Binary Numbers

Or… what’s on your DVD?

How does your computer show numbers, letters and pictures?

THE BINARY CODE

Showing numbers in a way easy enough for the computer to understand!

What’s the biggest number we can make with these five cards?

Making Number Thirteen in Binary

Card face up = 1

Card face down = 0

0 1 1 0 1

0 1 1 0 1 = 0 + 8 + 4 + 0 + 1 = thirteen

HOW DO WE REPRESENT LETTERS?

A B C D E F G

1 2 3 4 5 6 7

H I J K L M N

8 9 10 11 12 13 14

O P Q R S T U

15 16 17 18 19 20 21

V W X Y Z _

22 23 24 25 26 27 28

10011 =

00101 =

00011 =

10010 =

00101 =

10100 =

What word is this? A B C D E F G

1 2 3 4 5 6 7

H I J K L M N

8 9 10 11 12 13 14

O P Q R S T U

15 16 17 18 19 20 21

V W X Y Z _

22 23 24 25 26 27 28

19 =

5 =

3 =

18 =

5 =

20 =

s

e

c

r

e

t

Your Name in Binary

A B C D E F G

1 2 3 4 5 6 7

H I J K L M N

8 9 10 11 12 13 14

O P Q R S T U

15 16 17 18 19 20 21

V W X Y Z _

22 23 24 25 26 27 28Letters in your name

M

-------

-------

-------

-------

Corresponding number

13

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Binary value

01101

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How Do We Represent Pictures?

Pixels – Breaking a Picture Up into Squares

Each Square is Either Black or White…

Black and White in Binary Code

Running Ones and Zeros Together

Find the Secret Picture – Use the Number Code on the Left

(first number always represents a number of zeros)

15……………….

15……………….

15……………….

4,6,5…………….

3,1,6,1,4………...

2,1,7,1,4………...

1,1,9,3,1………...

1,1,11,1,1……….

1,1,11,1,1……….

1,13,1…………...

3,1,1,1,3,1,1,1,3...

4,1,5,1,4….…….

15………………

15………………

15………………

Find the Secret Picture - Solution

DVD surface imaged by Photon Tunnelling Microscope

Scanning Electron Microscope Picture of CD surface

50 concentric tracks are equal to the width of one human hair

Flat “land” reflects light, Deep “pits” do not- Think of binary 1s and 0s