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Join this group to post and comment. # Digital electronics problem

A logic circuit has three Boolean inputs X,Y and Z. Its output is F(X,Y,Z) such that:
F(X,Y,Z) = 1 if aX + bY +cZ > d
= 0 otherwise.
a,b,c,d are real constants.
For which of the following values of a,b,c,d does this circuit represent an implementation
of a three-input NAND gate with inputs X,Y and Z?
I. a = b = c = 1; d = 2.5
II. a = b = c = 1; d = 1.5
III. a = b = c = -1; d = 0
IV. None of the above nowire9 • Apr 24, 2012
IV. None of the above sreeraghuma • Apr 29, 2012
nowire9 can u please explain this answer
how did u get it? nowire9 • May 1, 2012
1. Refer to the 3-input NAND truth table (the only case where F(X,Y,Z)=1 is when X=Y=Z=1, else F(X,Y,Z)=0):

X,Y,Z | F(X,Y,Z)
-----------------------
0,0,0 | 1
... | 1
1,1,1 | 0

2. Test to rule out false answers...
I. if X=1,Y=1,Z=1, then aX+bY+cZ>d is satisfied, but F(X,Y,Z)=0, not 1
II. if X=0,Y=0,Z=1, then aX+bY+cZ>d is NOT satisfied, but F(X,Y,Z)=1, not 0
III. if X=0,Y=1,Z=1, then aX+bY+cZ>d is NOT satisfied, but F(X,Y,Z)=1, not 0

3. This only leaves IV as a possible answer