Gray code
The reflected binary code (RBC), also known as reflected binary (RB) or Gray code after Frank Gray, is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit).
| Lucal code | |||||
|---|---|---|---|---|---|
| 5 | 4 | 3 | 2 | 1 | |
| Gray code | |||||
| 4 | 3 | 2 | 1 | ||
| 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 1 |
| 2 | 0 | 0 | 1 | 1 | 0 |
| 3 | 0 | 0 | 1 | 0 | 1 |
| 4 | 0 | 1 | 1 | 0 | 0 |
| 5 | 0 | 1 | 1 | 1 | 1 |
| 6 | 0 | 1 | 0 | 1 | 0 |
| 7 | 0 | 1 | 0 | 0 | 1 |
| 8 | 1 | 1 | 0 | 0 | 0 |
| 9 | 1 | 1 | 0 | 1 | 1 |
| 10 | 1 | 1 | 1 | 1 | 0 |
| 11 | 1 | 1 | 1 | 0 | 1 |
| 12 | 1 | 0 | 1 | 0 | 0 |
| 13 | 1 | 0 | 1 | 1 | 1 |
| 14 | 1 | 0 | 0 | 1 | 0 |
| 15 | 1 | 0 | 0 | 0 | 1 |
For example, the representation of the decimal value "1" in binary would normally be "001" and "2" would be "010". In Gray code, these values are represented as "001" and "011". That way, incrementing a value from 1 to 2 requires only one bit to change, instead of two.
Gray codes are widely used to prevent spurious output from electromechanical switches and to facilitate error correction in digital communications such as digital terrestrial television and some cable TV systems. The use of Gray code in these devices helps simplify logic operations and reduce errors in practice.