Minimal cost of circuit implementation

[shamieh]

A cheap way to implement this circuit is to use NOR gates. Draw the circuit diagram for the lowest cost implementation using these gates.
f(w,x,y,z) = (w + y) * (x + z)
SOLVED.

Solution: w + y with ! inverters and x + z with not inverters to another NOR gate which makes them positive again.

 

[Tom.G]

I beg to differ:

Only three NOR gates are needed; the first two handle the W,Y and X,Z inputs; which are then fed directly to a 3rd NOR. Since the 3rd NOR is fed the negation of the input requirements, it acts as a Negative logic AND gate. And since the 3rd NOR is also inverting, the final output is back to Positive logic.

Consider:
Assuming Positive logic.
1) label the output of the 1st NOR gate as A= (W + Y). A will be Lo if either W or Y is Hi (True)

2) same approach for 2nd NOR gate B= (X + Z). B will be Lo if either if either X or Z is HI (True)

3) 3rd NOR gate as Out= (A + B). Out will be Hi if-and-only-if inputs both A and B are Lo

Cheers,
Tom