A category of error detecting (and correcting) code, called the Hamming code, is a code in which d_min = 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.