1
GATE CSE 2021 Set 2
Numerical
+1
-0
If x and y are two decimal digits and (0.1101)2 = (0.8xy5)10, the decimal value of x + y is ______
Your input ____
2
GATE CSE 2021 Set 2
MCQ (Single Correct Answer)
+1
-0.33

The format of the single-precision floating-point representation of a real number as per the IEEE 754 standard is as follows:

sign

exponent

mantissa


Which one of the following choices is correct with respect to the smallest normalized positive number represented using the standard?
A
exponent = 00000000 and mantissa = 00000000000000000000001
B
exponent = 00000001 and mantissa = 00000000000000000000000
C
exponent = 00000001 and mantissa = 00000000000000000000001
D
​exponent = 00000001 and mantissa = 000000000000000000000001
3
GATE CSE 2021 Set 2
MCQ (Single Correct Answer)
+2
-0.66

Suppose we want to design a synchronous circuit that processes a string of 0’s and 1’s. Given a string, it produces another string by replacing the first 1 in any subsequence of consecutive 1’s by a 0. Consider the following example.

Input sequence : 00100011000011100

Output sequence : 00000001000001100

A Mealy Machine is a state machine where both the next state and the output are functions of the present state and the current input.

The above mentioned circuit can be designed as a two-state Mealy machine. The states in the Mealy machine can be represented using Boolean values 0 and 1. We denote the current state, the next state, the next incoming bit, and the output bit of the Mealy machine by the variables s, t, b and y respectively.

Assume the initial state of the Mealy machine is 0.

What are the Boolean expressions corresponding to t and y in terms of s and b ?

A

t = b

y = sb

B

t = s + b

y = sb

C

t = s + b

y = sb̅

D

t = b

y = sb̅ 

4
GATE CSE 2021 Set 2
Numerical
+2
-0

Consider a Boolean function f(w, x, y, z) such that 

f(w, 0, 0, z) = 1

f(1, x, 1, z) = x + z

f(w, 1, y, z) = wz + y

The number of literals in the minimal sum-of-products expression of f is ______

Your input ____
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