October 3, 2023
October 3, 2023
October 3, 2023
###### Operating-Systems
October 3, 2023
 Question 1
A decimal has 25 digits. the number of bits needed for its equivalent binary representation is approximately
 A 50 B 74 C 40 D 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​ 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.
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.