Some Random Information, Lecture Notes - Computer Science, Study notes of Introduction to Computers

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Some Random Information

Bits^

How many bits do I need to store oneboolean value?
^

How many bits do I need to store theoutcome of one home pregnancy test?
^

A home pregnancy test reveals 1 bit ofinformation.

It may be the most important

life-changing bit of information, but it's stilljust 1 bit.

Information^

More Digits = More Information

Right?

Memorizing^ Volunteer to memorize 10 digits^

Volunteer to memorize 100 digits
^

Memorizing^ Another volunteer to memorize 100 digits^

4859937766824805299839179081504751450913524367800673622844553973169223820421306174607612086978543115 Is that harder to memorize than:
^

4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444 Why?Which contains more information?

Information:

a definition

The amount of informationin a sequence of digitsis equal tothe length of the shortest programthat prints those digits.

Write a program to print

print "

Memorizing Programs^ print "

is harder to memorize than

repeat 100:

print "4"

Information^

More Random = More Information

Pi and Information^ 3.14159265358979323846264338327...^

How much information is stored in thedigits of pi?

a program that prints pi^ sign

n

pi

repeat:

pi

pi

sign

×

n

print

pi

sign

sign

n

n

Information in Pi^

The digits of pi are output by a shortprogram.
^

So what?
^

So, pi must not contain very muchinformation.
^

Then what does???

An Exercise^

Start with a number from 1 to 10.

Multiply by 7, and find remainder whendivided by 11.

That's the next number.

Repeat.

An Exercise^

n

) mod 11

Let's start with 4.What sequence do we get?

Does it look random?