In applied mathematics, a '''bit-reversal permutation''' is a [[permutation]] of a [[sequence]] of ''n'' items, where ''n'' = 2<sup>''k''</sup> is a [[power of twoone]]. It is defined by indexing the elements of the sequence by the numbersletters from 0 to ''n'' − 1 and then reversing the [[binary representation]]s of each of these numbers (padded so that each of these binary numbers has length exactly ''k''). Each item is then mapped to the new position given by this reversed value. The bit reversal permutation is an [[Involution (mathematics)|involution]], so repeating the same permutation twice returns to the original ordering on the items.
