Operating-Systems
October 3, 2023Operating-Systems
October 3, 2023Nielit Scientific Assistance CS 15-10-2017
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Question 1
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A decimal has 25 digits. the number of bits needed for its equivalent binary representation is approximately
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50
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74
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40
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None of the above
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Question 1 Explanation:
Consider three digits(1,2,3) of decimal numbers.Maximum number, we can generate by that three digits are 10 3 -1 which is 999.
Then, Decimal number has 25 digits, so maximum number is 10 25 -1
Similarly, in the binary representation with “n” bits the maximum number is 2 25 -1
So we can write 10 25 –1 = 2 n – 1 → 10 25 = 2 n
After taking log 2 on both sides
log 2 2 n =log 2 10 25
n log 2 2=25 log 2 10
n = 25 log 2 10
n = 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.
Then, Decimal number has 25 digits, so maximum number is 10 25 -1
Similarly, in the binary representation with “n” bits the maximum number is 2 25 -1
So we can write 10 25 –1 = 2 n – 1 → 10 25 = 2 n
After taking log 2 on both sides
log 2 2 n =log 2 10 25
n log 2 2=25 log 2 10
n = 25 log 2 10
n = 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 3 -1 which is 999.
Then, Decimal number has 25 digits, so maximum number is 10 25 -1
Similarly, in the binary representation with “n” bits the maximum number is 2 25 -1
So we can write 10 25 –1 = 2 n – 1 → 10 25 = 2 n
After taking log 2 on both sides
log 2 2 n =log 2 10 25
n log 2 2=25 log 2 10
n = 25 log 2 10
n = 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.
Then, Decimal number has 25 digits, so maximum number is 10 25 -1
Similarly, in the binary representation with “n” bits the maximum number is 2 25 -1
So we can write 10 25 –1 = 2 n – 1 → 10 25 = 2 n
After taking log 2 on both sides
log 2 2 n =log 2 10 25
n log 2 2=25 log 2 10
n = 25 log 2 10
n = 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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