class16-Informatio

# class16-Informatio - Information and Randomness Bits How...

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Information and Randomness

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Bits How many bits do I need to store one boolean value? How many bits do I need to store the outcome of one home pregnancy test? A home pregnancy test reveals 1 bit of information. It may be the most important life-changing bit of information, but it's still just 1 bit.

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Memorizing Volunteer to memorize 10 digits 2737761413 Volunteer to memorize 100 digits 4444444444444444444444444444444444444 4444444444444444444444444444444444444 44444444444444444444444444

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Memorizing 10-digit volunteer: What was the 8th digit? 100-digit volunteer: What was the 78th digit? Which is easier to memorize? Which contains more information?
Memorizing Another volunteer to memorize 100 digits 4859937766824805299839179081504751450913 5243678006736228445539731692238204213061 74607612086978543115 Is that harder to memorize than: 4444444444444444444444444444444444444444 4444444444444444444444444444444444444444 44444444444444444444 Why? Which contains more information?

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Information: a definition The amount of information in a sequence of digits is equal to the length of the shortest program that prints those digits.
Write a program to print 44444444444444444444444444444444 44444444444444444444444444444444 44444444444444444444444444444444 4444 repeat 100: print "4"

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Write a program to print 4859937766824805299839179081504751 4509135243678006736228445539731692 23820421306174607612086978543115 print "4859937766824805299839179081504 75145091352436780067362284455397 31692238204213061746076120869785 43115"
Memorizing Programs print "4859937766824805299839179081504 75145091352436780067362284455397 31692238204213061746076120869785 43115" is harder to memorize than repeat 100: print "4"

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Therefore 4859937766824805299839179081504751
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## This note was uploaded on 09/14/2010 for the course CS 15-100 taught by Professor Dave during the Spring '08 term at Carnegie Mellon.

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class16-Informatio - Information and Randomness Bits How...

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