Consider a (7, 4) Hamming code with a four-bit dataword (a0a1a2a3) and three parity check bits {r0r1r2} defined based on the following equations: r0 = a0 + a1 + a2 r1 = a1 + a2 + a3 r2 = a0 + a1 + a3 a) If the codewords are defined as {a0a1a2a3r0r1r2}, calculate the codeword for dataword 1001. b) Suppose in a system that uses this scheme, the codeword 1101010 is received. Determine if the received codeword contains any error. If so, what is the correct codeword (assuming single bit error)? c) If this scheme can detect a maximum of three bit errors and correct a maximum of one bit error, what is its minimum Hamming distance