This preview shows page 1. Sign up to view the full content.
Unformatted text preview: to extend this construction to any
number of data bits, remembering to add additional parity bits at indices that are a power
Allocating the data bits to parity computations is accomplished by looking at their respective indices in the table above. Note that we’re talking about the index in the table, not
the subscript of the bit. Speciﬁcally, di is included in the computation of pj if (and only if)
the logical AND of index(di ) and index(pj ) is non-zero. Put another way, di is included in
the computation of pj if, and only if, index(pj ) contributes to index(di ) when writing the
latter as sums of powers of 2.
So the computation of p1 (with an index of 1) includes all data bits with odd indices: d1 ,
d2 and d4 . And the computation of p2 (with an index of 2) includes d1 , d3 and d4 . Finally,
the computation of p3 (with an index of 4) includes d2 , d3 and d4 . You should verify that
these calculations match the Ei equations given above.
If the parity/syndrome computations are constructed this way, it turns out that E3 E2 E1 ,
treated as a binary number, gives the index of the bit that should be corrected. For example, if E3 E2 E1...
View Full Document
This document was uploaded on 02/26/2014 for the course CS 6.02 at MIT.
- Fall '13