Digital electronics problem

Banashree Patra

Banashree Patra

@banashree-patra-m0OJwR • Oct 27, 2024
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
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  • nowire9

    nowire9

    @nowire9-vwkGOI • Apr 23, 2012

    IV. None of the above
    0
  • sreeraghuma

    sreeraghuma

    @sreeraghuma-VQ3h4u • Apr 29, 2012

    #-Link-Snipped-# can u please explain this answer
    how did u get it?
    0
  • nowire9

    nowire9

    @nowire9-vwkGOI • Apr 30, 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
    0