Question

question 7 (4 points)
3 minutes given the code 1101011001, what would be the parity bit given even parity?
the hamming code consists of both data bits and parity bits. given the hamming code consists of 8 parity bits, what is the maximum number of data bits the hamming code can carry?

Explanation:

Step1: Calculate parity bit for 1101011001

Count the number of 1s in 1101011001. There are 6 1s. For even - parity, since the number of 1s is already even, the parity bit is 0.

Step2: Calculate maximum data bits for Hamming code with 8 parity bits

The formula for the relationship between the number of data bits $d$ and the number of parity bits $p$ in a Hamming code is $2^p\geq d + p+ 1$. We want to find $d$ when $p = 8$.
We can rewrite the formula as $d\leq2^p - p - 1$.
Substitute $p = 8$ into the formula: $d\leq2^8-8 - 1=256 - 8 - 1 = 247$.

Answer:

0
247