A Hamming (7,4 ) code uses the following check bit rulesc1 = k1 + k4 c2 = k1 + k2 + k3 c3 = k1 + k3Construct a complete table for the code set.
Question
A Hamming (7,4) Code Check Bit Rules
The check bit rules are defined as follows:
- c1 = k1 + k4
- c2 = k1 + k2 + k3
- c3 = k1 + k3
Construct a complete table for the code set.
Solution
Sure, here is the complete table for the Hamming (7,4) code set:
| k1 | k2 | k3 | k4 | c1 | c2 | c3 |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 1 | 1 | 1 | 1 |
| 0 | 1 | 0 | 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 | 1 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 | 0 | 1 | 1 |
| 1 | 0 | 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 1 | 0 | 1 |
| 1 | 1 | 0 | 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 | 1 | 1 | 0 |
| 1 | 1 | 1 | 1 | 0 | 1 | 0 |
This table is constructed by calculating the values of c1, c2, and c3 for each possible combination of k1, k2, k3, and k4 using the given check bit rules.
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