$4-11.$ Determine the minimum expression for each $K$ map in Figure $4-67.$

Pay particular attention to step $5$ for the map in $($a$).$

$($a$){?}^{**}$

$($b$)$

$($c$)$

$4-13.$ Starting with the truth table in Table $4-11,$ use a $K$ map to find the

simplest SOP equation.

$4-14.$ Simplify the expression in $($a$)^$ Problem $4-1($e$)$ using a K map.

$($b$)$ Problem $4-1($g$)$ using a K map. $($c$)$ Problem $4-1($h$)$ using a K map.

$4-15..$ Obtain the output expression for Problem $4-7$ using a K map.