Editing Exponentiation (section)

===={{anchor|Base 2}}Powers of two====
{{Main|Power of two}}
The first negative powers of {{math|2}} have special names: <math>2^{-1}</math>is a ''[[one half|half]]''; <math>2^{-2}</math> is a ''[[4 (number)|quarter]].''

Powers of {{math|2}} appear in [[set theory]], since a set with {{math|''n''}} members has a [[power set]], the set of all of its [[subset]]s, which has {{math|2<sup>''n''</sup>}} members.

Integer powers of {{math|2}} are important in [[computer science]]. The positive integer powers {{math|2<sup>''n''</sup>}} give the number of possible values for an {{math|''n''}}-[[bit]] integer [[binary number]]; for example, a [[byte]] may take {{math|1=2<sup>8</sup> = 256}} different values. The [[binary number system]] expresses any number as a sum of powers of {{math|2}}, and denotes it as a sequence of {{math|0}} and {{math|1}}, separated by a [[binary point]], where {{math|1}} indicates a power of {{math|2}} that appears in the sum; the exponent is determined by the place of this {{math|1}}: the nonnegative exponents are the rank of the {{math|1}} on the left of the point (starting from {{math|0}}), and the negative exponents are determined by the rank on the right of the point.