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GATE CS 2021: Digital logic 5 (App update required to attempt this test)

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Question 1

Consider the following sequence of instructions:

a=ab

b=ab

a= ba

This sequence

Question 2

Which one of the following expressions does NOT represent exclusive NOR of x and y?

Question 3

The orange box in the below figure consists of a minimum complexity circuit that uses only AND , OR and NOT gates. The function f(x,y,z) = 1 where any of the following conditions are satisfied :
•  x is not equal to y and z is grounded
•  y is equal to z , and x is set low
•  x is equal to y , y is equal to z but x not equal to z

Then which of the following equations leads to correct design for the minimum complexity circuit :

Question 4

A circuit which is working as NAND gate with positive level logic system will work as ______ gate with negative level logic system.

Question 5

If a 64x1 Mux is constructed using 4x1 Mux, then how many of the 4x1 Mux are required at 2nd level (consider level start from 1).

Question 6

Consider the following circuit:

The above circuit counts from 0 to ____.

Question 7

Consider a code converter as shown in a figure -

Then the equation of D in terms of (B3,B2,B1,B0) is -

Question 8

Consider the following circuit. A = a2a1a0 and B = b2b1b0 are three bit binary numbers input to the circuit. The output is Z = z3z2z1z0. R0, R1 and R2 are registers with loading clock shown. The registers are loaded with their input data with the falling edge of a clock pulse (signal CLOCK shown) and appears as shown. The bits of input number A, B and the full adders are as shown in the circuit. Assume Clock period is greater than the settling time of all circuits.

For 8 clocks pulses on the CLOCK terminal and the inputs A, B as shown, obtain the output Z (sequence of 4-bit values of Z). Assume initial contents of R0, R1 and R2 as all zeros.
A= 110 011 111 101 000 000 000 000
B= 101 101 011 110 000 000 000 000
Clock No 1 2 3 4 5 6 7 8

Question 9

A decimal number has 18 digits, The number of bits needed for its equivalent binary representation is(Approximately)?

Question 10

What will be the 10’s complement of (715)base 8 is

Question 11

Consider the unsigned 8-bit fixed point binary number representation below :

Where the position of the binary point is between and Assume is the most significant bit. Some of the decimal numbers listed below cannot be represented exactly in the above representation:
i. 31.500 ii. 0.875
iii. 12.100 iv. 3.001
Which one of the following statements is true?

Question 12

How many of following statements are true?

A) Function must be neutral function is a necessary as well as sufficient condition for a function to be a dual function.

B) For a n variable function, there are 2n-1 mutually exclusive pairs.

C) f(x,y,z) = Σm( 1 , 2 , 4 , 6 ) is a dual function.

D) Dual functions are a subset of Neutral functions.

E) For n=4 , total 256 dual functions are possible.

Question 13

The above synchronous sequential circuit built using JK flip-flops is initialized with

Q2Q1Q0 = 000 The state sequence for this circuit for the next 3 clock cycles is

Question 14

Given Counter is:

What can be said about above counter? If the initial states are reset.

Question 15

Following the state diagram shown clocked sequential circuit:

How many states the sequential circuit has?
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