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The Boolean expression for the output $f$ of the 4x1 multiplexer shown below:

1.

 

2.

 

3.

Both a and b

 

4.

None of the above

in Digital Logic by (116 points)
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This MUX diagram is not correct. But answer can predict as 2).

just use MUX general formula, will able to get result.
+1

I was able to solve it later and i have ans as 3.Both

as XOR and XNOR gives same results for odd number of elements

1 Answer

+1 vote
$P’Q’R +P’QR’ + PQ’R’ + PQR$ is the output of MUX.

$P\odot (Q \odot R) $

$= P\odot (QR + Q’R’) $

$= P’(QR+Q’R’)’ + P(QR + Q’R’) $

$= P’(Q’+R’)(Q+R) + PQR + PQ’R’ $

$= P’(Q’R +QR’) + PQR + PQ’R’ $

$= P’Q’R +P’QR’ + PQR + PQ’R’$


$P \oplus (Q \oplus R)$

$= P \oplus (Q’R +QR’)$

$= P(Q’R +QR’)’ + P’(Q’R +QR’) $

$= P(Q+R’)(Q’+R) + P’Q’R +P’QR’ $

$= P(QR+R’Q’) + P’Q’R +P’QR’ $

$= PQR+P’Q’R’ + P’Q’R +P’QR’ $


So both $a$ and $b$  are correct, so $3$ is correct option
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