EECE $140$ Computer Engineering

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Homework $2$ Due at the beginning of class Wednesday, $7/10/24.$ No exceptions! Please include this sheet with your submission.

NO LATE ASSIGNMENTS WILL BE ACCEPTED FOR GRADING.

Answer the following questions, showing your work to receive credit.

Answer the following questions, showing your work to receive credit.

Given $P(w,x,y,z)={\displaystyle \underset{?}{\overset{?}{}}}(0,1,3,4,5,8,10,13,15)$

$($a$)$ Implement a most simplified gate implementation of $P^{\text{'}}$ using only Nand gates. $(10$ points$)$

$($b$)$ Implement $P$ using a minimal number of only Nor gates. $(10$ points$)$

Expand this Boolean Algebraic expression to a fully expanded Sum of Products $($SOP$)$ and identify the minterms. $(15$ points$)$

$T(w,x,y,z)=x^{\text{'}}*z*(w+y^{\text{'}})*(y^{\text{'}}+z)+y*z^{\text{'}}$

Design a digital circuit that compares two $6-$bit values and displays $\text{'}>\text{'},\text{'}=\text{'},$ or $\text{'}<mtext\; id="EditorElement\_1040357"></mtext><mi\; id="EditorElement\_1040358">\text{'}</mi>$ on a $7-$segment display if $a>b,a=b,$ or $a_5{a}_4{a}_3{a}_2{a}_1{a}_0$a respectively. You may use logic gates and $HA$ and $FA$ blocks $(label$ outputs $on$ each block$)as$ necessary. The input values should $be$ described $by$ these variable names: $a_5{a}_4{a}_3{a}_2{a}_1{a}_0$ and $b_5{b}_4{b}_3{b}_2{b}_1{b}_0*(15$ points $)$

Show a gate implementation $ofa4$ input Decoder. $(15$ points$)$

Implement a circuit $to$ compute the FEC bits for $a7-$bit ASCII encoding $.(20$ points$)$

Design a digital circuit, using logic gates $to$ display the following characters $ona7-$segment display: $P,L,U,S.(15$ points$)$