Operating-Systems
October 21, 2023
UGC NET CS 2013 Dec-paper-2
October 21, 2023
Operating-Systems
October 21, 2023
UGC NET CS 2013 Dec-paper-2
October 21, 2023

Digital-Logic-Design

Question 2

Two numbers are chosen independently and uniformly at random from the set {1, 2, …, 13}. The probability (rounded off to 3 decimal places) that their 4-bit (unsigned) binary representations have the same most significant bit is ______.

A
0.502
B
0.461
C
0.402
D
0.561
Question 2 Explanation: 
Correct answer is 0.502
1 – 0001
2 – 0010
3 – 0011
4 – 0100
5 – 0101
6 – 0110
7 – 0111
8 – 1000
9 – 1001
10 – 1010
11 – 1011
12 – 1100
13 – 1101
The probability that their 4-bit binary representations have the same most significant bit is
= P(MSB is 0) + P(MSB is 1)
= (7×7)/(13×13) + (6×6)/(13×13)
= (49+36)/169
= 85/169
= 0.502
Correct Answer: A
Question 2 Explanation: 
Correct answer is 0.502
1 – 0001
2 – 0010
3 – 0011
4 – 0100
5 – 0101
6 – 0110
7 – 0111
8 – 1000
9 – 1001
10 – 1010
11 – 1011
12 – 1100
13 – 1101
The probability that their 4-bit binary representations have the same most significant bit is
= P(MSB is 0) + P(MSB is 1)
= (7×7)/(13×13) + (6×6)/(13×13)
= (49+36)/169
= 85/169
= 0.502
0 0 votes
Article Rating
Subscribe
Notify of
0 Comments
Inline Feedbacks
View all comments
0
Would love your thoughts, please comment.x
()
x
error: Alert: Content selection is disabled!!