Question $1$:

Let F$($A$,$ B$,$ C$)$ be a Boolean function with the following description:

F $($A$,$B$,$C$)=1$ if A$=0$ AND B$=$C

F$($A$,$B$,$C$)=1$ if A$=$B$=1$

F$($A$,$B$,$C$)=0$ otherwise

$1.$ Fill in the truth table for F$($A$,$ B$,$ C$)$

$2.$ Write the functionality as sum of minterms

$3.$ Simplify the functionality using K$-$map

$4.$Using logic gates, build the digital circuit for implementing the simplified functionality. You may assume that the gates are available with any number of inputs.

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Question $2$: Repeat the steps from above for problem below

Let F$($A$,$ B$,$ C$)$ be a Boolean function with the following description:

F $($A$,$B$,$C$)=1$ if A$=1$ or C$=0$

F$($A$,$B$,$C$)=0$ otherwise