Hamming's Correction of Single Errors, continued

A data bit contributes to the parity of all bits in its decomposition into a sum of powers of 2.

For example :

     3 = 2 + 1
     7 = 4 + 2 + 1
    11 = 8 + 2 + 1

Making a list of these :

    1 is contributed to by 3, 5, 7, 9, 11
    2                      3, 6, 7, 10, 11
    4                      5, 6, 7
    8                      9, 10, 11

We then put the data bits in their positions and calculate each check bit.