K-map Minimization

karnaugh map

I'm having trouble minimizing this k-map for ∑m(0,5,9,12,15) and converting the SOP into a design using only NAND's and NOR's. I think the SOP should be (ABD')+(A'B'D')+(AC)+(A'BC'D)+(AB'D), but I'm confused because there is a single 1 that I can't group. Sorry for the poor formatting and thanks in advance for any answers, explanations are always a plus for me.
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Best Answer

The SOP you have got is correct.

F = (ABD')+(A'B'D')+(AC)+(A'BC'D)+(AB'D)

You can not reduce this further. Now implementing using NAND is simple.

F = [F']' = [(ABD')' . (A'B'D')'. (AC)' . (A'BC'D)' . (AB'D)']'

F can be implemented as the output of a NAND gate whose inputs are the five terms as shown above. It is clear from the expression that each of these five terms can be implemented using NAND gates.

Similarly, writing POS will give easy NOR only implementation.

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