1. Introduction to Binary

2. Why Bother with Binary? This is all about electronics
We don’t use binary because electronics do
We designed electronics to use binary because it is very easy to do so
Trying to use decimal inside electronics would be crazy difficult

3. Why Bother with Binary?
Operations are easy in electronics (just wait!)
Binary numbers can be used to represent anything

4. Why Bother with Binary?
Operations are easy in electronics (just wait!)
Binary numbers can be used to represent anything
Numbers!

5. Why Bother with Binary?
Operations are easy in electronics (just wait!)
Binary numbers can be used to represent anything
Numbers! π = [and more!]

6. Why Bother with Binary?
Operations are easy in electronics (just wait!)
Binary numbers can be used to represent anything
Numbers! π = [and more!]
Words “To be, or not to be!”
Pictures
Videos

7. Why Bother with Binary?
Operations are easy in electronics (just wait!)
Binary numbers can be used to represent anything
Numbers! π = [and more!]
Words “To be, or not to be!”
Pictures
Videos
Programs (like games!)

8. Number Systems Ways to organize and write numbers Set of digits
Set of operations
Addition
Subtraction

9. Number Systems – Decimal
Digits
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Operations
Addition ( )
Subtraction ( 5 – 3 )

10. Number Systems – Decimal
Written Form
Every “place” is 10 times the place to the right
Number
1000
100 10 1 17 7 51 5
5281 2 8

11. Number Systems – Decimal
What’s going on, here?
1000 * 5
* 2
* 8
* 1
= 5281
Number
1000
100 10 1
5281 5 2 8

12. Number Systems – Binary
Digits
0, 1
Operations
Addition ( )
Subtraction ( 101 – 011 )
Fun new things (and, or, not, xor)

13. Number Systems – Binary
States can be easily represented in electronics
Off
False On
True 1

14. Number System - Binary Written Form
Every “place” is twice the place to the right
Number
4096
2048
1024
512
256
128 64 32 16 8 4 2 1 17 51
5281

15. Number Systems – Binary
Same number as before =
Number
4096
2048
1024
512
256
128 64 32 16 8 4 2 1
5280

16. Familiar Numbers Decimal: 25 Binary: 11001 10 * 2 + 1 * 5 25 10000
11001
Number
1000
100 10 1 25 2 5
Number
128 64 32 16 8 4 2 1
11001

17. Converting to Binary Decimal 128 64 32 16 8 4 2 1 Binary 29 00011101 31 33
100
111
125

18. Binary Numbers
Just another way to “write” the numbers you see every day

19. Numbers with Meaning
How do we represent words in computers?

20. Numbers with Meaning
How do we represent words in computers?
Numbers!

21. Numbers with Meaning How do we represent words in computers? Numbers!
(Bet you didn’t see what one coming...)

22. ASCII American Standard Code for Information Interchange
A special set of numbers to represent letters
All letters have a number assigned to them

23. ASCII □■□□□□□■ □■□□■■■■ □■□□□□■□ P 80 □■□■□□□□ □■□□□□■■ □■□■□□□■
Letter
Decimal
Binary
Pattern A 65
□■□□□□□■ O 79
□■□□■■■■ B 66
□■□□□□■□ P 80
□■□■□□□□ C 67
□■□□□□■■ Q 81
□■□■□□□■ D 68
□■□□□■□□ R 82
□■□■□□■□ E 69
□■□□□■□■ S 83
□■□■□□■■ F 70
□■□□□■■□ T 84
□■□■□■□□ G 71
□■□□□■■■ U 85
□■□■□■□■ H 72
□■□□■□□□ V 86
□■□■□■■□ I 73
□■□□■□□■ W 87
□■□■□■■■ J 74
□■□□■□■□ X 88
□■□■■□□□ K 75
□■□□■□■■ Y 89
□■□■■□□■ L 76
□■□□■■□□ Z 90
□■□■■□■□ M 77
□■□□■■□■ ! 33
□□■□□□□■ N 78
□■□□■■■□ ? 63
□□□■■■■■
Letter
Decimal
Binary
Pattern A 65
□■□□□□□□■ B 66 C 67 D 68 E 69 F 70 G 71 H 72 I 73 J 74 K 75 L 76 M 77 N 78 O 79

24. Making Words From Letters
How do we write our ABCs?

25. Making Words From Letters
How do we write our ABCs?
Like this:
□■□□□□□■□■□□□□■□□■□□□□■■

26. Making Words From Letters
How do we write our ABCs?
Like this:
□■□□□□□■□■□□□□■□□■□□□□■■
How about XYZ?

27. Making Words From Letters
How do we write our ABCs?
Like this:
□■□□□□□■□■□□□□■□□■□□□□■■
How about XYZ?
□■□■■□□□□■□■■□□■□■□■■□■□

