Recursive Method for Generating the Gray Code

摘要

The Gray code is a mapping of the naturally ordered B-bit binary numbers to all ordering in which the binary representations of successive integers differ by exactly one bit. For example, the 4-bit Gray code representations of 7 and 8 are 0100 and 1100, respectively, which differ by one bit. The natural' representations are 0111 and 1000, which differ by three bits. The purpose of this correspondence is to present a simple recursive method for generating the Gray code.