NIST

Gray code

(definition)

Definition: An ordering of 2n binary numbers such that only one bit changes from one entry to the next. Gray codes for 4 or more bits are not unique, even allowing for permutation or inversion of bits.

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Note: Gray codes are particularly useful in mechanical encoders since a slight change in position only affects one bit. Using a typical binary code, up to n bits could change, and slight misalignments between reading elements could cause wildly incorrect readings.

An n-bit Gray code corresponds to a Hamiltonian cycle on an n-dimensional hypercube.

A Gray code was used in a telegraph demonstrated by French engineer Émile Baudot in 1878. Frank Gray, a Bell Labs researcher, patented a method using the codes in 1953.

See the Wikipedia entry for Gray code for more information.

There are polynomial-time algorithms to convert between binary numbers and certain Gray codes.

Author: PEB

More information

Image of a Gray code rotary railroad control.

Frank Gray, Pulse Code Communication, U.S. Patent 2,632,058, filed 13 November 1947, issued 17 March 1953.


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Entry modified 7 June 2014.
HTML page formatted Sat Jun 7 11:55:29 2014.

Cite this as:
Paul E. Black, "Gray code", in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 7 June 2014. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/graycode.html