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 uses the following check bit rulesc1 = k1 + k4 c2 = k1 + k2 + k3 c3 = k1 + k3Construct 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.
Similar Questions
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.Construct the Generator Matrix for the code setConstruct the Check Matrix for the code set.Using the Generator matrix, determine the encoded form of the data word <1001>Using the Check matrix decode the following received codeword <1001001>.
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