Gray code - Revision history

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2019-06-22T19:29:01Z

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2018-12-16T04:12:43Z

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2016-12-31T14:37:15Z

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2016-12-28T22:32:16Z

A decent start

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A '''Gray code''' (named after their inventor) is a coding system in which 'neighbour' code only differ in one bit. In a classic binary code, many transitions involve multi-bit changes; e.g. going from 3 (011) to 4 (100) involves changes in all three bits.

This behaviour can be an issue when a binary code is used in a state machine; if the binary-coded state is fed into combinatorial circuitry, with real counters, the output bits do not all change at the exact same instant. So (for example), the counter output might very briefly display 7 (111) in the process of going from 3 of 4. The combinatorial circuity might therefore produce [[glitch]]es on its output during the brief period when a false intermediate outputs are present.

Gray codes have other uses, though - for example in transmission codings.

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 The multiple bit changing behaviour of a classic binary code can be an issue when one is used, for example, in a state machine: when using a counter to hold the state, if the binary-coded state is fed into combinatorial circuitry, the output bits do not all change at the exact same instant. So (to give a concrete instance), the counter output might very briefly display 7 (111) in the process of going from 3 (011) to 4 (100). The combinatorial circuity might therefore produce [[glitch]]es on its output during the brief period when a false intermediate outputs are present.
-Gray codes have other uses too, though - for example in transmission codings.
+Gray codes have other uses too, though - for example in [[run-length limited coding|transmission codings]].
 [[Category: Theory]]

← Older revision		Revision as of 04:12, 16 December 2018
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	Gray codes have other uses too, though - for example in transmission codings.		Gray codes have other uses too, though - for example in transmission codings.
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		+	[[Category: Theory]]

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-A '''Gray code''' (named after their inventor) is a coding system in which 'neighbour' code only differ in one bit. In a classic binary code, many transitions involve multi-bit changes; e.g. going from 3 (011) to 4 (100) involves changes in all three bits.
+A '''Gray code''' (named after their inventor) is a coding system in which 'neighbour' codes only differ in one bit. In a classic binary code, many transitions from one value to the next involve multi-bit changes; e.g. going from 3 (011) to 4 (100) involves changes in all three bits.
-This behaviour can be an issue when a binary code is used in a state machine; if the binary-coded state is fed into combinatorial circuitry, with real counters, the output bits do not all change at the exact same instant. So (for example), the counter output might very briefly display 7 (111) in the process of going from 3 of 4. The combinatorial circuity might therefore produce [[glitch]]es on its output during the brief period when a false intermediate outputs are present.
+As an example, here is the simplest three-bit Gray code (note that the transition from value 07, counting up and wrapping around to 00, also changes only one bit):
-Gray codes have other uses, though - for example in transmission codings.
+{| class="wikitable"