Thread Subject: Converting decimal to binary

How do i convert these eigen-coefficients to binary in matlab?

688.192179500702
1.54987134237672e-13
5.13126867385250e-14
1.54543045027822e-13
-8.27671264858054e-14
2.44387843295613e-14
1.83464354819307e-14
-1.45383705074664e-13
1.33448807559944e-13
-2.48412401759879e-14

is there a function for it?
Thanks

Do you want to find the binary representation of the data in
ieee-754 format, or do you want to find the binary
representation of the actual numerical values?

The first is not possible within matlab, although you of
course can write a function yourself to do it (The
specification is available on Wikipedia. It isn't difficult.
I have done it)

The second would have been possible, had the numbers been
integers (dec2bin), but now you have to do it yourself as
well. But it is easy to do. Start by finding the highest bit
that fits inside the number, then subtract 2^(whatever the
bit was). Rinse and repeat.

--DA

"Daniel Armyr" <firstname@lastname.se> wrote in message
<fsi831$7e5$1@fred.mathworks.com>...
> Do you want to find the binary representation of the data in
> ieee-754 format, or do you want to find the binary
> representation of the actual numerical values?
>
> The first is not possible within matlab, although you of
> course can write a function yourself to do it (The
> specification is available on Wikipedia. It isn't difficult.
> I have done it)
>
> The second would have been possible, had the numbers been
> integers (dec2bin), but now you have to do it yourself as
> well. But it is easy to do. Start by finding the highest bit
> that fits inside the number, then subtract 2^(whatever the
> bit was). Rinse and repeat.
>
> --DA
>

I'm not really sure about the second method, but as far as i
know, if decimal fraction will result in a decimal place in
the binary format, example, 0.101001.

I'm trying to implement these values as 1s and 0s, and i
don't see any way of representing the notation ".".

On Mar 28, 4:58=A0am, "Christopher Ngau" <chris...@msn.com> wrote:
> "Daniel Armyr" <firstn...@lastname.se> wrote in message
>
> <fsi831$7e...@fred.mathworks.com>...
>
>
>
> > Do you want to find the binary representation of the data in
> > ieee-754 format, or do you want to find the binary
> > representation of the actual numerical values?
>
> > The first is not possible within matlab, although you of
> > course can write a function yourself to do it (The
> > specification is available on Wikipedia. It isn't difficult.
> > I have done it)
>
> > The second would have been possible, had the numbers been
> > integers (dec2bin), but now you have to do it yourself as
> > well. But it is easy to do. Start by finding the highest bit
> > that fits inside the number, then subtract 2^(whatever the
> > bit was). Rinse and repeat.
>
> > --DA
>
> I'm not really sure about the second method, but as far as i
> know, if decimal fraction will result in a decimal place in
> the binary format, example, 0.101001.

Internally, they are represented in scientific notation
in binary. So if you were to actually decode the IEEE-754
notation, you would already have your number in the
form 1.xxxxx * 2^yyyy

Is that what you want?

>
> I'm trying to implement these values as 1s and 0s, and i
> don't see any way of representing the notation ".".

I don't understand what you mean. If you want a
decimal point, you just write one.

If you found out a number was
    1.01011101 * 2^-7
what difficulty would you have in "representing
the notation '.'"?

Most of your numbers are on the order of 10^-13, which
is about 2^-43, so if you didn't want to use scientific notation
you'd have to precede them with 0.00... (43 zeros).

                 - Randy

Randy Poe <poespam-trap@yahoo.com> wrote in message
<ba43f950-ab12-4e64-a020-4c21827034ce@n58g2000hsf.googlegroups.com>...
> On Mar 28, 4:58=A0am, "Christopher Ngau"
<chris...@msn.com> wrote:
> > "Daniel Armyr" <firstn...@lastname.se> wrote in message
> >
> > <fsi831$7e...@fred.mathworks.com>...
> >
> >
> >
> > > Do you want to find the binary representation of the
data in
> > > ieee-754 format, or do you want to find the binary
> > > representation of the actual numerical values?
> >
> > > The first is not possible within matlab, although you of
> > > course can write a function yourself to do it (The
> > > specification is available on Wikipedia. It isn't
difficult.
> > > I have done it)
> >
> > > The second would have been possible, had the numbers been
> > > integers (dec2bin), but now you have to do it yourself as
> > > well. But it is easy to do. Start by finding the
highest bit
> > > that fits inside the number, then subtract 2^(whatever the
> > > bit was). Rinse and repeat.
> >
> > > --DA
> >
> > I'm not really sure about the second method, but as far as i
> > know, if decimal fraction will result in a decimal place in
> > the binary format, example, 0.101001.
>
> Internally, they are represented in scientific notation
> in binary. So if you were to actually decode the IEEE-754
> notation, you would already have your number in the
> form 1.xxxxx * 2^yyyy
>
> Is that what you want?
>
> >
> > I'm trying to implement these values as 1s and 0s, and i
> > don't see any way of representing the notation ".".
>
> I don't understand what you mean. If you want a
> decimal point, you just write one.
>
> If you found out a number was
> 1.01011101 * 2^-7
> what difficulty would you have in "representing
> the notation '.'"?
>
> Most of your numbers are on the order of 10^-13, which
> is about 2^-43, so if you didn't want to use scientific
notation
> you'd have to precede them with 0.00... (43 zeros).
>
> - Randy
>
sorry for the clarify of my question. Actually i'm trying to
represent my eigen coefficients as in 4 bytes per coefficient.

