1. Lesson 1-5 AP Computer Science Principles
Binary Numbers
Lesson 1-5
AP Computer Science Principles

2. Objectives Students will be able to:
Describe how to use bits to create a functioning number system
Understand the relationship between the powers of 2 and the number of bits needed to express a number of a certain magnitude. e.g. How many bits do I need to represent the number “15”, or “32”, or “1492”?
Determine, for a given number of bits, both the number of possible numbers that can be represented and also the range of those numbers

3. Recall…
In the previous lesson you created 27 different 3-place patterns out of circles, triangles and squares, and tried to define a system of rules to generate all of the patterns.

4. Journal
What if you only had a circle and square? With only a circle and square, how many 3-place patterns are there? Here’s a start, you make the rest. How many are there?

5. Consider this…
How large of numbers do you think this system can represent? How could we go higher?

6. Circle, Triangle, Square → Towards → The Binary Number System

7. 1 place = 3, 1-shape patterns
Previously on CSP….
1 place = 3, 1-shape patterns
Who: baker
@TeachCode | #TeacherCon | #CSforAll

8. 2 places = 9, 2-shape patterns
Previously on CSP….
2 places = 9, 2-shape patterns
Who: baker
@TeachCode | #TeacherCon | #CSforAll

9. 2 places = 9, 2-shape patterns
Previously on CSP….
2 places = 9, 2-shape patterns
Who: baker
@TeachCode | #TeacherCon | #CSforAll

10. 3 places = 27, 3-shape patterns
Previously on CSP….
3 places = 27, 3-shape patterns
Who: baker
@TeachCode | #TeacherCon | #CSforAll

11. 3 places = 27, 3-shape patterns
Previously on CSP….
3 places = 27, 3-shape patterns
Who: baker
@TeachCode | #TeacherCon | #CSforAll

12. Number each pattern to make a shape -> number mapping
Previously on CSP….
Number each pattern to make a shape -> number mapping 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Who: baker
@TeachCode | #TeacherCon | #CSforAll

13. What if we had 10 shapes? Previously on CSP….
Who: baker
@TeachCode | #TeacherCon | #CSforAll

14. 1 place = Ten 1-shape patterns
Previously on CSP….
1 place = Ten 1-shape patterns 1 2 3 4 5 6 7 8 9
← These are just shapes!
Who: baker
@TeachCode | #TeacherCon | #CSforAll

15. 0 9 9 _ _ _ Quiz: What comes next? Previously on CSP…. Ten shapes 1 21 2 3 4 5 6 7 8 9
0 9 9
_ _ _
Who: baker
@TeachCode | #TeacherCon | #CSforAll

16. 0 9 9 _ _ _ 1 0 0 Quiz: What comes next? Previously on CSP….
Ten shapes 1 2 3 4 5 6 7 8 9
0 9 9
_ _ _
1 0 0
Who: baker
@TeachCode | #TeacherCon | #CSforAll

17. Place Values... Previously on CSP….
Who: baker
@TeachCode | #TeacherCon | #CSforAll

18. __ __ __ __ __ __ Place Values...
Previously on CSP….
Place Values...
With Ten “shapes” every time you add a place, you multiply by 10 the number of numbers... __
10 possibilities (0 - 9)
__ __
100 possibilities ( )
__ __ __
1000 possibilities ( )
Who: baker
@TeachCode | #TeacherCon | #CSforAll

19. __ __ __ __ __ __ Place Values...
Previously on CSP….
Place Values...
With Three “shapes” every time you add a place, you multiply by 3 the number of numbers... __
3 possibilities ( )
__ __
9 possibilities ( )
__ __ __
27 possibilities ( )
Who: baker
@TeachCode | #TeacherCon | #CSforAll

20. Four thousand and seventeen
Previously on CSP….
Write the number…
Four thousand and seventeen
Who: baker
@TeachCode | #TeacherCon | #CSforAll

21. 4 0 1 7 Place Values...Remember what it means? Previously on CSP….
1000s s s s
4 * * * * 1
Who: baker
@TeachCode | #TeacherCon | #CSforAll

22. Where is this heading? ...binary... Previously on CSP….
Who: baker
@TeachCode | #TeacherCon | #CSforAll

23. 01 “Binary” is a number system with 2 shapes... Previously on CSP….
Who: baker
@TeachCode | #TeacherCon | #CSforAll

24. __ __ __ __ __ __ __ __ __ __ The pattern holds...
Previously on CSP….
The pattern holds...
With two “shapes” every time you add a place, you multiply by 2 the number of numbers... __
2 possibilities (0 1)
__ __
4 possibilities ( )
__ __ __
8 possibilities ( )
__ __ __ __
16 possibilities ( )
Who: baker
@TeachCode | #TeacherCon | #CSforAll

25. 1 1 0 1 Place Values...powers of 2 Previously on CSP…. 8s 4s 2s 1s
8s 4s 2s 1s
1 * * * * 1
= 13
Who: baker
@TeachCode | #TeacherCon | #CSforAll

26. Previously on CSP….
Constructing a binary number means figuring out which powers of 2 add up to the number you want
Who: baker
@TeachCode | #TeacherCon | #CSforAll

27. Previously on CSP….
Constructing a binary number means figuring out which powers of 2 add up to the number you want 32
= 41
Who: baker
@TeachCode | #TeacherCon | #CSforAll

28. To the flippy do! Previously on CSP….
Who: baker
@TeachCode | #TeacherCon | #CSforAll

29. Previously on CSP….
Flippy Do Quiz:
What’s the binary number? 5 17 63 64
100
127
What’s the decimal number?
100
101
1101
1 0000
Who: baker
@TeachCode | #TeacherCon | #CSforAll

30. Binary Odometer
Go to the Binary Odometer (
See how it works…
What’s the largest number you can make in binary with the binary odometer?”
What happens when the odometer run out of numbers?

31. Activity Guide
Complete the Activity Guide and turn it in.

32. Stage 5
Complete Stage 5.