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=Gray Codes= | =Gray Codes= | ||
Revision as of 23:07, 14 January 2023
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 | BCD | Gray Code |
| 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
To get an excess-3 code of a decimal number simply add 3 to each decimal digit. And then we write the 4-bit binary number for each digit of the decimal number. We can find the excess-3 code of the given binary number by using the following steps:
- We find the decimal number of the given binary number.
- Then we add 3 in each digit of the decimal number.
- Now, we find the binary code of each digit of the newly generated decimal number.
We can also add 0011 in each 4-bit BCD code of the decimal number for getting excess-3 code.
| Decimal | BCD | Excess-3 | |
| 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 |