GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
477 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

(A) $P+Q$

(B) $\overline{P+Q}$

(C) $P \oplus Q$

(D) $\overline {P \oplus Q}$

asked in Digital Logic by Veteran (73.2k points)   | 477 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 (272k points)  
edited
+5 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 (3.2k 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 (227 points)  
Top Users Jan 2017
  1. Debashish Deka

    7050 Points

  2. Habibkhan

    4674 Points

  3. Vijay Thakur

    4224 Points

  4. saurabh rai

    4008 Points

  5. sudsho

    3960 Points

  6. Arjun

    3108 Points

  7. GateSet

    3088 Points

  8. santhoshdevulapally

    3004 Points

  9. Bikram

    2976 Points

  10. Sushant Gokhale

    2744 Points

Monthly Topper: Rs. 500 gift card

18,810 questions
23,779 answers
51,413 comments
20,128 users