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24 votes
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The Boolean expression of the output $f$ of the multiplexer shown below is

  1. $\overline {P \oplus Q \oplus R}$
  2. $P \oplus Q \oplus R$
  3. $P+Q+R$
  4. $\overline{P+Q+R}$
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2 Answers

Best answer
36 votes
36 votes
$f = S_0'S_1' R + S_0'S_1R' + S_0S_1'R' + S_0S_1R$
$\quad=Q'P'R + Q'PR' + QP'R' + QPR $
$\quad= Q'(P⊕R) + Q(P⊕R)' $
$\quad= Q⊕P⊕R = P⊕Q⊕R$

Doing truth value substitution,
$${\begin{array}{|cccc|c|}\hline
\textbf{P}&    \textbf{Q}&  \textbf{R}&\bf{f}& \bf{P \oplus Q \oplus R } \\\hline
0&0&0&0&0 \\ 0&0&1&1&1\\     0&1&0&1&1\\    0&1&1&0&0\\    1&0&0&1&1\\  1&0&1&0& 0  \\    1&1&0&0&0\\    1&1&1&1& 1\\ \hline
\end{array}}$$ Correct Answer: $B$
edited by
1 votes
1 votes

Draw the k-map, and the pattern like this is always of XOR therefore, the answer will be P⊕Q⊕R

Answer:

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