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==Example==
Consider the sequence of eight letters ''{{not a typo|abcdefgh}}''. Their indexes are the binary numbers 000, 001, 010, 011, 100, 101, 110, and 111, which when reversed become 000, 100, 010, 110, 001, 101, 011, and 111.
Thus, the letter ''a'' in position 000 is mapped to the same position (000), the letter ''b'' in position 001 is mapped to the fifth position (the one numbered 100), etc., giving the new sequence ''{{not a typo|aecgbfdh}}''. Repeating the same permutation on this new sequence returns to the starting sequence.
Writing the index numbers in decimal (but, as above, starting with position 0 rather than the more conventional start of 1 for a permutation), the bit-reversal permutations of size 2<sup>''k''</sup>, for ''k'' = 0, 1, 2, 3, ... are
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