Gray Codes
This is a technique where we convert number from binary to grays. We do this because Gray reduces the bits we need to change to get to the next number. e.g. changing from 2 to 3 decimal requires a 1 bit change.
| Decimal (base 10) | BCD Binary (base 2) | Gray Binary-Reflected (no base) |
| 0 | 0000 | 0000 |
| 1 | 0001 | 0001 |
| 2 | 0010 | 0011 |
| 3 | 0011 | 0010 |
| 4 | 0100 | 0110 |
| 5 | 0101 | 0111 |
| 6 | 0110 | 0101 |
| 7 | 0111 | 0100 |
| 8 | 1000 | 1100 |
| 9 | 1001 | 1101 |
| 10 | 1010 | 1111 |
Excess-3 Codes
| Decimal | (base 10) | BCD Binary (base 2) | |
| 0 | 0000 | 0011 | |
| 1 | 0001 | 0100 | |
| 2 | 0010 | 0101 | |
| 3 | 0011 | 0110 | |
| 4 | 0100 | 0111 | |
| 5 | 0101 | 1000 | |
| 6 | 0110 | 1001 | |
| 7 | 0111 | 1010 | |
| 8 | 1000 | 1011 | |
| 9 | 1001 | 1100 | |