National Champion Test - GATE 2018 CS : Digital Logic for GATE & PSU CS Exams

Question 1

Let,

where

are Boolean variables, and ⊕ is the XOR operator.
Which one of the following must always be TRUE?

Question 2

if x'y'= 0, then ⊕ is

Question 3

If x number of 4x1 multiplexer, y number of 2x1 multiplexer and z number of 16x1 multiplexer are needed to implement a 128x1 multiplexer, then which of the following can be value of (x+y+z)?

Question 4

The output F of the 4-to-1 MUX shown in the figure is?

Question 5

The number of min-terms after minimizing the following Boolean expression is_________.
[D’ + AB’ + A’C + AC’D + A’C’D]’

Question 6

Given the function F = P’ + QR, where F is a function in three Boolean variables P, Q and R and P’ =! P, consider the following statements.
(S1) F=^∑ (4, 5, 6)
(S2)F=^∑ (0, 1, 2, 3, 7)
(S3)F=^{∏ (}4, 5, 6⁾
(S4)F=^{∏ (}0, 1, 2, 3, 7⁾
Which of the following is true?

Question 7

Consider the equation (43)_x = (y3)₈ where X and Y are unknown. The number of possible solutions is___________

Question 8

When two 8-bit numbers A₇…A₀ and B₇…B₀ in 2’s complement representation (with A₀ and B₀ as the least significant bits) are added using a ripple-carry adder, the sum bits obtained are S₇….S₀ and the carry bits are C₇…..C₀. An overflow is said to have occurred if

Question 9

The representation of the value of a 16-bit unsigned integer X in hexadecimal number system is BCA9. The representation of the value of X in octal number system is

Question 10

The value of a float type variable is represented using the single-precision 32-bit floating point format of IEEE-754 standard that uses 1 bit for sign, 8 bits for biased exponent and 23 bits for mantissa. A float type variable X is assigned the decimal value of −14.25. The representation of X in hexadecimal notation is

Question 11

Let k = 2ⁿ. A circuit is built by giving the output of an n-bit binary counter as input to an n to 2ⁿ bit decoder. This circuit is equivalent to a

Question 12

Consider the circuit in the diagram. The operator represents Ex-OR. The D flipflops are initialized to zeroes (cleared).

The following data: 100110000 is supplied to the “data” terminal in nine clock cycles. After that the values of q₂ q₁ q₀are:

Question 13

Consider the circuit given below with initial state Q₀ =1, Q₁ = Q₂ = 0. The state of the circuit is given by the value 4Q₂+ 2Q₁+ Q₀ . LSB output is denoted by Q₀, and MSB output is denoted by Q₂.

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

Question 14

Consider the following statements:
A multiplexer
1. selects one of the several inputs and transmit it to a single output.
2. routes the data from a single input to one of many output
3. converts parallel data into serial data.
4. is a combinational circuit
Which of the statements are correct?

Question 15

The Boolean expression of the logic circuit shown in figure is