Gray coding

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:

Binary Code

Input position	Output 3	Output 2	Output 1
0	0	0	0
1	0	0	1
2	0	1	0
3	0	1	1
4	1	0	0
5	1	0	1
6	1	1	0
7	1	1	1

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:

Gray Code

Input position	Output 3	Output 2	Output 1
0	0	0	0
1	0	0	1
2	0	1	1
3	0	1	0
4	1	1	0
5	1	1	1
6	1	0	1
7	1	0	0

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