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.
carl
--
carl lowenstein marine physical lab u.c. san diego
[EMAIL PROTECTED]
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