---
tag: 2XHP775V1A
kind: concept
name: Bit-reversal permutation
aliases: [bit-reversal, bit-reversed-order, digit-reversal-permutation]
sources:
  - wikipedia: en:25692725@r1374351544
    locator: Bit-reversal permutation
    note: adopted
    mention: wikipedia://en/25692725
    sections: [Summary]
same_as:
  wikidata: Q4918660
  wikipedia: Bit-reversal permutation
inventory: [VA6AWAA8G9]
---

## Summary

In applied mathematics, a **bit-reversal permutation** is a [[permutation|05RWFKVTJ7]] of a [[sequence|0G9EKM0E15]] of $n$ items, where $n=2^k$ is a power of two. It is defined by indexing the elements of the sequence by the numbers from $0$ to $n-1$, representing each of these numbers by its binary representation (padded to have length exactly $k$), and mapping each item to the item whose representation has the same bits in the reversed order.