$3\mathrm{.}16$ Simplify the following functions, and implement them with two$-$level NAND gate circuits:

$($a$)F(A,B,C,D)=A{C}^{\text{'}}{D}^{\text{'}}+A^{\text{'}}C+$ABC$+A{B}^{\text{'}}C+A^{\text{'}}{C}^{\text{'}}{D}^{\text{'}}$

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

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

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