$(25$ pts$)$ Second Degree Polynomial

Design a digital logic circuit as a Read Only Memory $($ROM$)[$Decoder plus OR gates$].$ A

ROM accepts a three$-$bit number $x$:$(x_2{x}_1{x}_0)$ and generates an output binary number equal

to the input squared $+2.$

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

$($a$)$ Set$-$up the truth$-$table

$[$Binary inputs: $(x)$; Binary outputs: $...,A_2,A_1,A_0]$

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

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

$($d$)$ Show in detail the final memory layout.