THis excerise examines the signle 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?

Sectio n$5\mathrm{.}5$ states that modern server memory modules $($DIMMs$)$ employ SEC$/$DED ECC to protect each $64$ bits with $8$ parity bits. Compute the cost$/$performance ratio of this code to the code from Exercise$\mathrm{.}5\mathrm{.}14\mathrm{.}1.$ In this case, cost is the relative number of parity bits needed while performance is the ralative number of errors that can be corrected. Which is better?

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