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Product of Sums Problem. Can someone check my work? Couldn't find the problem via Google.

shamieh

Active member
Sep 13, 2013
539
Just need someone to check my work. Couldn't find the problem via Google.

$f$(W,X,Y,Z) M (0,1,2,7,12,15) + d(3,13).

1)Find the minimum Product of Sums equation using a K-Map.

2)Draw a schematic of a minimized circuit implementing the logic using NOR gates.

1) My Answer: \(\displaystyle (\bar{w} + x)(\bar{y} + z + \bar{x})(y + w + \bar{x})\)

2) My Answer: pphoto.png
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,493
I agree with 1). As for 2), NOR can express AND, OR and NOT: see Wikipedia. However, expressing the usual connectives through NOR requires duplication of inputs. For example, PQ (the conjunction of P and Q) equals (P NOR P) NOR (Q NOR Q). If P is itself a big expression, the resulting expression is at least twice as big because P is used two times. So when constructing a circuit, you probably should split the output of P and feed it into both inputs of NOR instead of having two sub-circuits representing P.
 

shamieh

Active member
Sep 13, 2013
539
on)

Thank you.