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Re: entropy of a binary file with conditions

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pierre wrote:
) hi,
)
) let's suppose we have a binary file (runs of zeroes and ones) and its 
) length is 1024 bits.
)
) any of these runs is not bigger than 8 (00000000 or 11111111)
)
) how can one compute the entropy of such a file ?

I assume you want to know the entropy of a model where all files are
allowed, as long as they do not have a run of longer than 8, and that
all other files are equally likely.

For this, you need to calculate the probability that a 1024-bit contains
a run of more than 8.  Or alternatively, the probability that you get 9
heads or tails in a row when you flip a fair coin 1024 times.

This can probably be found in most probability textbooks.

Then simply add the base-2 log of this number to 1024 and there's your
'entropy'.


SaSW, Willem
-- 
Disclaimer: I am in no way responsible for any of the statements
            made in the above text. For all I know I might be
            drugged or something..
            No I'm not paranoid. You all think I'm paranoid, don't you !
#EOT

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entropy of a binary file with conditions pierre <pierre@invalid.invalid> - 2012-03-03 10:04 +0100
  Re: entropy of a binary file with conditions glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2012-03-03 09:41 +0000
    Re: entropy of a binary file with conditions pierre <pierre@invalid.invalid> - 2012-03-03 10:47 +0100
      Re: entropy of a binary file with conditions glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2012-03-03 10:00 +0000
        Re: entropy of a binary file with conditions pierre <pierre@invalid.invalid> - 2012-03-03 11:34 +0100
          Re: entropy of a binary file with conditions Alex Mizrahi <alex.mizrahi@gmail.com> - 2012-03-04 00:08 +0200
          Re: entropy of a binary file with conditions "George Johnson" <matrix29@charter.net> - 2012-03-03 22:45 -0500
            Re: entropy of a binary file with conditions "George Johnson" <matrix29@charter.net> - 2012-03-04 01:08 -0500
  Re: entropy of a binary file with conditions biject <biject.bwts@gmail.com> - 2012-03-03 12:34 -0800
    Re: entropy of a binary file with conditions glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2012-03-03 21:11 +0000
    Re: entropy of a binary file with conditions pierre <pierre@invalid.invalid> - 2012-03-04 20:57 +0100
  Re: entropy of a binary file with conditions "George Johnson" <matrix29@charter.net> - 2012-03-03 22:30 -0500
    Re: entropy of a binary file with conditions Phil Carmody <thefatphil_demunged@yahoo.co.uk> - 2012-03-20 18:49 +0200
  Re: entropy of a binary file with conditions James Dow Allen <jdallen2000@yahoo.com> - 2012-03-03 22:07 -0800
    Re: entropy of a binary file with conditions pierre <pierre@invalid.invalid> - 2012-03-04 20:59 +0100
  Re: entropy of a binary file with conditions Willem <willem@toad.stack.nl> - 2012-03-04 15:41 +0000
    Re: entropy of a binary file with conditions Alex Mizrahi <alex.mizrahi@gmail.com> - 2012-03-04 21:39 +0200
    Re: entropy of a binary file with conditions glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2012-03-04 22:45 +0000
      Re: entropy of a binary file with conditions Alex Mizrahi <alex.mizrahi@gmail.com> - 2012-03-05 10:03 +0200
        Re: entropy of a binary file with conditions glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2012-03-05 09:52 +0000
          Re: entropy of a binary file with conditions Alex Mizrahi <alex.mizrahi@gmail.com> - 2012-03-05 18:05 +0200
        Re: entropy of a binary file with conditions James Dow Allen <jdallen2000@yahoo.com> - 2012-03-05 06:03 -0800
          Re: entropy of a binary file with conditions James Dow Allen <jdallen2000@yahoo.com> - 2012-03-05 16:16 -0800
            Re: entropy of a binary file with conditions James Dow Allen <jdallen2000@yahoo.com> - 2012-03-05 16:27 -0800

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