information:extraction, structural:scholar_edition
Powers of two

The first negative powers of 2 are commonly used, and have special names, e.g.: half and quarter.

Powers of 2 appear in set theory, since a set with n members has a power set, the set of all of its subsets, which has 2 members.

Integer powers of 2 are important in computer science. The positive integer powers 2 give the number of possible values for an n - bit integer binary number; for example, a byte may take 2 = 256 different values. The binary number system expresses any number as a sum of powers of 2, and denotes it as a sequence of 0 and 1, separated by a binary point, where 1 indicates a power of 2 that appears in the sum; the exponent is determined by the place of this 1: the nonnegative exponents are the rank of the 1 on the left of the point (starting from 0), and the negative exponents are determined by the rank on the right of the point.