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+10 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. $\overline{P+Q+R}$
asked in Digital Logic by Veteran (101k points)
edited by | 1.8k views

2 Answers

+22 votes
Best answer

$f = S_0'S_1' R + S_0'S_1R' + S_0S_1'R' + S_0S_1R$

$=Q'P'R + Q'PR' + QP'R' + QPR \\= Q'(P⊕R) + Q(P⊕R)' \\= Q⊕P⊕R = P⊕Q⊕R$

Doing truth value substitution, 

$P$ $Q$ $R$ $f$ ${P \oplus Q \oplus R}$
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
answered by Veteran (357k points)
edited
+1
 
QQ'(PR)+Q(PR')
HOW TO SIMPLIFY IT:
0
@Arjun sir, dosent the answer hold good for option A too?? as we have odd number of variables , xor and xnor give same ans right ?
0

Let : Y = P XOR R

So : Q' Y + Q Y' 

= Q XOR Y

= Q XOR P XOR R

0 votes
answer - B
answered by Loyal (9k points)


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