$(25$ pts$)$ Second Degree PolynomialDesign a digital logic circuit as a Read Only Memory $($ROM$)[$Decoder plus OR gates$].$ AROM accepts a threebit number x : $($x$2$x$1$x$0)$ and generates an output binary number equalto the input squared $+2.$A $=$ x$2+2,$ with input $($x$)$ : $0($x$)7($a$)$ Setup the truthtable$[$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.decimal x$2$ x$1$ x$0...$ A$1$ A$000001001201030114100510161107111$