Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In applied mathematics, a bit-reversal permuation is a permutation of a sequence with n = 2m (a power of two) elements, defined by reversing the binary digits of the index (0 to n – 1) of each element. The generalization to n = bm for an arbitrary integer b > 1 is a base-b digit-reversal permutation, in which the base-b (radix-b) digits of the index of each element are reversed to obtain the permuted index. A further generalization to arbitrary composite sizes is a mixed-radix digit reversal (in which the elements of the sequence are indexed by a number expressed in a mixed radix, whose digits are reversed by the permutation).

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