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The number of bits (in binary) required to represent 25-digit decimal number

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The concept is the maximum number of 10 digit number by 10 digit should be equal to x digit number in base 2.

so $10^{25}$-1 = $2^x$-1

taking log both side . take log of base 2 so that RHS can become x

25log10 base 2 = x.

x=82.5 .so to represent we will need 83 digits.
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