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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 [2026/10/12 18:17] (current) – [Example 1.] knehez
@@ Line 41: / Line 41: @@
 ^ 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 |
 | 16 | 5 | 21 | 31 |
@@ Line 96: / Line 96: @@
 **p1**: Covers 1, 0, 0 (positions 1, 3, 5, 7), so p1 = 1 (to make the total even).
-**p2**: Covers 0, 1, 0 (positions 2, 3, 6, 7), so p2 = 1 (to make the total even).
+**p2**: Covers 1, 1, 0 (positions 2, 3, 6, 7), so p2 = 0 (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:
-<code>1 1 1 1 0 1 0</code>
+<code>1 0 1 1 0 1 0</code>
-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.
+Suppose the 3rd bit is wrong due to an error. In this case, **p1** and **p2** will be wrong. Because of the **3rd** bit the first and second parity bits will give us wrong values, but the others will not because they do not calculate with the bit standing at the **3rd** place.
 The common values of the first and second parity bits are the following: 1, 2, 3, 5, 6, 7. The defective one has to be among these.
@@ Line 130: / Line 130: @@
 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|