$($a$)$ The decimal diglts $0$ though $9$ are represented using five bits $A,B,C,D,$ and $E.$ The bits $A,B,C,$ and $D$ are the Excess$-3$ representation of the decimal digit, and bit $E$ is a parity bit that makes the five bits have even parity $(Ao+Bo+Co+D).$ The function $,$ C$,$ D$,$ E $)$ has value $1$ if the decimal digit represented by $A,B,C,D,$ and E is divisible by either $3$ or $4.$ Find a reduced function for $F$ and $\frac{?}{\text{b}\text{a}\text{r}}(F)$ in sum$-$of$-$product form by first finding prime implicants.

$($CO$2)$

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