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[[File:Hammersley set 2D.svg|thumb|A [[Hammersley set]] whose coordinates are the integers from 0 to 255 and their bit-reversals]]
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 two]]. It is defined by indexing the elements of the sequence by the numbers 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.
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