A Less Complex Algorithmic Procedure for Computing Gray Codes

Abstract

Abstract:The purpose of this paper is to present a new and faster algorithmic procedure for generating the nbit Gray codes. Thereby, through this paper we have presented the derivation, design and implementation of a newly developed algorithm for the generation of an n-bit binary reflected Gray code sequences. The developed algorithm is stemmed from the fact of generating and properly placing the min-terms from the universal set of all the possible min-terms [m 0 m 1 m 2 …. m N ] of Boolean function of n variables, where, 0 < N < 2 n -1. The resulting algorithm is in concise form and trivial to implement. Furthermore, the developed algorithm is equipped with added attributes of optimizing of time and space while executed.

Determining the possible minimal Boolean expressions via a newly developed procedure and tool

“…The MATLAB R2014a student version is used for running the written MATLAB codes for the algorithm. For each of the values of n = [10,15,20,21,22,23,24,25,26,27] the respective elapsed program execution time (t) is recorded as t = [0.143473, 0.170081, 0.391752, 6.127743, 12.484156, 23.874971] in seconds. The plot of the data set is shown in Figure 7.…”

“…In previous research works [19] - [21], algorithmic ways have been devised to generate efficiently the Gray code for large orders, special Gray codes and their properties. The theorem below relates the minterms and Gray code and provide extensive help in constructing the Kmaps for large number of input variables n. By using this procedure samples of K-maps for n = 6 and n = 8 are shown in Figures 1 and Figure 2 respectively.…”

Constructive and Clustering Methods

“…Further, since the existence of latches is a basic building block of any digital system then by exploiting latches in generating GC reduces the extra burden of hardware to generate the 'true' GC. Moreover, a new and faster algorithmic procedure for generating the n-bit Gray codes has been presented in 18 . Further, more efficient algorithmic procedures for computing n-bit GCs have been developed and presented through research publications 19,20 .…”