$5\mathrm{.}14$ This exercise examines the single error correcting, double error detecting $($SEC$/$DED$)$ Hamming code.

$5\mathrm{.}14\mathrm{.}1$ What is the minimum number of parity bits required to protect a $128-$bit word using the SEC$/$DED code?

$5\mathrm{.}14\mathrm{.}2$ Consider a SEC code that protects $8$ bit words with $4$ parity bits. If we read the value $0375,$ is there an error? If so$,$ correct the error.