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<H1>Gray code</H1>
<P>
(definition)

<P>
<strong>Definition:</strong>
An ordering of 2<sup>n</sup> binary numbers such that only one bit changes from one entry to the next.
<P><strong>See also</strong>
<a href="karnaughmap.html" tppabs="http://hissa.nist.gov/dads/HTML/karnaughmap.html"><em>Karnaugh map</em></a>.
<P><em>Note:
Gray codes are useful in mechanical encoders since a slight change in location 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. <br> One Gray code for 3 bits is (000, 010, 011, 001, 101, 111, 110, 100). A Gray code corresponds to a <a href="hamilcyc.html" tppabs="http://hissa.nist.gov/dads/HTML/hamilcyc.html"><em>Hamiltonian cycle</em></a> on an n-dimensional hypercube.  Note: Gray codes are not unique. <br> One way to construct a Gray code for n bits is to take a Gray code for n-1 bits with each code prefixed by 0 (for the first half of the code) and append the n-1 Gray code reversed with each code prefixed by 1 (for the second half).  Here is an example of creating a 3-bit Gray code from a 2-bit Gray code. <br> 00 01 11 10 A Gray code for 2 bits<br> 000 001 011 010 the 2-bit code with a zero prefix<br> 10 11 01 00 the 2-bit code reversed<br> 110 111 101 100 the reversed code with a one prefix<br> 000 001 011 010 110 111 101 100 A Gray code for 3 bits</em>
<P>Author: <a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>

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Entry modified Thu Dec 16 09:42:47 1999.<BR>
HTML page formatted Wed Dec 22 09:35:27 1999.

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