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

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

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

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