Problem $1(20$ pts$)$: Consider the following Boolean function

$F(A,B,C,D)={\displaystyle \underset{?}{\overset{?}{}}}m(0,1,2,8,9,10,11,12,13,14,15)$

Use a K$-$map to find a minimum SOP expression for F$.$ Circle your finale answer.

Problem $2(20$ pts$)$: Consider the following Boolean function

Use a K$-$map to find a minimum SOP expression for F$.$ Circle your finale answer.

Problem $3(20$ pts$)$: Consider the following diagram:

What's the standard SOP expression of output F$?$ Express your answer in short$-$hand notation and circle your finale answer.

Problem $4(40$ pts$)$: Design a $2-$bit comparator. The circuit takes two $2-$bit numbers A and $B$ as input and outputs $1$ if and only if $AB.$ Draw a block diagram $(5$ pts$),$ generate a truth table for the circuit $(10$ pts$),$ get a minimum SOP expression for the output$(10$ pts$),$ and draw a logic diagram of the circuit $(5$ pts$).$ Simulate your circuit using Logisim and submit a screenshot of your Logisim circuit diagram $(10$ pts$).$ Use paper and a pencil