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ā‡± Quiz about GATE || DIGITAL LOGIC || LOGIC GATE || PYQ (2010 TO 2025)

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Question 1

Which one of the following circuits is NOT equivalent to a 2-input XNOR (exclusive NOR) gate? [GATE||2011||MCQ||1MARKS]

šŸ‘ 13-A
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Question 2

The truth table  represents the Boolean function [GATE||2012||MCQ||1MARKS]

X

Y

(X,Y)

0

0

0

0

1

0

1

0

1

1

1

1

  • X

  • X + Y


  • X āŠ• Y

  • Y


Question 3

Which one of the following expressions does NOT represent exclusive NOR of x and y? [GATE 2013 || MCQ || 1 MARKS ]


  • xy+x'y'

  • xāŠ•y'


  • x'āŠ•y

  • x'āŠ•y'


Question 4

Let āŠ• denote the Exclusive OR (XOR) operation. Let ā€˜1ā€™ and ā€˜0ā€™ denote the binary constants. Consider the following Boolean expression for F over two variables P and Q:

F(P, Q) = ((1āŠ•P)āŠ•(PāŠ•Q)) āŠ• ((PāŠ•Q) āŠ• (QāŠ•O))

The equivalent expression for F is [GATE||2014||SET3||MCQ||2MARKS]


  • P+Q

  • (P+Q)'

  • Pā؁Q

  • (Pā؁Q)'

Question 5

Let, x1āŠ•x2āŠ•x3āŠ•x4 = 0 where x1, x2, x3, x4 are Boolean variables, and āŠ• is the XOR operator. Which one of the following must always be TRUE? [GATE||2016||SET2||1MARKS]


  • x1x2 x3x4 = 0

  • x1x3+x2 = 0

  • x1 'āŠ•x3 '= x2 'āŠ• x4 '

  • x1 + x2 + x3 + x4 = 0


Question 6

Consider the Boolean operator # with the following properties: x#0 = x, x#1 = x', x#x = 0 and x#x' = 1 Then x#y is equivalent to [GATE||2016||SET1||1MARKS]

  • x'y + xy'

  • xy' + (xy)

  • x'y + xy

  • xy + (xy)'

Question 7

Which one of the following is NOT a valid identity?[GATE|| 2019 || MCQ || 1 Mark]

  • (x + y) āŠ• z = x āŠ• (y + z)

  • (x āŠ• y) āŠ• z = x āŠ• (y āŠ• z)


  • x āŠ• y = x + y, if xy = 0

  • x āŠ• y = (xy + x'y')'


Question 8

Consider the following logic circuit diagram.

šŸ‘ Logic_Gate1

Which is/are the CORRECT option(s) for the output function F ? [GATE || 2025 || SET 2|| MSQ || 2-mark]

  • (XY)'

  • X' + Y' + XY'

  • (XY)' + X' + XY'

  • X + Y'

Question 9

Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur instantaneously and that wires have no delays.

šŸ‘ q18

Which of the following statements about the circuit is/are CORRECT? [GATE|| 2024 ||SET 1||MSQ || 2-mark ]

  • With no propagation delays, the output Y is always logic Zero

  • With no propagation delays, the output Y is always logic One

  • With propagation delays, the output Y can have a transient logic One after X transitions from logic Zero to logic One

  • With propagation delays, the output Y can have a transient logic Zero after X transitions from logic One to logic Zero

Question 10

Consider 4-variable functions f1, f2, f3, f4 expressed in sum-of-minterms form as given below. 

f1 = āˆ‘(0,2,3,5,7,8,11,13) 

f2 = āˆ‘(1,3,5,7,11,13, 15) 

f3 = āˆ‘(0,1,4,11) 

f4 = āˆ‘(0,2,6,13)

šŸ‘ 19_Q
.

With respect to the circuit given above, which of the following options is/are CORRECT? [GATE|| 2024 SET2|| MSQ ||1-mark]

  • Y= āˆ‘(0,1,2,11,13)

  • Y= Ī  (3,4,5,6,7,8,9,10,12,14,15)

  • Y= āˆ‘(0,1,2,3,4,5,6,7)

  • Y= Ī  (8,9,10,11,12,13,14,15)

There are 11 questions to complete.

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