Design a Read Only Memory $($ROM$)$ to implement the following polynomial

A $=3(2$x$2+1),$ with input $($x$)$ : $0($x$)7$

$($a$)$ What is the size of the initial $($unsimplified$)$ ROM $?$

$($b$)$ What is the size of the final $($simplified$)$ ROM $?$

$($c$)$ Show in detail the final ROM layout, using LogiSim.

Without LogiSim $50\%$ of the grade will be deducted