Question $4$

Draw logic diagram using AND, OR and NOT gates to represent the expression:

$($a$)K\frac{+}{b}ar\frac{K}{b}ar(L)M\frac{+}{b}ar\frac{K}{b}ar\frac{L}{b}ar(M)\frac{+}{b}ar(K)LM\frac{+}{b}ar(K)\frac{L}{b}ar(M).$

$[5$ marks$]$

$($b$)$ Use Boolean Algebra to simplify this expression, $K\frac{+}{b}ar\frac{K}{b}ar(L)M\frac{+}{b}ar\frac{K}{b}ar\frac{L}{b}ar(M)\frac{+}{b}ar(K)LM\frac{+}{b}ar(K)\frac{L}{b}ar(M).$

$[5$ marks$]$