Design a combinational circuit that generates the $9\text{'}$s complement of an excess$-3$ code digit; The $4-$bits input $($A$,$B$,$C$,$D$),$ and the $9\text{'}$s complement output bits $(w,x,y,z)$

$w=A^{\text{'}},x=B^{\text{'}},y=C^{\text{'}},z=D^{\text{'}}$

$w=A^{\text{'}}B,x=A{B}^{\text{'}},y=C^{\text{'}}{D}^{\text{'}},z=C^{\text{'}}D$

$w=A^{\text{'}}B+CD,x=A{B}^{\text{'}}+CD,y=C^{\text{'}}{D}^{\text{'}}+A^{\text{'}}{C}^{\text{'}},z=C^{\text{'}}D+BC$