In mathematics, a power of two is any of the nonnegative integer powers of the number two; in other words, two times itself a certain number of times. Note that one is a power (the zeroth power) of two. Written in binary, a power of two always has the form 10000...0, just like a power of ten in the decimal system. Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations by or about: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero. ... In mathematics, exponentiation is a process generalized from repeated multiplication, in much the same way that multiplication is a process generalized from repeated addition. ... 2 (two) is the natural number following 1 and preceding 3. ... The binary or base-two numeral system is a system for representing numbers in which a radix of two is used; that is, each digit in a binary numeral may have either of two different values. ... Decimal, or less commonly, denary, usually refers to the base 10 numeral system. ...

Because two is the base of the binary system, powers of two are important to computer science. Specifically, two to the power of n is the number of ways the bits in a binary integer of length n can be arranged, and thus numbers that are one less than a power of two denote the upper bounds of integers in binary computers (one less because 0, not 1, is used as the lower bound). As a consequence, numbers of this form show up frequently in computer software. As one example, in the video game The Legend of Zelda for the 8-bit Nintendo, one can only hold 255 rupees at one time - the result of a byte, which is 8 bits long, being used to store the number, giving a maximum value of 2⁸-1 = 255. Wikibooks Wikiversity has more about this subject: School of Computer Science Open Directory Project: Computer Science Collection of Computer Science Bibliographies Belief that title science in computer science is inappropriate Categories: Computer science | Academic disciplines ... A bit (abbreviated b) is the most basic information unit used in computing and information theory. ... In computer science, the term integer is used to refer to any data type which can represent some subset of the mathematical integers. ... A computer game is a game composed of a computer-controlled virtual universe that players interact with in order to achieve a defined goal or set of goals. ... This article is about the first game in the series. ... The Nintendo Entertainment System (North America, Europe, and Australia) The Nintendo Entertainment System, or NES, is an 8-bit video game console released by Nintendo in North America, Europe and Australia. ... This article is about the number 255. ... Rupees from Zelda 1 and 3 Rupees are the unit of currency in the fictional land of Hyrule in the Legend of Zelda series of video games, acquired primarily by defeating enemies, by cutting tall grasses or bushes, or from treasure chests, and used primarily to purchase items in shops. ... This article refers to the unit of binary information. ...

Powers of two also measure computer memory. A byte is eight (2³) bits, and a kilobyte (some prefer the word kibibyte) is 1 024 (2¹⁰) bytes. Nearly all processor registers have sizes that are powers of two (32 being currently used in most personal computers). A kibibyte (a contraction of kilo binary byte) is a unit of information or computer storage, commonly abbreviated KiB (never kiB). 1 kibibyte = 210 bytes = 1 024 bytes The kibibyte is closely related to the kilobyte, which can be used either as a synonym for kibibyte or to refer to... In computer architecture, a processor register is a small amount of very fast computer memory used to speed the execution of computer programs by providing quick access to commonly used values—typically, the values being in the midst of a calculation at a given point in time. ...

Powers of two occur in a range of other places as well. For many disk drives, at least one of the sector size, number of sectors per track, and number of tracks per surface is a power of two. The logical block size is almost always a power of two. Disk Drive is the afternoon show on CBC Radio Two. ...

Numbers which are not powers of two occur in a number of situations such as video resolutions, but they are often the sum or product of only two or three powers of two, or powers of two minus one. For example, 640 = 512 + 128, and 480 = 32 × 15. Put another way, they have fairly regular bit patterns.

A prime number that is one less than a power of two is called a Mersenne prime. For example, the prime number 31 is a Mersenne prime because it is 1 less than 32 (2⁵). In mathematics, a prime number (or prime) is a natural number greater than one whose only positive divisors are one and itself. ... In mathematics, a Mersenne prime is a prime number that is one less than a power of two. ... 31 is the natural number following 30 and preceding 32. ...

The first forty powers of two

2 (two) is the natural number following 1 and preceding 3. ... 4 (four) is a number, numeral, and glyph. ... 8 (eight) is the natural number following 7 and preceding 9. ... 16 (sixteen) is the natural number following 15 and preceding 17. ... 32 is the natural number following 31 and preceding 33. ... 64 is the natural number following 63 and preceding 65. ... 128 is the natural number following 127 and preceding 129. ... 256 (two hundred [and] fifty-six, CCLVI) is the natural number following 255 and preceding 257. ... 1024 is the natural number following 1023 and preceding 1025. ...

Powers of two whose exponents are powers of two

Because modern memory cells and registers often hold a number of bits which is a power of two, the most frequent
powers of two to appear are those whose exponent is also a power of two.  –   A short list of some of these follows :

Several of these numbers represent the number of values representable using common computer data types. For example, a 32-bit word consisting of 4 bytes can represent 2³² distinct values, which can either be regarded as mere bit-patterns, or are more commonly interpreted as the unsigned numbers from 0 to 2³²-1, or as the range of signed numbers between -2³¹ and 2³¹-1. 2 (two) is the natural number following 1 and preceding 3. ... 4 (four) is a number, numeral, and glyph. ... 16 (sixteen) is the natural number following 15 and preceding 17. ... 256 (two hundred [and] fifty-six, CCLVI) is the natural number following 255 and preceding 257. ...

Other recognizable powers of two

• 2²⁴ = 16 777 216   –   The number of unique colors that can be displayed in truecolor, which is used by common computer monitors.
  

This number is the result of using the three-channel RGB system, with 8 bits for each channel, or 24 bits in total. Color is an important part of the visual arts. ... Truecolour (or Truecolor, Millions on a Macintosh) graphics is a method of storing image information in a computers memory such that each pixel is represented by three or more bytes. ... Nineteen inch (48 cm) CRT computer monitor A computer display, monitor or screen is a computer peripheral device capable of showing still or moving images generated by a computer and processed by a graphics card. ... The RGB color model utilizes the additive model in which red, green, and blue light are combined in various ways to create other colors. ...