A function F is defined such that it equals $1$ when a $4-$bit input code is equivalent to any of the decimal numbers $3,6,9,12,$ or $15.$ Function F is $0$ for input codes $0,2,8,$ and $10.$ Other input values cannot occur. Consider the inputs as A$,$ B$,$ C$,$ and D$.$

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NOTE: This is a multi$-$part question. Once an answer is submitted, you will be unable to return to this part.

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Determine a minimal expression for this function using a Karnaugh map.