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

  1. $50$
  2. $74$
  3. $40$
  4. $60$
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Maximum 25 digit decimal number = $10^{25} – 1$
Maximum x bit binary number = $2^x – 1$
$10^{25} – 1 = 2^x – 1$
taking log
$log 10^{25} = x$
$x = 25 log 10$
$x = 25 * 3.3$
$x = 82.5 $(approximately 83)

So none of these are correct.

Ref: https://www.geeksforgeeks.org/isro-isro-cs-2015-question-77/

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