On Apr 28, 2010, at 20:49, Michael Ash wrote: > Actually, while there are finite decimal numbers with no finite binary > representation, the reverse is not true. Every binary number can be > represented by a finite number of decimal digits. I believe this is > because 2 is a factor of 10. To prove it to yourself, just take > successive negative powers of two and notice how you never get a > repeating decimal. The fractional part of a binary float is just a sum > of various negative powers of two, and if the individual components > are finite, the result must be as well.
I'm pretty sure that what I said was 100% accurate this morning, but that the fundamental mathematical laws of the universe have changed since then and now I'm wrong. You're right. >> Plus, you'd have to expect that encoding doubles would require, in the worst >> case, at least 309 significant digits, which is a much longer string than I >> want in my archive. > > I think you've flipped your math around somewhere here. Yup, I noticed earlier I'd gone overboard with this, and got myself mixed up with the maximum exponent. Good thing I published a disclaimer earlier, or otherwise I've have to feel embarrassed now. _______________________________________________ Cocoa-dev mailing list (Cocoa-dev@lists.apple.com) Please do not post admin requests or moderator comments to the list. Contact the moderators at cocoa-dev-admins(at)lists.apple.com Help/Unsubscribe/Update your Subscription: http://lists.apple.com/mailman/options/cocoa-dev/archive%40mail-archive.com This email sent to arch...@mail-archive.com
