tanszek:oktatas:techcomm:error_detection_and_correction
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| tanszek:oktatas:techcomm:error_detection_and_correction [2025/10/27 20:04] – [Example 2.] knehez | tanszek:oktatas:techcomm:error_detection_and_correction [2025/10/28 08:30] (current) – [Example 1.] knehez | ||
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| ^ Data bits (\(m\)) ^ number of parity bits (\(r\)) ^ whole bit length (\(n = m + r\)) ^ % of added bits ^ | ^ Data bits (\(m\)) ^ number of parity bits (\(r\)) ^ whole bit length (\(n = m + r\)) ^ % of added bits ^ | ||
| - | | 4 | 3 | 7 | 66 | | + | | 4 | 3 | 7 | 75 | |
| | 8 | 4 | 12 | 50 | | | 8 | 4 | 12 | 50 | | ||
| | 16 | 5 | 21 | 31 | | | 16 | 5 | 21 | 31 | | ||
| Line 94: | Line 94: | ||
| |p1|p2|1|p4|0|1|0| | |p1|p2|1|p4|0|1|0| | ||
| - | **p1**: Covers 1, 0, 0 (positions 1, 3, 5, 7), so p1 = 1 (to make the total even). | + | **p1**: Covers 1, 0, 1 (positions 1, 3, 5, 7), so p1 = 0 (to make the total even). |
| - | **p2**: Covers | + | **p2**: Covers |
| **p4**: Covers 0, 1, 0 (positions 4, 5, 6, 7), so p4 = 1 (to make the total even). | **p4**: Covers 0, 1, 0 (positions 4, 5, 6, 7), so p4 = 1 (to make the total even). | ||
| Thus, the final transmitted Hamming code is: | Thus, the final transmitted Hamming code is: | ||
| - | < | + | < |
| Let's suppose that because of an error the 3rd bit goes wrong. In this case **p1** and **p2** will be wrong. Because of the **3rd** bit the first and second parity bit will give us wrong values, but the others will not because they do not calculate with the bit standing at the **3rd** place. | Let's suppose that because of an error the 3rd bit goes wrong. In this case **p1** and **p2** will be wrong. Because of the **3rd** bit the first and second parity bit will give us wrong values, but the others will not because they do not calculate with the bit standing at the **3rd** place. | ||
| Line 130: | Line 130: | ||
| Encoded message with parity bits will be: | Encoded message with parity bits will be: | ||
| - | | 1| 2|3| 4|5|6|7| 8|9|10|11|12|13|14|15|16 |17|18|19|20|21| | + | | 1| 2|3| 4|5|6|7| 8|9|10|11|12|13|14|15|16|17|18|19|20|21| |
| - | | 1| 0|1| 1|0|0|1| 0|0|1 |1 |1 |0 |1 |0 | 0|1 |1 |0 |1 |1 | | + | | 1| 0|1| 1|0|0|1| 0|0|1 | 1| 1| 0| 1| 0| 0| 1| 1| 0| 1| 1| |
tanszek/oktatas/techcomm/error_detection_and_correction.1761595488.txt.gz · Last modified: 2025/10/27 20:04 by knehez