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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

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