ISRO | ISRO CS 2015 | Question 77

The decimal number has 64 digits.The number of bits needed for its equivalent binary representation is?
(A) 200
(B) 213
(C) 246
(D) 277

Answer: (B)
Explanation: Maximum 64 digit decimal number = 10⁶⁴ – 1
Maximum x bit binary number = 2^x – 1
10⁶⁴ – 1 = 2^x – 1
taking log
log ₂10⁶⁴ = x
x = 64 log ₂10
x = 64 x 3.3
x = 211.2 (approximately 213)
So, correct option is (B)
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