GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
642 views

Let $\oplus$ denote the exclusive OR (XOR) operation. Let '1' and '0' denote the binary constants. Consider the following Boolean expression for $F$ over two variables $P$ and $Q$:

$$F(P,Q)=\left( \left(1 \oplus P \right) \oplus \left( P \oplus Q \right )\right ) \oplus \left(\left(P \oplus Q\right) \oplus \left(Q \oplus 0\right)\right)$$

The equivalent expression for $F$ is

  1. $P+Q$
  2. $\overline{P+Q}$
  3. $P \oplus Q$
  4. $\overline {P \oplus Q}$
asked in Digital Logic by Veteran (75.6k points)   | 642 views

3 Answers

+10 votes
Best answer

XOR is associative and commutative. Also, $A \oplus A = 0$ and $A \oplus 1 = \overline{ A}$ and $A \oplus 0 = A$.  So
$\left( \left(1 \oplus P \right) \oplus \left( P \oplus Q \right )\right ) \oplus \left(\left(P \oplus Q\right) \oplus \left(Q \oplus 0\right)\right)$
$\implies \left(1 \oplus P \right) \oplus \left( \left( P \oplus Q \right ) \oplus \left(P \oplus Q \right) \right) \oplus \left(Q \oplus 0\right)$
$\implies  \left(1 \oplus 0 \right) \oplus \left( P \oplus Q \right) $
$\implies 1 \oplus \left(  P\oplus Q \right)$
$\implies \overline {\left( P \oplus Q\right)}$

answered by Veteran (280k points)  
edited
+6 votes

D)
Since there are only 2 variables putting in pair of values of P and Q in F and checking with the options is a time saving method.
But Lets solve it.


 

answered by Loyal (3.3k points)  
0 votes
observe the common term p ex or q in both

consider a case where p and q are equal

then p ex or q results in 0

1)in first p is ex ored  with 1

2)in second q is ex ored with 0

so if p, q are same then either of one oresults in 1 and another to 0

1 ex or  0

it is exnor
answered by (333 points)  
Top Users Feb 2017
  1. Arjun

    5288 Points

  2. Bikram

    4230 Points

  3. Habibkhan

    3952 Points

  4. Aboveallplayer

    3086 Points

  5. Debashish Deka

    2378 Points

  6. sriv_shubham

    2308 Points

  7. Smriti012

    2236 Points

  8. Arnabi

    2008 Points

  9. mcjoshi

    1690 Points

  10. sh!va

    1684 Points

Monthly Topper: Rs. 500 gift card

20,860 questions
26,012 answers
59,674 comments
22,114 users