Question $8$

$12\mathrm{.}5pts$

Cindy transmitted a four$-$letter word to Donald. After her computer took the ASCII representation for the word and applied the Hamming $(7,4)$ code, Donald received this:

$1100011001100110011100111101100100101001101101010$

Unfortunately, there were a number of errors in the transmission. Fortunately, however, there was never more than one bit error in any $7-$bit block, and hence the Hamming $(7,4)$ code was able to fix them all. Type in the four$-$letter word $($using letters of the alphabet$)$ that Cindy originally sent, in lower case. $($Note: Assume that the data occurs in the format we described in class whereby the three parity bits follow the four data bits, i$.$e$.d_1{d}_2{d}_3{d}_4{p}_1{p}_2{p}_3.$ This may differ from the order found in descriptions of Hamming $(7,4)$ found on the web.$)$