28. Can You Write Your Initials?
Letter
Decimal
Binary
Pattern A 65
□■□□□□□■ O 79
□■□□■■■■ B 66
□■□□□□■□ P 80
□■□■□□□□ C 67
□■□□□□■■ Q 81
□■□■□□□■ D 68
□■□□□■□□ R 82
□■□■□□■□ E 69
□■□□□■□■ S 83
□■□■□□■■ F 70
□■□□□■■□ T 84
□■□■□■□□ G 71
□■□□□■■■ U 85
□■□■□■□■ H 72
□■□□■□□□ V 86
□■□■□■■□ I 73
□■□□■□□■ W 87
□■□■□■■■ J 74
□■□□■□■□ X 88
□■□■■□□□ K 75
□■□□■□■■ Y 89
□■□■■□□■ L 76
□■□□■■□□ Z 90
□■□■■□■□ M 77
□■□□■■□■ ! 33
□□■□□□□■ N 78
□■□□■■■□ ? 63
□□□■■■■■

29. Bonus
Can you decode the binary code on my shirt?

30. Arithmetic in Binary Easy
You only need to know how to add 0 and 1
Hardest operation you ever have to do is 1 + 1
Hint: the answer isn’t “2”

31. Addition – Decimal
2 + 2 =
2 + 8 =
7 + 8 =

32. Addition – Binary
0 + 0 =
0 + 1 =
1 + 0 =
1 + 1 =

33. Addition – Binary 10 + 10 = ( 2 + 2 ) 10 + 1000 = ( 2 + 8 )
= ( )
= ( )
= ( )
= ( )

34. Funny Operators
And
0 ∧ 0 = 0
0 ∧ 1 = 0
1 ∧ 0 = 0
1 ∧ 1 = 1 Or

35. Programs in Binary
Everything in a computer is represented with binary numbers
Programs in a computer are (of course!) represented in binary numbers

36. Programs in Binary Instructions Program Storage
List of things you can do
Program
List of instructions, in order
Storage
Instructions, encoded into binary, in the computer’s memory

37. Programs in Binary - Instructions
Human Robots
Just like our first week in Coding Club
Can move forward
Can turn right
Can turn left

38. Programs in Binary
Program
Move forward
Turn left
Turn right
etc.

39. Programs in Binary Instructions .. in binary! We have 3 instructions
We will need two “bits” for each instruction
2 bits can represent 0, 1, 2, or 3 in decimal
We only need 3 of these 4; one of them will be unused

40. Programs in Binary Instructions .. in binary! Turn left: 01
Turn right: 10
Move forward: 11

41. Programs in Binary Program Instructions Move forward Turn left
Turn right
etc.
Instructions 11 01 10
etc.

42. Programs in Binary Program in computer memory 111101111011 or
■■■■□■■■■□■■

43. How Does a Computer Run a Program?
Program is in memory
■■■■□■■■■□■■
Computer knows all instructions are 2-bits wide
Computer starts at the beginning
Read 2 bits
Decide which instruction is represented
Perform instruction (e.g. turn, move)
Repeat

44. Complicated Programs Human Robots Real Computer Programs
Limited to turn, move
Real Computer Programs
Can do much more

45. Complicated Programs Perform arithmetic Make decisions Run loops
Load/store information

46. Complicated Programs Require lots of instructions Examples:
load, store
add, subtract
compare
jump!

47. Complicated Programs Instructions Instructions Load Add Jump
Jump-if-equal
Instructions
0001
0011
0101
0110

48. Complicated Programs Instructions Instructions Extra Load Add Jump
Jump-if- equal
Instructions
0001
0011
0101
0110
Extra
What?
Where?
What/Where ?

49. Let’s Count to Ten Instructions Instructions Extra Load Add Jump
Jump-if- equal
Instructions
0001
0011
0101
0110
Extra
0000
0001
0101
1010

50. Let’s Count to Ten Instructions Instructions Extra Load Add Jump
Jump-if- equal
Instructions
0001
0011
0101
0110
Extra
0000
0001
0101
1010

51. Let’s Count to Ten Instructions Instructions Extra Load Add Jump
Jump-if- equal
Instructions
0001
0011
0101
0110
Extra
0000
0001
0101
1010
code code code code

52. Let’s Count to Ten Instructions Instructions Extra Load Add Jump
Jump-if- equal
Instructions
0001
0011
0101
0110
Extra
0000
0001
0101
1010
data data data data data

53. Complicated Programs Instructions Instructions Extra Load Add Jump
Jump-if- equal
Instructions
0001
0011
0101
0110
Extra
0000
0001
0101
1010
data data data data data ?

54. } Complicated Programs Instructions Instructions Extra Load Add Jump
Jump-if- equal
Instructions
0001
0011
0101
0110
Extra
0000
0001
0101
1010 }
data data data data data

55. } { Complicated Programs Instructions Instructions Extra Load Add Jump
Jump-if- equal
Instructions
0001
0011
0101
0110
Extra
0000
0001
0101
1010 }
code data code data code data data code data {