Logic gate design.

In this problem, we design $7-$segment decoder. $7-$segment decoder converts $4-$bit binary number $ABC{D}_2$ into $7$ signal lines $($from a to f$),$ which turn on $7-$segment display. Assume $A$ is MSB$,D$ is LSB$.)$

$ABC{D}_2$ is $4-$bit binary number, which ranges from $0_{10}$ to $9_{10}.$ The display will present decimal numbers as follows.

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Find a Boolean function $($Boolean expression$)$ describing $d$ as a function $A,B,C$ and $D.$

$($a$)$ Use Sum$-$of$-$product expression

$($b$)$ Use product$-$of$-$sum expression