway chained arrow notation, created by mathematician John Horton Conway, is a means of expressing certain extremely large numbers.

## Cross-polytope

In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in n-dimensions.

## Data Encryption Standard

The Data Encryption Standard (DES) is a symmetric-key algorithm for the encryption of electronic data.

## Data type

In computer science and computer programming, a data type or simply type is a classification of data which tells the compiler or interpreter how the programmer intends to use the data.

## Decimal

The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary) is the standard system for denoting integer and non-integer numbers.

## Disk storage

Disk storage (also sometimes called drive storage) is a general category of storage mechanisms where data is recorded by various electronic, magnetic, optical, or mechanical changes to a surface layer of one or more rotating disks.

## Divisor

In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder.

## Double exponential function

A double exponential function is a constant raised to the power of an exponential function.

## Double-precision floating-point format

Double-precision floating-point format is a computer number format, usually occupying 64 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point.

In mathematics, a dyadic fraction or dyadic rational is a rational number whose denominator, when the ratio is in minimal (coprime) terms, is a power of two, i.e., a number of the form \frac where a is an integer and b is a natural number; for example, 1/2 or 3/8, but not 1/3.

## Euclid's Elements

The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.

## Exa-

Exa is a decimal unit prefix in the metric system denoting 1018 or.

## Exabyte

The exabyte is a multiple of the unit byte for digital information.

## Exbibyte

The exbibyte is a multiple of the unit byte for digital information.

## Exponentiation

Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.

## Fermat number

In mathematics a Fermat number, named after Pierre de Fermat who first studied them, is a positive integer of the form where n is a nonnegative integer.

## Finite field

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.

## Fraction (mathematics)

A fraction (from Latin fractus, "broken") represents a part of a whole or, more generally, any number of equal parts.

## Fundamental theorem of arithmetic

In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers and that, moreover, this representation is unique, up to (except for) the order of the factors.

## Geometric progression

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

## Gibibyte

The gibibyte is a multiple of the unit byte for digital information.

## Giga-

Giga is a unit prefix in the metric system denoting a factor of a (short-form) billion (109 or 000).

## Gigabyte

The gigabyte is a multiple of the unit byte for digital information.

## Googol

A googol is the large number 10100.

## Gould's sequence

Gould's sequence is an integer sequence named after Henry W. Gould that counts the odd numbers in each row of Pascal's triangle.

## Hypercube

In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.

## Hyperoperation

In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations) that starts with the unary operation of successor (n.

## Inchworm (song)

"Inchworm", also known as "The Inch Worm", is a song originally performed by Danny Kaye in the 1952 film Hans Christian Andersen.

## Integer

An integer (from the Latin ''integer'' meaning "whole")Integer&#x2009;'s first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

## Integer (computer science)

In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers.

## International System of Units

The International System of Units (SI, abbreviated from the French Système international (d'unités)) is the modern form of the metric system, and is the most widely used system of measurement.

An Internet Protocol address (IP address) is a numerical label assigned to each device connected to a computer network that uses the Internet Protocol for communication.

## IPv4

Internet Protocol version 4 (IPv4) is the fourth version of the Internet Protocol (IP).

IPv4 address exhaustion is the depletion of the pool of unallocated IPv4 addresses.

## IPv6

Internet Protocol version 6 (IPv6) is the most recent version of the Internet Protocol (IP), the communications protocol that provides an identification and location system for computers on networks and routes traffic across the Internet.

An Internet Protocol Version 6 address (IPv6 address) is a numerical label that is used to identify a network interface of a computer or a network node participating in an IPv6 computer network.

## Irrational number

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.

## Irrationality sequence

In mathematics, a sequence of positive integers an is called an irrationality sequence if it has the property that for every sequence xn of positive integers, the sum of the series exists (that is, it converges) and is an irrational number.

## Java (programming language)

Java is a general-purpose computer-programming language that is concurrent, class-based, object-oriented, and specifically designed to have as few implementation dependencies as possible.

## Key space (cryptography)

In cryptography, an algorithm's key space refers to the set of all possible permutations of a key.

## Kibibyte

The kibibyte is a multiple of the unit byte for quantities of digital information.

## Kilo-

Kilo is a decimal unit prefix in the metric system denoting multiplication by one thousand (103).

