The geometric progression 1, 2, 4, 8, 16, 32. The numbers that can be represented as sums of consecutive positive integers are called polite numbers they are exactly the numbers that are not powers of two. A fraction that has a power of two as its denominator is called a dyadic rational. Similarly, a prime number (like 257) that is one more than a positive power of two is called a Fermat prime-the exponent itself is a power of two. For example, the prime number 31 is a Mersenne prime because it is 1 less than 32 (2 5). Put another way, they have fairly regular bit patterns.Ī prime number that is one less than a power of two is called a Mersenne prime. Numbers that 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. The logical block size is almost always a power of two. 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. Powers of two occur in a range of other places as well. Nearly all processor registers have sizes that are powers of two, 32 or 64 being very common. Binary prefixes have been standardized, such as kibi (Ki) meaning 1,024. However, in general, the term kilo has been used in the International System of Units to mean 1,000 (10 3). (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 (2 10).

$number is apower of 2$

A byte is now considered eight bits (an octet), resulting in the possibility of 256 values (2 8). Powers of two are often used to measure computer memory. 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.

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 2 8 − 1 = 255. As a consequence, numbers of this form show up frequently in computer software. Either way, one less than a power of two is often the upper bound of an integer in binary computers. Corresponding signed integer values can be positive, negative and zero see signed number representations. A word, interpreted as an unsigned integer, can represent values from 0 ( 000.000 2) to 2 n − 1 ( 111.111 2) inclusively. Two to the power of n, written as 2 n, is the number of ways the bits in a binary word of length n can be arranged. 6 Powers of two whose exponents are powers of two.

Number is apower of 2