Question $01$

CLO $2$

marks$]$

Implement the following Boolean function with one multiplexer $(8-$to$-1)$ and minimal number of needed logical gates? $($Show your detailed work step by step$).$

$F_{(D,C,B,A)}={\displaystyle \underset{?}{\overset{?}{}}}(2,3,4,6,9,10,11,12).$

Question $02$

CLO $4$

$[2$ marks$]$

For the below combinational$-$logical circuit, derive the Boolean function of $\text{'}Z\text{'}$ function $($output$)?$

Question $03$

CLO $5$

marks$]$

For the below sequential circuit where the flip$-$flops are D$-$type.

$($a$)$ Find the logical equations for the state variables $\{QA,QB\}$ and for the output variable $\text{'}Y\text{'}?(2\mathrm{.}5$ points$)$

$($b$)$ Analyse this circuit and write the "state transition Table" which includes the current states, next states, input variable $\text{'}x\text{'},$ and the output variable $\text{'}Y\text{'}?(1\mathrm{.}5$ points$)$