###### 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 ______.

0.502 | |

0.461 | |

0.402 | |

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

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

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

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