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
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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
