GATE CS 2016 Set 1 — Question 16
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Digital Logic → Boolean Algebra & Logic Gates → Boolean Laws & Theorems
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Question
Consider the Boolean operator # with the following properties:
and . Then is equivalent to
and . Then is equivalent to
Correct answer
(A) xy + xy
Solution
Given the properties of the operator :
This truth table corresponds to the Exclusive OR (XOR) operation ().
The Boolean expression for XOR is .Checking the options:
(A) (Matches XOR)
(B)
(C)
(D) (Matches XNOR)Thus, the correct expression is .
1.
2.
3.
4.
Let's construct the truth table for :- If : . So, and .
- If : . So, and .
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
The Boolean expression for XOR is .Checking the options:
(A) (Matches XOR)
(B)
(C)
(D) (Matches XNOR)Thus, the correct expression is .
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