Carl Lowenstein wrote: > On 6/29/07, Carl Lowenstein <[EMAIL PROTECTED]> wrote: >> On 6/29/07, James G. Sack (jim) <[EMAIL PROTECTED]> wrote: >> > Andrew Lentvorski wrote: >> > > Christopher Smith wrote: >> > >.. >> > >> And of course his problem with "knowing" that a binary calculator >> > >> cannot represent 0.1 exactly, fails to recognize the capabilities of >> > >> calculators that maintain internal results as rational numbers >> > > >> > > None that I am aware of as still being in production do this. >> > >> > Out of curiosity, how do the current crop of calculators deal with (eg) >> > "representing 0.1" exactly? >> > >> > Do they use different representations in different ranges? (seems >> > unlikely to really work), or do they maybe recognize & distinguish >> > rationals? >> >> The only calculators I have readily to hand are various vintages of >> HP. As far as I can tell by some button pushing, they have no problem >> with representing 0.1 exactly. I think that they are binary-coded >> decimal and base 10 floating point internally. Somewhere I have a >> book on programming the internal machine language of the HP 45, but I >> am not looking for it right now. >> >> It is the vast majority of digital computers that do not represent >> decimal fractions such as 0.1 exactly. But this is a different part >> of the problem space. > > Other thoughts and probing of calculator foibles. The HP calculators, > which work internally with decimal arithmetic and base-10 floating > point, show some interesting results when probed with numbers that can > not be represented exactly, such as 1/3. > > 1 <enter> 3 <divide> 3 <multiply> 1 <subtract> gives an answer of > -1.00e-12 on my newest calculator (HP 32SII) and an answer of > -1.00 -10 on a rather older one (HP 10C). > So the new one carries more digits internally. > > I can't locate the '45 or '80 to try an older one. >
hp45 gives -1.0x10-10 Regards, ..jim -- [email protected] http://www.kernel-panic.org/cgi-bin/mailman/listinfo/kplug-lpsg
