Hamming FEC

Refer to this $4$:$7$ SEC$-$SED chart, as desired$/$needed$.$

$8\mathrm{.}1$ Given the following $4-$bit data $($D$4$:D$1)$ sequences, write the $7-$bit Hamming encoding of

each, in the format: D$4$ D$3$ D$2$ P$4$ D$1$ P$2$ P$1(5$ points$)$

D$4$D$3$D$2$D$1$ D$4$D$3$D$2$P$4$D$1$P$2$P$1$

$1,1,0,1$

$1001$

$8\mathrm{.}2$ Given the following $7-$bit encoded sequences, which may contain $1$ error each, write the

corresponding decoded and, if necessary, corrected, $4-$bit data sequences and indicate whether

a Parity or a Data bit was corrupted bits of $(Y$ or $N),$ under DataError and ParityError. $(20$ points$)$

D$4$D$3$D$2$P$4$D$1$P$2$P$1$ D$4$D$3$D$2$D$1$ DataError? ParityError?

$1,0,1,0,1,0,1$

$1,0,0,0,1,0,1$

$1,1,1,0,1,1,1$

$\{\begin{array}{ccc}\text{:}[1,& 0,1,0,1,0,& 0]\end{array}$

$\{\begin{array}{ccc}\text{:}[0,& 0,0,1,0,1,& 1]\end{array}$