Test 1- Digital Logic | Computer Science(CS)

Description: GATE Previous year Topic Wise Questions and Answers | Digital Logic
Number of Questions: 15
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Tags: digital logic GATE CS
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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


Correct Option: C
Explanation:

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


Correct Option: B
Explanation:

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


Correct Option: A
Explanation:

$f_i(x,y,z) = \sum(0,1,3,5)$

What are the states of the Auxiliary Carry (AC) and Carry Flag (CY) after executing the following 8085 program? MIV H, 5DH MIV L, 6BH MIV L, 6BH ADD L

  1. AC = 0 and CY = 0

  2. AC = 1 and CY = 1

  3. AC = 1 and CY = 0

  4. AC = 0 and CY = 1


Correct Option: C
Explanation:

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


Correct Option: C
Explanation:

                

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


Correct Option: A
Explanation:

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.


Correct Option: A
Explanation:

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


Correct Option: A
Explanation:

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


Correct Option: B
Explanation:

In 2's complement addition, overflow

  1. Relational algebra is more powerful than relational calculus

  2. Relational algebra has the same power as relational calculus.

  3. Relational algebra has the same power as safe relational calculus.

  4. None of the above.


Correct Option: B
Explanation:

In 2's complement addition, overflow occurs when the carries from sign bit & previous bit doesn't match. So overflow can't occur when a positive value is added to some negative value.

Sign extension is a step in

  1. floating point multiplication

  2. signed 16 bit integer addition

  3. arithmetic left shift

  4. converting a signed integer from one size to another.


Correct Option: A
Explanation:

Sign extension is the operation in computer arithmetic of increasing no. of bits of a binary no., while preserving sign and value done by appending MSB's. In the floating point multiplication to bring the no. in desired no. of significant digits sign extension is done.

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


Correct Option: C
Explanation:

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

  1. ABE

  2. DBC

  3. DE5

  4. 9E7


Correct Option: C
Explanation:

Binary of 539 = 1000011011

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

  1. 1111

  2. 11111

  3. 111111

  4. 10001


Correct Option: D
Explanation:

Given (− 15)10 Binary of 15 = (01111)2 2's complement of 15 would represent (− 15). 01111 (10001)2

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.


Correct Option: B
Explanation:

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