Binary number digits <- > Decimal number digits

A friend told me something about the RSA Challenge. Navigating the
Wikipedia's page of the RSA Challenge, I see a table in the section of
prizes and records (http://en.wikipedia.org/wiki/
RSA_Factoring_Challenge#The_prizes_and_records) that caught my
attention: how is calculated the number of digits of the binary
number, starting from the number of digits of the decimal number?

For example, what calculus was made to arrive that a decimal number of
617 digits must have 2048 digits in binary? (Obviously, without make
the conversion of the decimal number 999999...99999 [617 9 numbers] to
binary) And: how to generalize for any decimal number of any length?

I'm sorry if this is a "dumb" question, but I don't see the answer...
Thanks and best regards, FC.
.

Relevant Pages

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