###### Operating-Systems

October 3, 2023###### Operating-Systems

October 3, 2023# Nielit Scientific Assistance CS 15-10-2017

Question 1 |

A decimal has 25 digits. the number of bits needed for its equivalent binary representation is approximately

50 | |

74 | |

40 | |

None of the above |

Question 1 Explanation:

Consider three digits(1,2,3) of decimal numbers.Maximum number, we can generate by that three digits are 10

Then, Decimal number has 25 digits, so maximum number is 10

Similarly, in the binary representation with “n” bits the maximum number is 2

So we can write 10

After taking log

log

n log

n = 25 log

n = 25 x 3.3 [ log

n = 82.5

Note: Original question paper given option D is 60. But actual answer is 82.5.

^{ 3} -1 which is 999.Then, Decimal number has 25 digits, so maximum number is 10

^{ 25} -1Similarly, in the binary representation with “n” bits the maximum number is 2

^{25} -1So we can write 10

^{25} –1 = 2^{ n} – 1 → 10^{ 25} = 2^{ n}After taking log

_{2} on both sideslog

_{2}2^{n} =log_{ 2} 10^{25}n log

_{2} 2=25 log _{2} 10n = 25 log

_{2} 10n = 25 x 3.3 [ log

_{2} 2=1 & log_{2} 10 =3.322]n = 82.5

Note: Original question paper given option D is 60. But actual answer is 82.5.

Correct Answer: D

Question 1 Explanation:

Consider three digits(1,2,3) of decimal numbers.Maximum number, we can generate by that three digits are 10

Then, Decimal number has 25 digits, so maximum number is 10

Similarly, in the binary representation with “n” bits the maximum number is 2

So we can write 10

After taking log

log

n log

n = 25 log

n = 25 x 3.3 [ log

n = 82.5

Note: Original question paper given option D is 60. But actual answer is 82.5.

^{ 3} -1 which is 999.Then, Decimal number has 25 digits, so maximum number is 10

^{ 25} -1Similarly, in the binary representation with “n” bits the maximum number is 2

^{25} -1So we can write 10

^{25} –1 = 2^{ n} – 1 → 10^{ 25} = 2^{ n}After taking log

_{2} on both sideslog

_{2}2^{n} =log_{ 2} 10^{25}n log

_{2} 2=25 log _{2} 10n = 25 log

_{2} 10n = 25 x 3.3 [ log

_{2} 2=1 & log_{2} 10 =3.322]n = 82.5

Note: Original question paper given option D is 60. But actual answer is 82.5.

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