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

#### shamieh

##### Active member
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: $$\displaystyle (\bar{w} + x)(\bar{y} + z + \bar{x})(y + w + \bar{x})$$

#### Evgeny.Makarov

##### Well-known member
MHB Math Scholar
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.

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Thank you.