Setting Precision in Binary Digits

Q: I would like to specify the precision of my numbers in binary digits rather than decimal digits. Is there any way of doing this?

A: Rob Knapp (rknapp@wolfram.com) answers: The precision of numbers in Mathematica is kept as a real quantity. This means that you can easily specify a precision in binary digits by multiplying it by . For example, here we specify to 20 binary digits.

By default, Precision rounds to the nearest integer.

In Mathematica 4 there is an option to prevent this rounding.

If we examine the RealDigits of n in base 2,

we see that there are 20 binary digits.

You can enter a number in an arbitrary base using base^^digits see Sections 3.1.3 and A.2.5 of The Mathematica Book).

The result is identical to that obtained using SetPrecision.