## Kilobyte

The kilobyte is a multiple of the unit byte for digital information.

## Knuth's up-arrow notation

In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976.

## Largest known prime number

The largest known prime number is 277,232,917 − 1, a number with 23,249,425 digits.

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

## Mebibyte

The mebibyte is a multiple of the unit byte for digital information.

## Mega-

Mega is a unit prefix in metric systems of units denoting a factor of one million (106 or 000).

## Megabyte

The megabyte is a multiple of the unit byte for digital information.

## Mersenne prime

In mathematics, a Mersenne prime is a prime number that is one less than a power of two.

## Microsoft Excel

Microsoft Excel is a spreadsheet developed by Microsoft for Windows, macOS, Android and iOS.

## 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.

## Multiplicative group of integers modulo n

In modular arithmetic, the integers coprime (relatively prime) to n from the set \ of n non-negative integers form a group under multiplication modulo n, called the multiplicative group of integers modulo n. Equivalently, the elements of this group can be thought of as the congruence classes, also known as residues modulo n, that are coprime to n. Hence another name is the group of primitive residue classes modulo n. In the theory of rings, a branch of abstract algebra, it is described as the group of units of the ring of integers modulo n. Here units refers to elements with a multiplicative inverse, which in this ring are exactly those coprime to n. This group, usually denoted (\mathbb/n\mathbb)^\times, is fundamental in number theory.

## Multiplicative order

In number theory, given an integer a and a positive integer n with gcd(a,n).

## Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

## Nimber

In mathematics, the nimbers, also called Grundy numbers, are introduced in combinatorial game theory, where they are defined as the values of heaps in the game Nim.

## Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

## Octave (electronics)

In electronics, an octave (symbol oct) is a doubling or halving of a frequency.

## Octet (computing)

The octet is a unit of digital information in computing and telecommunications that consists of eight bits.

## Pac-Man

, stylized as PAC-MAN, is an arcade game developed by Namco and first released in Japan as Puck Man in May 1980.

## Page (computer memory)

A page, memory page, or virtual page is a fixed-length contiguous block of virtual memory, described by a single entry in the page table.

## Pascal (programming language)

Pascal is an imperative and procedural programming language, which Niklaus Wirth designed in 1968–69 and published in 1970, as a small, efficient language intended to encourage good programming practices using structured programming and data structuring. It is named in honor of the French mathematician, philosopher and physicist Blaise Pascal. Pascal was developed on the pattern of the ALGOL 60 language. Wirth had already developed several improvements to this language as part of the ALGOL X proposals, but these were not accepted and Pascal was developed separately and released in 1970. A derivative known as Object Pascal designed for object-oriented programming was developed in 1985; this was used by Apple Computer and Borland in the late 1980s and later developed into Delphi on the Microsoft Windows platform. Extensions to the Pascal concepts led to the Pascal-like languages Modula-2 and Oberon.

## Pebibyte

The pebibyte is a multiple of the unit byte for digital information.

## Perfect number

In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum).

## Peta-

Peta is a decimal unit prefix in the metric system denoting multiplication by 1015.

## Petabyte

The petabyte is a multiple of the unit byte for digital information.

## Pierre de Fermat

Pierre de Fermat (Between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.

## Polite number

In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers.

## Power of 10

In mathematics, a power of 10 is any of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer).

## Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

## Processor register

In computer architecture, a processor register is a quickly accessible location available to a computer's central processing unit (CPU).

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.

## Regional Internet registry

A regional Internet registry (RIR) is an organization that manages the allocation and registration of Internet number resources within a particular region of the world.

## RGB color model

The RGB color model is an additive color model in which red, green and blue light are added together in various ways to reproduce a broad array of colors.

## Series (mathematics)

In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.

## Signed number representations

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

## Signedness

In computing, signedness is a property of data types representing numbers in computer programs.

## Smooth number

In number theory, a smooth (or friable) number is an integer which factors completely into small prime numbers.

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

## Sum-free sequence

In mathematics, a sum-free sequence is an increasing positive integer sequence such that for each k, n_k cannot be represented as a sum of any subset of the preceding elements of the same sequence.

## Tebibyte

The tebibyte is a multiple of the unit byte for digital information.

