$1-$When reducing the following expression ABC'D $+$ A'BD $+$ ABCD to the minimum number of literals we will get:

$*$

a$-$B$+$D

b$-$BD

c$-$B$\text{'}$D

$2-$Design a combinational circuit that generates the $9$s complement of an excess$-3$ code digit ; The $4-$bits input $($A$,$B$,$C$,$D$),$ and the $9$s complement output bits $($w$,$x$,$y$,$z$)$

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

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

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