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+11 votes

Consider the following circuit.     

Which one of the following is TRUE?

  1. $f$ is independent of $x$

  2. $f$ is independent of $y$

  3. $f$ is independent of $z$

  4. None of $x, y, z$ is redundant

in Digital Logic by Veteran (52.2k points)
edited by | 2.1k views

3 Answers

+21 votes
Best answer

The expression will be

$f = [ ( x.y' )'.(y.z) ]'=[ (x'+y).(y.z) ]' =[ x'.y.z+y.z ]'=[ (x'+1).(y.z) ]'=[ 1.(y.z) ]'=[ y.z ]'=y'+z'$

The final expression only contains $y$ and $z$,

Therefore, answer will be (a) f is Independent of $x$

by (243 points)
edited by
f= (x'+y)'+(yz)'    //here i have applied "bubble OR Gate"



=y'+z'               //A+A'=1

Answer (A)
+6 votes

Simplify the given circuit, as dotted input OR gate is equal to NAND gate:

(A) is the correct option!

by Boss (44.2k points)
edited by
–3 votes
ans a)
by Loyal (5.2k points)
can you give solution??

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