Talk:Gray code
The following was at Gray_coding, and is moved here in case anyone wants to add some of it to the Gray_code article.
A gray code is a special coding system designed to prevent spurious output from practical electromechanical switches and is specifically relevant to encoding of position information for a rotating object. For example, if we create a device that indicates position by closing and opening switches, we could use the binary code to represent position:
| 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:
| 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.