- 2076 Asoj · 3 marks
Gray code compared with binary numbers
Short answer
Gray code is an unweighted code where successive values differ by only one bit. Compared to binary: binary is weighted and used for arithmetic but may change many bits at transitions (e.g., 3→4 changes 3 bits); Gray is unweighted, minimizes transition errors, but is not suitable for arithmetic. Example: (0111)₂ → Gray (0100).
What is a gray code? Compare with binary numbers.
Gray code is an unweighted, reflected binary code in which successive numbers differ in only one bit position. It is used in shaft position encoders, K-maps and ADCs to avoid errors during transitions.
| Decimal | Binary | Gray |
|---|---|---|
| 0 | 000 | 000 |
| 1 | 001 | 001 |
| 2 | 010 | 011 |
| 3 | 011 | 010 |
| 4 | 100 | 110 |
| 5 | 101 | 111 |
| 6 | 110 | 101 |
| 7 | 111 | 100 |
Comparison with binary numbers
| Point | Binary | Gray |
|---|---|---|
| Type | Weighted (positional) | Unweighted |
| Change between successive values | Many bits may change (3 → 4: 011 → 100) | Only one bit changes |
| Arithmetic | Easy to add and subtract | Not suitable for arithmetic |
| Error at transitions | False readings possible | Very small error |
| Conversion | — |
Example: → Gray .
✓ Answer checked by Claude Opus 5.5 (high effort)
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