Design a circuit which uses an SN$74151$ to implement a sum$-$of$-$products expression, as follows:

a$)$ Convert the following expression into summation form $($i$.$e$.,($:$F(A,B,C)={\displaystyle \underset{?}{\overset{?}{}}}(dots)\}$ :

$Y=f(A,B,C)=A{B}_{+}{B}_C$

b$)$ Sketch on Figure $3\mathrm{.}1$ the input connections necessary to implement the function in part $($a$).$ Observe that the inputs are connected to $0$ or $1$ depending on the value of the function for that min term.

Important: Please note that this way we can implement a $3-$input function $($A$,$ B$,$ C$)$ using an $8-$to$-1$ MUX. Later we will see how to implement a $4-$input function $($A$,$ B$,$ C$,$ D$)$ using an $8-$to$-1$ MUX. For that we will need to inspect the additional input $($say D$)$ with the corresponding function value. The possible inputs to the MUX are $0,1,D,D.$

Figure $3\mathrm{.}1$: Half$-$Adder Functional Diagram.

Design a circuit which uses an SN$74138$ Demultiplexer to implement a sum$-$ of$-$products expression, as follows:

a$)$ Convert the following expression into summation $($Sum of Products $-$SOP$-)$ form $($i$.$e$.$

$($:$F(A,B,C)={\displaystyle \underset{?}{\overset{?}{}}}(dots)\}$

$Y=f(A,B,C)\frac{?}{b}=ar(A)BC+\frac{B}{b}ar(C)$