In article <fsiimf$rg3$1@fred.mathworks.com>,
Christopher Ngau <chrisnwh@msn.com> wrote:

>sorry for the clarify of my question. Actually i'm trying to
>represent my eigen coefficients as in 4 bytes per coefficient.

single(number) will convert the number to IEEE754 single precision
(4 bytes) provided it is within range.

--
  "Eightly percent of the people in the world are fools and the
  rest of us are in danger of contamination." -- Walter Matthau

In article <fsi831$7e5$1@fred.mathworks.com>,
Daniel Armyr <firstname@lastname.se> wrote:
>Do you want to find the binary representation of the data in
>ieee-754 format, or do you want to find the binary
>representation of the actual numerical values?

>The first is not possible within matlab

sprintf( '%0.16X', typecast(number,'uint64') )
--
  "The whole history of civilization is strewn with creeds and
  institutions which were invaluable at first, and deadly
  afterwards." -- Walter Bagehot

Christopher <chrisnwh@msn.com> wrote in message
<13606225.1206679443088.JavaMail.jakarta@nitrogen.mathforum.org>...
> How do i convert these eigen-coefficients to binary in matlab?
>
> 688.192179500702
> 1.54987134237672e-13
> 5.13126867385250e-14
> 1.54543045027822e-13
> -8.27671264858054e-14
> 2.44387843295613e-14
> 1.83464354819307e-14
> -1.45383705074664e-13
> 1.33448807559944e-13
> -2.48412401759879e-14
>
> is there a function for it?
> Thanks
-------------
  This is a function I wrote for my own edification. Perhaps you can make use
of it. It converts a single scalar 'double' to a string of 53 binary digits,
including a binary (decimal) point, a sign, and an exponent of 2. This
representation is precise, giving exactly what is contained in the number as
stored in its internal IEEE 754 format.

%%%%%%%%%%%%%%%%%%%%%
function s = binstr(x)

if ~finite(x)|(length(x)~=1), error('x must be a finite scalar.'),end
b = (x<0); x = abs(x);
s = zeros(1,53);
[f,e] = log2(x);
for i = 1:53
 f = 2*f;
 d = floor(f);
 f = f - d;
 s(i) = d+48;
end
s = ['0.' s sprintf('*2^(%d)',e)];
if b, s = ['-' s]; end
s = char(s);
return
%%%%%%%%%%%%%%%%%%%%%

  Second comment: Nine of those ten eigenvalues look to me as those they
are values that would have been precisely zero except for round-off errors in
the eigenvector routine that produced them. Converting each of these nine
to binary, results in a bit string which, with the addition or subtraction of only
a small amount at the least significant bit end, are strings of only a short
length representing very small quantities followed by trailing zeros. (Very
likely those needed least significant bit end adjustments are primarily due to
the inherent imprecision of the decimal strings you have given above.)

Roger Stafford

Christopher <chrisnwh@msn.com> wrote in message
<13606225.1206679443088.JavaMail.jakarta@nitrogen.mathforum.org>...
> How do i convert these eigen-coefficients to binary in matlab?
>
> 688.192179500702
> 1.54987134237672e-13
> 5.13126867385250e-14
> 1.54543045027822e-13
> -8.27671264858054e-14
> 2.44387843295613e-14
> 1.83464354819307e-14
> -1.45383705074664e-13
> 1.33448807559944e-13
> -2.48412401759879e-14
>
> is there a function for it?
> Thanks

Search for 'num2bin' by Herman Gollwitzer on Matlab File
Exchange. The version I have is dated Oct 7, 2000, but there
may be an updated version.

Derek O'Connor

> >The first is not possible within matlab
> sprintf( '%0.16X', typecast(number,'uint64') )
I stand corrected. It has been a mystery to me that Matlab
couldn't do this, but I never found the typecast function.
Thank you.