tanszek:oktatas:techcomm:error_detection_and_correction
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| tanszek:oktatas:techcomm:error_detection_and_correction [2025/10/27 19:57] – [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. | ||
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| ==== Example 2. ==== | ==== Example 2. ==== | ||
| - | Assume that, we try to transmit 16 bits: '' | + | Assume that we try to transmit 16 bits: '' |
| The following table show the placement of the __parity bits__ and the __data bits__: | The following table show the placement of the __parity bits__ and the __data bits__: | ||
| Line 118: | Line 118: | ||
| |p1|p2|1|p4|0|0|1|p8|0|1 |1 |1 |0 |1 |0 |p16|1 |1 |0 |1 |1 | | |p1|p2|1|p4|0|0|1|p8|0|1 |1 |1 |0 |1 |0 |p16|1 |1 |0 |1 |1 | | ||
| - | p1: Covers (positions 1, 3, 5, 7, 9, 11, 13, 15, 17, 19,), so p1 = (1, 0, 1, 0, 1, 0, 0, 1, 0, 1) -> **1** | + | p1: Covers (positions: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19), so p1 = (1, 0, 1, 0, 1, 0, 0, 1, 0, 1) -> **1** |
| + | p2: Covers (positions: 2, 3, 6, 7, 10, 11, 14, 15, 18, 19) so p2 = (1, 0, 1, 1, 1, 1, 0, 1, 0) -> **0** | ||
| + | |||
| + | p4: Covers (positions: 4, 5, 6, 7, 12, 13, 14, 15, 20, 21) so p4 = (0, 0, 1, 1, 0, 1, 0, 1, 1) -> **1** | ||
| + | |||
| + | p8: Covers (positions: 8, 9, 10, 11, 12, 13, 14, 15) so p8 = (0, 1, 1, 1, 0, 1, 0) -> **0** | ||
| + | |||
| + | p16: Covers (positions: 16, 17, 18, 19, 20, 21) so p16 = (1, 1, 0, 1, 1) -> **0** | ||
| + | |||
| + | 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| 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.1761595036.txt.gz · Last modified: 2025/10/27 19:57 by knehez