Re: Decimal versus binary arithmetic was Re: J4 - presentation/discussion on "Future of the COBOL Standard"

Robert <no@[EMAIL PROTECTED]
> wrote in message
news:ebilv35o36sre1blnosdkfmqh6nrhv6o1o@[EMAIL PROTECTED]
> On Mon, 7 Apr 2008 11:08:23 -0500, "tlmfru" <lacey@[EMAIL PROTECTED]
> wrote:
> >>
> >> >Nope, all three numbers are binary INTEGERS. The fallacy is in
thinking
> >of quotient as a fraction. It is not a fraction, it is an integer.
> >> > The compiler SCALED two integers by multiplying by powers of 10,
then
> >divided two binary integers to get a quotient with no fraction.
> >> > Binary 10 divided by binary 5 gives binary 2.
> >>
> >> >101111101011110000100000000 / 1100001101010000 = 11111010000
> >
> >This isn't the point.  The point is that with very few exceptions a
decimal
> >number with figures on both sides of the decimal point can't be
represented
> >as a pure binary number, as the fractional ****tion is almost always
> >non-terminating. Binary ONE divided by binary 5 gives binary
..00110011.....
> >A scaled number is not the number itself: it's a transformation of the
> >original.
>
> By definition, integers are whole numbers. There is no fractional part
to
an integer.
>

Robert, you're either deliberately or obtusely missing the point.  The
point
is not whether a binary number with a fractional part can be converted to
a
scaled integer equivalent that can be manipulated by a computer.  Of
course
it can.  What you don't want to acknowledge is the simple fact that most
decimal fractions when converted into binary fractions come out as a
non-terminating string of ones & zeros.  How does it reflect adversely on
you to agree to this?


> >> >Incidentally - everybody knows about the simple algoritm to convert
base
> >10
> >> >numbers to base 2 - i.e. repeated division by 2 -
> >> >I had some fun working out the mirror algorithm to convert decimal
> >FRACTIONS
> >> >to binary fractions.  (Very easy, actually).  (Both algorithms work
for
> >any
> >> >base).  But what puzzles me is I've never seen this written up
anywhere.
> >> >I'm certain that the early developers of computers (or perhaps IBM
> >research
> >> >fellows) must have discovered the algorithm.  Has anyone seen it
written
> >up?
>
> It's of no use when dealing with integers, because they have no
fractional
part.

Can't you read?  It's an algorithm for dealing with fractional parts.  Of
course it's no use in dealing with integers.  So what?

>
> >Very interesting!  But doesn't answer my question.  I'd really like to
make
> >an original contribution to math or computer science but I can't
believe
> >that "my algorithm" is it.
>
> Now you're in the domain of abstraction and generalization, a faux pas
in
these parts.

You may think so.  Most of the arguments we've had over OO are in that
domain.

You needn't bother replying to this, Mr. Wagner.  This is my last word -
to
you, anyway - on the subject.

PL