The circuit below has a $2-$to$-4$ decoder with active high outputs connected to a $4-$to$-1$ MUX with an active low output.

$($a$)$ Give the expressions for the decoder outputs. $($Use the following as necessary: A and $B.)$

$($b$)$ Give the expression for the mux output $($use $I_0,I_1,I_2$ and $I_3$ for mux inputs$).$

$f=I_0^{\text{'}}C+I_1^{\text{'}}{C}^{\text{'}}+I_2^{\text{'}}{C}^{\text{'}}+I_3^{\text{'}}{C}^{\text{'}}D$

$f=I_0^{\text{'}}{C}^{\text{'}}{D}^{\text{'}}+I_1^{\text{'}}{C}^{\text{'}}D+I_2^{\text{'}}C{D}^{\text{'}}+I_{3}CD$

$f=I_0{O}^{\text{'}}{D}^{\text{'}}+I_1^{\text{'}}{C}^{\text{'}}+I_2^{\text{'}}C+I_3^{\text{'}}D$

$f=I_0{D}^{\text{'}}+I_1^{\text{'}}{C}^{\text{'}}D+I_2^{\text{'}}C{D}^{\text{'}}+I_3^{\text{'}}CD$

$($c$)$ Write the simplified minimum SOR expression for the output, $f(A,B,C,D).$

$f(A,B,C,D)=$