A switching circuit has four inputs as shown.

The variables A and $B$ represent the first and second bits of a binary number $N_1,$ respectively. The variables $C$ and $D$ represent the first and second bits of a binary number $N_2,$ respectively. The output is to be $1$ only if the product $N_{1}x{N}_2$ is less than or equal to $2.$

$($a$)$ Find the minterm expansion for $F.($Express your answers in both decimal notation and algebraic form. For decimal notation, enter your answers as a comma$-$separated list in ascending order.$)$

decimal notation

algebraic form $,F(A,B,C,D)=$

$($b$)$ Find the maxterm expansion for $F.($Express your answers in both decimal notation and algebraic form. For decimal notation, enter your answers as a comma$-$separated list in ascending order.$)$

decimal notation

algebraic form $,F(A,B,C,D)=$

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