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Concept
Power of two
Summary
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 considered, n is restricted to non-negative values, so there are 1, 2, and 2 multiplied by itself a certain number of times.
The first ten powers of 2 for non-negative values of n are:
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, ...
Because two is the base of the binary numeral system, powers of two are common in computer science. Written in binary, a power of two always has the form 100...000 or 0.00...001, just like a power of 10 in the decimal system.
Two to the exponent of n, written as 2n, is the number of ways the bits in a binary word of length n can be arranged. A word, interpreted as an unsigned integer, can represent values from 0 (000...0002) to 2n − 1 (111...1112) inclusively. Corresponding signed integer values can be positive, negative and zero; see signed number representations. Either way, one less than a power of two is often the upper bound of an integer in binary computers. As a consequence, numbers of this form show up frequently in computer software. As an example, a video game running on an 8-bit system might limit the score or the number of items the player can hold to 255—the result of using a byte, which is 8 bits long, to store the number, giving a maximum value of 28 − 1 = 255. For example, in the original Legend of Zelda the main character was limited to carrying 255 rupees (the currency of the game) at any given time, and the video game Pac-Man famously has a kill screen at level 256.
Powers of two are often used to measure computer memory. A byte is now considered eight bits (an octet), resulting in the possibility of 256 values (28). (The term byte once meant (and in some cases, still means) a collection of bits, typically of 5 to 32 bits, rather than only an 8-bit unit.) The prefix kilo, in conjunction with byte, may be, and has traditionally been, used, to mean 1,024 (210).
Official source
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