Algorithms for generating generalized gray codes

Abstract

Gray code is a code with the property that there is one and only one bit‐change between any two neighboring numbers. An algorithm for generating gray codes is presented. It turns out that there are other codes which have the same characteristics as gray codes. We call this class of codes generalized gray code (GGC). More precisely, a GGC is a code which has both the reflective property and the unit distance property. Algorithms for generating n‐bit GGC from the (n – 1)‐bit GGC are presented with illustrative examples. It is found that the number of n‐bit GGC is equal to 2n times the number of (n – 1)‐bit GGC. GGC generation trees are used to find GGC. Shows that GGC may be used in the two cases: where 1: gray code cannot be used, and as 2: member of the GGC is better suited than the gray code. Deduces that through the use of GGC, we have more choices than using just gray codes, and that we may obtain better results in terms of fan‐in, fan‐out, propagation delays, power consumption, or other related constraints in designing digital systems. The results obtained in this paper may also have useful applications in implementing special logic functions such as fuzzy threshold functions or fuzzy symmetric functions.

Citation

Lee, E.T. and Lee, M.E. (1999), "Algorithms for generating generalized gray codes", Kybernetes, Vol. 28 No. 6/7, pp. 837-844. https://doi.org/10.1108/03684929910283286