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

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Question 1

a=a⨁b

b=a⨁b

a= b⨁a

This sequence

Question 2

**NOT**represent exclusive NOR of x and y?

Question 3

- 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

Question 5

Question 6

The above circuit counts from 0 to ____.

Question 7

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

Question 8

_{2}a

_{1}a

_{0}and B = b

_{2}b

_{1}b

_{0}are three bit binary numbers input to the circuit. The output is Z = z

_{3}z

_{2}z

_{1}z

_{0}. 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.

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

Question 10

Question 11

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

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 2^{n-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

Q_{2}Q_{1}Q_{0} = 000 The state sequence for this circuit for the next 3 clock cycles is

Question 14

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

Question 15

How many states the sequential circuit has?

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