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Digital Logic - GATE Practice Questions

GATE previous year questions on digital logic including multiplexers, flip-flops, Boolean algebra, Karnaugh maps, state machines, and number representation

12 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

Consider the circuit shown below. The output of a 2:1 Mux is given by the function (ac' + bc).

Which of the following is true?

  1. f = x1' + x2
  2. f = x1'x2 + x1x2'
  3. f = x1x2 + x1'x2'
  4. f = x1 + x2
Question 2 Multiple Choice (Single Answer)

Consider the circuit given below the initial state Q0 = 1,Q1 = Q2 = 0. The state of the circuit is given by the value 4Q2+ 2Q1+ Q0

Which one of the following is the correct state sequence of the circuit?

  1. 1, 3, 4, 6, 7, 5, 2
  2. 1, 2, 5, 3, 7, 6, 4
  3. 1, 2, 7, 3, 5, 6, 4
  4. 1, 6, 5, 7, 2, 3, 5
Question 3 Multiple Choice (Single Answer)

Consider the following logic circuit whose inputs are functions f1, f2, f3 and output is f

Given that
f1(x,y, z) = $\sum$(0,1,3,5)
f2(x,y,z) = $\sum$(6,7), and
f (x,y,z) = $\sum$(1,4,5) f3 is

  1. $\sum$ (1,4,5)
  2. $\sum$ (6,7)
  3. $\sum$ (0,1,3,5)
  4. None of the above
Question 4 Multiple Choice (Single Answer)

Let f (A,B) = A' + B. Simplified expression for function f (f (x + y,y), z) is

  1. x' + z
  2. xyz
  3. xy' + z
  4. None of the above
Question 5 Multiple Choice (Single Answer)

Consider the following multiplexor where 10, 11, 12, 13 are four data input lines selected by two address line combinations A1A0 = 00,01,10,11 respectively and f is the output of the multiplexor. EN is the Enable input.

The function f (x,y,z) implemented by the above circuit is

  1. xyz'
  2. xy + z
  3. x + y
  4. None of the above
Question 6 Multiple Choice (Single Answer)

The finite state machine described by the following state diagram with A as starting state, where an arc label is $\dfrac{x}{y}$ and x stands for 1-bit input and y stands for 2-bit output.

  1. Outputs the sum of the present and the previous bits of the input.
  2. Outputs 01 whenever the input sequence contains 11
  3. Outputs 00 whenever the input sequence contains 10
  4. None of the above.
Question 7 Multiple Choice (Single Answer)

Given the following Karnaugh map, which one of the following represents the minimal sum-of-Products of the map?

  1. xy + y'z
  2. wx'y' + xy + xz
  3. w'x + y'z + xy
  4. xz + y
Question 8 Multiple Choice (Single Answer)

Minimum sum of product expression for f (w,x,y,z) shown in Karnaugh-map below is

  1. xz + y'z
  2. xz' + zx'
  3. x'y + zx'
  4. None of the above
Question 9 Multiple Choice (Single Answer)

Consider the following circuit with initial state Q0 = Q1 = 0. The D flip-flops are positive edged triggered and have set up times 20 nanosecond and hold times 0.

Consider the following timing diagrams of X and C ; the clock of C 40 nanosecond. Which one is the correct plot of Y

Question 10 Multiple Choice (Single Answer)

The 2's complement representation of (− 539)10 in hexadecimal is

  1. ABE
  2. DBC
  3. DE5
  4. 9E7
Question 11 Multiple Choice (Single Answer)

The 2's complement represent representation of the decimal value −15 is

  1. 1111
  2. 11111
  3. 111111
  4. 10001
Question 12 Multiple Choice (Single Answer)

The decimal value of 0.25

  1. is equivalent to the binary value 0.1
  2. is equivalent to the binary value 0.01
  3. is equivalent to the binary value 0.00111.....
  4. cannot be represented precisely in binary.
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