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It is necessary to formulate the hamming code for four data bits $D _3, D _5, D _6 and D _7$ together with three parity bits $P _1, P _2 and P _3$.

1. evaluate the 7-bit composite code word for the data word 0010.
2. Evaluate three Check bits $C _4, C _2 and C _1$, Assuming no error.
3. Assume an error in Bit $D _5$ during writing into memory. show how the error in the bit is detected and corrected.
4. Add parity bit $P _8$ to include the double bit error detection in the code. Assume that error occurs in the bit $D _5 and P _2$. Show how the error is detected.
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