Build the Codeword

The Codeword is Ready

The filled positions become one exact seven-bit codeword.

highlighted = computed this step

Fill every slot

After the data and parity slots are filled, the codeword is just the positions read left to right.

read positions left to right\text{read positions left to right}
The codeword is readyHamming encode and correction rows recomputed from pinned bits.The codeword is ready - codeword 0110011, syndrome 6rowvaluecheckdata3=1,5=0,6=1,7=1positions 3,5,6,7p10positions 1,3,5,7 evenp21positions 2,3,6,7 evenp40positions 4,5,6,7 evencodeword0110011positions 1..7flip6received bit is toggledreceived0110001one changed bits10positions 1,3,5,7s21positions 2,3,6,7s41positions 4,5,6,7syndrome6s4+s2+s1 as a positioncorrected0110011flip syndrome position

The parity bits are fixed

The recomputed parity bits are 0, 1, and 0.

p1,p2,p4p_1,p_2,p_4
The codeword is readyHamming encode and correction rows recomputed from pinned bits.The codeword is ready - codeword 0110011, syndrome 6rowvaluecheckdata3=1,5=0,6=1,7=1positions 3,5,6,7p10positions 1,3,5,7 evenp21positions 2,3,6,7 evenp40positions 4,5,6,7 evencodeword0110011positions 1..7flip6received bit is toggledreceived0110001one changed bits10positions 1,3,5,7s21positions 2,3,6,7s41positions 4,5,6,7syndrome6s4+s2+s1 as a positioncorrected0110011flip syndrome position

Read the seven bits

Reading positions 1 through 7 gives codeword 0110011.

codeword=0110011\text{codeword}=0110011
The codeword is readyHamming encode and correction rows recomputed from pinned bits.The codeword is ready - codeword 0110011, syndrome 6rowvaluecheckdata3=1,5=0,6=1,7=1positions 3,5,6,7p10positions 1,3,5,7 evenp21positions 2,3,6,7 evenp40positions 4,5,6,7 evencodeword0110011positions 1..7flip6received bit is toggledreceived0110001one changed bits10positions 1,3,5,7s21positions 2,3,6,7s41positions 4,5,6,7syndrome6s4+s2+s1 as a positioncorrected0110011flip syndrome position

Summary

The codeword 0110011 is not trusted from prose. The table recomputes it from the pinned data bits and even parity rule.

codeword=0110011\text{codeword}=0110011
The codeword is readyHamming encode and correction rows recomputed from pinned bits.The codeword is ready - codeword 0110011, syndrome 6rowvaluecheckdata3=1,5=0,6=1,7=1positions 3,5,6,7p10positions 1,3,5,7 evenp21positions 2,3,6,7 evenp40positions 4,5,6,7 evencodeword0110011positions 1..7flip6received bit is toggledreceived0110001one changed bits10positions 1,3,5,7s21positions 2,3,6,7s41positions 4,5,6,7syndrome6s4+s2+s1 as a positioncorrected0110011flip syndrome position