book chapter · 1992

The Gray Code Function

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Abstract

Abstract The Gray code of a positive integer m can be defined in terms of its binary expansion as follows. Shift m to the right, discarding the last digit, and then add the result to m without carrying (an exclusive or). Thus if we write ® for the exclusive or operation and ÷ for integer division, so that m÷2 is the right shift of m, then the Gray code of m is g(m) = m ® (m÷2). For each k, the function g permutes the integers between 0 and 2 k – 1. It has the property that the binary expansions of g(m) and (g(m+1) always differ in precisely one digit. This is true cyclically, in the sense that it holds for g(2 k – 1) = 2 k-1 and g(0) = 0. This provides a Hamiltonian circuit on the k-dimensional cube and is the basis of the construction of the diagram in Figure 1.

Cite this paper

APA 7

Clarke, F. (1992). The Gray Code Function. https://doi.org/10.1093/oso/9780198535942.003.0001

MLA 9

Clarke, Francis. “The Gray Code Function.” 1992, pp. 1–7, https://doi.org/10.1093/oso/9780198535942.003.0001.

Chicago

Clarke, Francis. 1992. “The Gray Code Function.” https://doi.org/10.1093/oso/9780198535942.003.0001.

Harvard

Clarke, F. (1992) ‘The Gray Code Function’. Available at: https://doi.org/10.1093/oso/9780198535942.003.0001.

BibTeX

@incollection{clarke1992gray,
  title = {{The Gray Code Function}},
  author = {Clarke, Francis},
  pages = {1--7},
  year = {1992},
  doi = {10.1093/oso/9780198535942.003.0001}
}

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