Hamming (15,11) Code Checker/Decoder
How This Converter Works
Checks a 15-bit Hamming (15,11) word, locates and flips a single-bit error from its even-parity syndrome, and extracts eleven data bits. A zero syndrome is displayed with the implementation label ON Error.
Formula or rule
The syndrome checks positions 1,3,5,7,9,11,13,15; 2,3,6,7,10,11,14,15; 4-7 and 12-15; and 8-15. The checker concatenates the checks in reverse order (position 8 check through position 1 check), interprets that as the one-based error position, and uses its position-name table for the error label.
Example
- Input
- 011001110100101
- Calculation
- The four checks produce syndrome 0000, so the codeword is left unchanged; extracting the eleven data positions gives 10110100101.
- Result
- ON Error <br> Data - 10110100101