1. Common Problem… Not for the beginning of the year.
Converting numbers is a significant part of the AP Exam but…
It is not a crowd pleaser …
And you will have to reteach it anyway…

2. Binary to decimal (Binary is base 2)
Step 1: have them draw a four column table
Step 2: put a one in the upper far right 1

3. Binary to decimal (Binary is base 2)
Step 3: For the next upper column multiply the previous column by the base number. (In this case binary is base 2)
Step 4: repeat
Step 5: repeat 2 1 4 2 1 8 4 2 1

4. Now let’s convert using our table
Convert to decimal. (decimal is base ten)
Use your table 8 4 2 1

5. Now let’s convert using our table
Convert to decimal. (decimal is base ten)
Use your table
1 x x x x 2
= 12 8 4 2 1

6. Let’s do a bigger number with a bigger table
Convert to decimal. (decimal is base ten)
Use your table (always start with one and multiply by the base)
Put your numbers in
= 206
128 64 32 16 8 4 2 1
128 64 32 16 8 4 2 1

7. Let’s try a crazy number base 8
Convert 1378 to decimal. (decimal is base ten)
Use your table (always start with one and multiply by the base)
Put your numbers in
64 x x x 7 = 95 64 8 1 64 8 1 3 7

8. Super common hex (sometimes called hexadecimal)
Hex is base 16 not base 6
Table is the same. Numbers will be smallish.
Convert 14 hex to decimal.
16 x x 4 = 20 16 1 4

9. Problem Base 10 goes from 0 to 9 0 to 9 is 10 numbers
test with your fingers

10. Problem Binary goes from 0 to 1 0 to 1 is 2 numbers
test with your fingers

11. Problem Base 8 goes from 0 to 7 0 to 7 is 8 numbers
test with your fingers

12. Problem So………… form the earlier slide 14 hex is 20
Hexadecimal goes from
0 to 15
0 to 15 is 16 numbers
test with your fingers
Problem is 14hex a 14 or a 1 and a 4
form the earlier slide 14 hex is 20
So…………

13. Solution to the hexadecimal problem1 2 3 4 5 6 7 8 9 10 A 11 B 12 C 13 D 14 E 15 F
Convert 2D hex to decimal 16 1 2 D
2 x x 13 = 45

14. Solution to the hexadecimal problem1 2 3 4 5 6 7 8 9 10 A 11 B 12 C 13 D 14 E 15 F
Convert 16hex to decimal 16 1 6
1 x x 6 = 22

15. Hexadecimal to binary problem1 2 3 4 5 6 7 8 9 10 A 11 B 12 C 13 D 14 E 15 F
Convert 16hex to decimal 16 1 6
1 x x 6 = 22
Each hex number is 4 binary numbers…..

16. Hexadecimal to binary problem1 2 3 4 5 6 7 8 9 10 A 11 B 12 C 13 D 14 E 15 F
Convert 16hex to decimal
Start with the 6 8 4 2 1
Now do the 1 8 4 2 1
Add them together cutting off the leading 0s
16 hex =

17. Did it work? 16 hex = 10110 2 = 22 decimal??? 16 8 4 2 1
= 22

18. Common Theme of AP test is abstractions
Different programming languages offer different levels of abstraction (a)
Example: JAVA uses more abstractions than older languages like COBOL
High-level languages provide more abstractions for the programmer making it easier for people to read and write a program (b)
Code in a programming language is often translated into code in another (lower-level) language to be executed on a computer.(c)
Higher level languages are easier to debug and code than lower level languages.
Early programming languages used NO abstractions so coding was all in binary
EK 2.2.3A, B, C

19. Abstraction
In computer science, abstraction is a central problem-solving technique.
Abstraction is a process, a strategy, and the result of reducing detail to focus on concepts relevant to understanding and solving problems.
Reduces information and detail
Facilitates focus on relevant concepts
Helps in writing programs, creating computational artifacts, and solving problems

20. EK 2.2.3D

21. A logic gate is a hardware abstraction that is modeled by a Boolean function.
True
False
AND
FALSE
True
False
EK 2.2.3F OR
TRUE

22. Hardware Abstraction Computer Video Card
High Level
Video Card
Chip - low level components and circuits
that perform a specific function
EK 2.2.3G
EK 2.2.3H
Transistor
Low Level

23. Hardware Abstraction
Hardware is built using multiple levels of abstraction
* transistors
* logic gates
* chips
* memory
* motherboards
* special purpose cards
* storage devices
EK 2.2.3I

24. EK J

25. EK 2.2.3K

26. MODELING
LO 2.3.1
EK 2.3.1A-D

27. Modeling

28. Fixed number of bits to represent real numbers
Example:
3 bit system used to store numbers
____ ____ _____
EK 2.1.1B,D,EG
EK 2.1.2C
What is the largest number that can be stored?
What type of error if the number is to large?
What type of error if the number is repeating like
1/3?

33. LO 2.3.1, 2.3.2
EK 2.3.1A, 2.3.1D, 2.3.2A, 2.3.2D, 2.3.2E

34. LO 2.1.1
EK 2.1.1D-G

35. LO 2.2.2
EK 2.2.2A

36. LO 2.1.1, 2.1.2
EK 2.1.1A-E, 2.1.2F

37. LO 7.2.1
EK 7.2.1F

38. LO 2.2.3, 5.5.1
EK 2.2.3E-F, 5.5.1E-G

39. LO 2.2.3, 4.1.2
EK 2.2.3A, 2.2.3B, 2.2.3C, 4.1.2A-C, 4.1.2F, 4.1.2H

40. LO 3.3.1, 2.1.1
EK 3.3.1C, 3.3.1D, 3.3.1E, 2.1.1C

41. LO 2.1.1, 2.1.2
EK 2.1.1B, 2.1.1D, 2.1.2F, 2.1.1B, 2.1.1C, 2.1.1E

42. LO 2.3.2, 2.3.1
EK 2.3.2A, 2.3.2B, 2.3.2F, 2.3.1A

43. LO 5.4.1, 2.2.2
EK 5.4.1C, 2.2.2A

44. LO 2.3.1, 5.2, 5.5
EK 2.3.1A, 2.3.1B, 5.2.1C, 5.5.1A

45. Videos
Multiple Choice Questions Review with Explanations
Great for teacher review of binary addition and overflow. Do not show students…too boring. Do this in your way. ☺