USE

$[$ Circuit design $][$ ROM design $][$ MIPS Assembly implementation $]$

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.

$2.$ Design a Read Only Memory $($ROM$)$ to implement the following polynomial

$A=3(2x^2+1),$ 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.

$3.$ Using MIPS assembly$-$language evaluate the following, polynomial:

$A=3(2x^2+1),$ for $,x=1,7$

$($a$)$ The program should be simple modularized and well$-$documented

$($b$)$ Appropriate comments in the program are necessary

$($c$)$ Place the results, in the command line window $($console$).$ In the report include a clear screenshot of the DECIMAL results $($command line window$-$console area$)$ and the REGISTERS with the DECIMAL results $($registers area$)$

$($d$)$ Indicate if the program runs successfully according to specifications and clearly state the results $($DECIMAL numbers$).$