Design a combinational circuit that generates the $9\text{'}$s complement of

a BCD digit; The $4-$bits input $($A$,$B$,$C$,$D$),$ the $9\text{'}$s complement output bits

$(w,x,y,z)$

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

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

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

When reducing the following expression $A^{\text{'}}B(D^{\text{'}}+C^{\text{'}}D)+B(A+A^{\text{'}}CD)$ to the

minimum number of literals we will get:

$A+B$

$B^{\text{'}}$

B

The output function in product of maxterms: $*$

$F=(0,3,5,6)$

$F=(0,1,3,6,5)$

$F=(x+y+z)(x+y+z^{\text{'}})(x+y^{\text{'}}+z^{\text{'}})(x^{\text{'}}+y+z^{\text{'}})$