## Tera-

Tera is a unit prefix in the metric system denoting multiplication by 1012 or (one trillion short scale; one billion long scale).

## Terabyte

The terabyte is a multiple of the unit byte for digital information.

## Tetration

In mathematics, tetration (or hyper-4) is the next hyperoperation after exponentiation, and is defined as iterated exponentiation.

## The Legend of Zelda (video game)

The Legend of Zelda is an action-adventure video game developed and published by Nintendo and designed by Shigeru Miyamoto and Takashi Tezuka.

## 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.

## Universally unique identifier

A universally unique identifier (UUID) is a 128-bit number used to identify information in computer systems.

## Unix time

Unix time (also known as POSIX time or UNIX Epoch time) is a system for describing a point in time, defined as the number of seconds that have elapsed since 00:00:00 Coordinated Universal Time (UTC), Thursday, 1 January 1970,.

## Vertex (geometry)

In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.

## Video game

A video game is an electronic game that involves interaction with a user interface to generate visual feedback on a video device such as a TV screen or computer monitor.

## Wheat and chessboard problem

The wheat and chessboard problem (sometimes expressed in terms of rice grains) is a mathematical problem expressed in textual form as: The problem may be solved using simple addition.

## Word (computer architecture)

In computing, a word is the natural unit of data used by a particular processor design.

## X86

x86 is a family of backward-compatible instruction set architectures based on the Intel 8086 CPU and its Intel 8088 variant.

## Year 2038 problem

The Year 2038 problem relates to representing time in many digital systems as number of seconds passed since 1 January 1970 and storing it as a signed 32-bit integer.

## Yobibyte

The yobibyte is a multiple of the unit byte for digital information.

## Yotta-

Yotta is the largest decimal unit prefix in the metric system, denoting a factor of 1024 or; that is, one million million million million, or one septillion.

## Yottabyte

The yottabyte is a multiple of the unit byte for digital information.

## Zebibyte

The zebibyte is a multiple of the unit byte for digital information.

## Zetta-

Zetta is a decimal unit prefix in the metric system denoting a factor of 1021 or.

## Zettabyte

The zettabyte is a multiple of the unit byte for digital information.

## 1

1 (one, also called unit, unity, and (multiplicative) identity) is a number, numeral, and glyph.

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## 1/2 + 1/4 + 1/8 + 1/16 + ⋯

In mathematics, the infinite series is an elementary example of a geometric series that converges absolutely.

## 1/4 + 1/16 + 1/64 + 1/256 + ⋯

In mathematics, the infinite series is an example of one of the first infinite series to be summed in the history of mathematics; it was used by Archimedes circa 250–200 BC.

## 1024 (number)

1024 is the natural number following 1023 and preceding 1025.

## 128 (number)

128 (one hundred twenty-eight) is the natural number following 127 and preceding 129.

## 16 (number)

16 (sixteen) is the natural number following 15 and preceding 17.

## 16-bit

16-bit microcomputers are computers in which 16-bit microprocessors were the norm.

## 2

2 (two) is a number, numeral, and glyph.

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## 24-bit

Notable 24-bit machines include the CDC 924 – a 24-bit version of the CDC 1604, CDC lower 3000 series, SDS 930 and SDS 940, the ICT 1900 series, and the Datacraft minicomputers/Harris H series.

## 256 (number)

256 (two hundred fifty-six) is the natural number following 255 and preceding 257.

## 257 (number)

257 (two hundred fifty-seven) is the natural number following 256 and preceding 258.

## 31 (number)

31 (thirty-one) is the natural number following 30 and preceding 32.

## 32 (number)

32 (thirty-two) is the natural number following 31 and preceding 33.

## 32-bit

32-bit microcomputers are computers in which 32-bit microprocessors are the norm.

## 4

4 (four) is a number, numeral, and glyph.

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## 512 (number)

512 (five hundred twelve) is the natural number following 511 and preceding 513.

## 64 (number)

64 (sixty-four) is the natural number following 63 and preceding 65.

## 64-bit computing

In computer architecture, 64-bit computing is the use of processors that have datapath widths, integer size, and memory address widths of 64 bits (eight octets).

## 65,536

65536 is the natural number following 65535 and preceding 65537.

## 8

8 (eight) is the natural number following 7 and preceding 9.

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## References

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