For single-error correction in memory, we construct a 4:7 Hamming code as given below: po = do d1d3 d2d3 p1 = do p2 d1d2d3 di represents data bits, pi represents parity bits, and is the logical exclusive-OR (XOR) function. a) Draw the syndrome impact table for the given code, and show that it is not properly designed because it cannot correct single-bit errors. Explain your answer briefly. b) Change only the given equation for p2 to construct a real Hamming code that can correct single-bit errors.