$5.$ Create a $3$ input $(\backslash ($ x$,$ y$,$ z $\backslash ))$ encoder that assigns a $2$ input $($a$,$b$)$ code $($as input for the next module$)$ to each of the $3$ different inputs.

Optimal design, $\backslash ($ a$=$x$^\{\backslash$prime$\},$ b$=$y$^\{\backslash$prime$\}\backslash ).$

Create a simple truth table and also a state transition truth table for the following graph$-$

U$/0$

Explain the backdoor vulnerabilities and fault injection attack. Also discuss the trojan if following states are added as the backdoor vulnerabilities. Create a countermeasure for this.