Re: Binary number digits <- > Decimal number digits

On Sun, 9 Dec 2007, fc wrote:

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?

The number of digits of x in some base b is, not regarding rounding to
integers, the logarithm of x with respect to base b, which is log x / log
b (log to arbitrary base).

So the number of decimal digits of x is log 2 / log 10 = 0.30103 .

--
Helmut Richter
.

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