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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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Consider three digits of decimal numbers.Maximum number, we can generate by that three digits are 103-1 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 $2^{n} -1$
So we can write $10^{25} -1 = 2^{n} - 1 $

$10^{25} = 2 ^{n}$   After taking log 2 on both sides
$log 2^{n}=log 10^{25}$
$n log 2=25 log10$
$n=25*(3.322)/ log 2$
n=83
Answer:

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