# Gray code

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## Gray code

n
(Computer Science) a modification of a number system, esp a binary code, in which any adjacent pair of numbers, in counting order, differ in their digits at one position only, the absolute difference being the value 1
[named after Frank Gray, 20th-century American physicist]
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
References in periodicals archive ?
Gray codes are known as least change code in which a bit in the code aggregate changes while moving starting with one point onto the next.
Gray codes are otherwise called Reflected code in light of the fact that the slightest critical bits for [2.sub.n] through ([2.sub.n+1]- 1) are impressions of those for 0 to ([2.sub.n-1]).
Gray codes can be calculated by first computing the binary representation of a number and then converting it using the following process: copy the most significant bit as it is, and replace the remaining bits (taking one bit at a time) with the result of an XOR operation of the current bit, with the previous bit of higher significance in the binary form.
These can be Gray codes, phase-shifted sinusoidal stripes, or binary codes; a hybrid method may also be used, applying both Gray codes and sine stripes.
The present study employed a scanner projecting a hybrid set of images, consisting of sinusoidal stripes preceded by a Gray code sequence .
The algebraic complexity of the AES S-box is further enhanced by introducing a new S-box based on Gray codes in .
Gardner, "The binary Gray code," in Knotted Doughnuts and Other Mathematical Entertainments, chapter 2, W.
After setting out the basic tools of the book, he covers preliminary results, subword and non-subword statistics, avoidance of patterns, multi-restrictions, asymptotics and random set partition, gray codes and loopless algorithms, and normal ordering.
This paper takes an altogether different approach and describes a visually satisfying geometrical technique to generate Gray codes.
Table 1 gives a Maple procedure and program to generate Gray codes using the [[C.sub.K].sup.N] recursive formulas.
A Maple program to generate Gray codes for sequences of length LL given the alphabet {0,1,2,3,..., N-1)}.
On generating the N-ary reflected Gray codes. IEEE transactions on computers, 33:739-741.
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