Show that the Hamming code C(7,4) of Table 10.4 can detect two-bit errors but not necessarily three-bit errors by testing the code in the following cases. The character "B" (bad) and "G" (good) mean error and no error, respectively, on the corresponding bit of the codeword. It is required that you should use the formulas for r2, r1, and r0 (as shown) to find the three redundant bits, and your error detection should be based on the syndrome bits (4 points)

a) Dataword: 0101 burst error: GBBGGGG

b) Dataword: 0110 burst error: BGGGGGB

c) Dataword: 1110 burst error: BGBGGGB

d) Dataword: 0001 burst error: BBGBGGG

In detail show and explain all steps

Computer networking

Datawords Codewords 0001 0010 0011 0100 0101 01 10 0111 0001101 0010111 001101(0 0100011 0101110 0110100 0111001 Datawords 1000 1001 1010 1011 1100 1101 1110 Codewords 100011 1001011 1010001 1011100 1100101 1101000 1110010 + b1 + bo +42 + a +a modulo-2 modulo-2 a2 +a +a modulo-2 b2 + b+bo S 0 1 0 1 Syndromes,s,s, 000 001 010 011 100 101 110 Error None 40