Design a digital logic circuit $($all steps are required$),$ using minimal amount of gates,

that will realize a digital logic circuit corresponding to the following polynomial :

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

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

$[$Binary inputs: $(x)$; Binary outputs: $A_1,A_2,A_3,A_4,$dots $]$

$($b$)$ Derive the output expressions

$($c$)$ Simplify $($optimally$)$ the derived expressions, USING ONLY K$-$Maps

$($d$)$ Implement the simplified digital logic circuit, using LogiSim.

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