Problem $2.$

This exercise examines the single error correcting, double error detecting $($SEC$/$DED$)$ Hamming code.

What is the minimum number of parity bits required to protect a $128-$bit word using the SEC$/$DED code?

Many modern server memory modules $($DIMMs$)$ employ SEC$/$DED error correction coding $($ECC$)$ to protect each $64$ bits with $8$ parity bits. Compute the cost$/$performance ratio of this code to the minimum parity bit SEC$/$DEC code $($using the method developed in part a$.)$ In this case, cost is the relative number of parity bits needed while performance is the relative number of errors that can be corrected. Which is better?

Consider a SEC code that protects $8$ bit words with $4$ parity bits. If we read the value $0$x$375,$ is there an error? If so$,$ correct the erro