a$.(10$ points$)$ Draw the logic diagram for the following Boolean expression. The diagram should correspond exactly to the equation $($do not simplify$).$ Assume that the complements of the inputs are available.

$F=AB(C^{\text{'}}+D)+A^{\text{'}}{B}^{\text{'}}(C^{\text{'}}+D)+CD(A^{\text{'}}+B)+C^{\text{'}}{D}^{\text{'}}(A^{\text{'}}+B)$

b$.(10$ points$)$ Simplify the Boolean expression in $($a$)$ using a Karnaugh Map, then draw the corresponding two$-$level logic diagram as a sum of products implementation. Assume that the complements of the inputs are available.