Gray coding: Difference between revisions

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#REDIRECT [[Gray code]] {{R from modification}}

A gray code is a special coding system designed to prevent spurious output

from practical electromechanical switches. For example, if we create a

device that indicates position by closing and opening switches, we could use

the binary code to represent position:

<table>

<caption>Binary Code</caption>

<tr>

<td>Input position</td>

<td>Output 3</td>

<td>Output 2</td>

<td>Output 1</td>

</tr>

<tr>

<td>0</td>

<td>0</td>

<td>0</td>

<td>0</td>

</tr>

<tr>

<td>1</td>

<td>0</td>

<td>0</td>

<td>1</td>

</tr>

<tr>

<td>2</td>

<td>0</td>

<td>1</td>

<td>0</td>

</tr>

<tr>

<td>3</td>

<td>0</td>

<td>1</td>

<td>1</td>

</tr>

<tr>

<td>4</td>

<td>1</td>

<td>0</td>

<td>0</td>

</tr>

<tr>

<td>5</td>

<td>1</td>

<td>0</td>

<td>1</td>

</tr>

<tr>

<td>6</td>

<td>1</td>

<td>1</td>

<td>0</td>

</tr>

<tr>

<td>7</td>

<td>1</td>

<td>1</td>

<td>1</td>

</tr>

</table>

The problem is that, with real (mechanical) switches, it is very unlikely

that two switches will change states exactly in synchrony. For example, in

the transistion from state 3 to state 4, all three switches change state.

In the brief period while all are changing, the switches will read some spurious position.

A gray code solves this problem by changing only one switch at a time, so

there is never any ambiguity of position:

<table>

<caption>Gray Code</caption>

<tr>

<td>Input position</td>

<td>Output 3</td>

<td>Output 2</td>

<td>Output 1</td>

</tr>

<tr>

<td>0</td>

<td>0</td>

<td>0</td>

<td>0</td>

</tr>

<tr>

<td>1</td>

<td>0</td>

<td>0</td>

<td>1</td>

</tr>

<tr>

<td>2</td>

<td>0</td>

<td>1</td>

<td>1</td>

</tr>

<tr>

<td>3</td>

<td>0</td>

<td>1</td>

<td>0</td>

</tr>

<tr>

<td>4</td>

<td>1</td>

<td>1</td>

<td>0</td>

</tr>

<tr>

<td>5</td>

<td>1</td>

<td>1</td>

<td>1</td>

</tr>

<tr>

<td>6</td>

<td>1</td>

<td>0</td>

<td>1</td>

</tr>

<tr>

<td>7</td>

<td>1</td>

<td>0</td>

<td>0</td>

</tr>

</table>

Notice also that state seven can roll over to state zero with only one

switch change.