A category of error$-$detecting $($and correcting$)$ code, called the Hamming code, is a code in which dmin $=3.$ This code can detect up to two errors $($or correct one single error$).$ In this code, the values of n$,$ k$,$ and r are related as: n $=2$r $1$ and k $=$ n $$ r$.$ Find the number of bits in the dataword and the codewords if r is $3.$