Chapter 2, Problem 70E

Explanation of Solution

Error correcting code using hamming algorithm:

The length of memory word is 12.

The number of parity bits is 5.

The number of bits present in the code word is 17.

The given code word is 01100101001001001.

The number bits starts from right to left with 1.

The number equal to the power of 2 is known as parity bit.

For example; $2^0=1$, $2^1=2$, $2^2=4$, $2^3=8$ and $2^4=16$

The positions of the parity bits are 1, 2, 4, 8 and 16.

Now, write the sum of the numbers with powers of 2.

$\begin{array}{l}1=1\\ 2=2\\ 3=1+2\\ 4=4\\ 5=1+4\\ 6=2+4\\ 7=1+2+4\\ 8=8\\ 9=1+8\\ 10=2+8\\ 11=1+2+8\\ 12=4+8\\ 13=1+4+8\\ 14=2+4+8\\ 15=1+2+4+8\\ 16=8+8\\ 17=1+8+8\end{array}$

The given code word as follows

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