Chapter 2, Problem 69E

Explanation of Solution

Error correcting code using hamming algorithm:

The length of memory word is 7.

The number of parity bits is 4.

The number of bits present in the code word is 11.

The given code word is 01111010101.

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: $2^0=1$, $2^1=2$, $2^2=4$ and $2^3=8$

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

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

$\begin{array}{l}1=1\\ 2=2\\ 3=1+2\\ 4=4\\ 5=1+4\\ 6=2+4\\ 7=1+2+4\\ 8=8\\ 9=1+8\\ 10=2+8\\ 11=1+2+8\end{array}$

The given code word as follows,

$\begin{array}{}\end{array}$