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1. Unit 7
Number Systems and Bases
Presentation 1 Binary and Base 10
Presentation 2 Adding Binary Numbers
Presentation 3 Subtracting Binary Numbers
Presentation 4 Binary Multiplication
Presentation 5 Examples in Base 5
Presentation 6 Examples in Base 7

2. Unit 7
Number Systems and Bases
Binary and Base 10

3. Convert the binary numbers 1011, 11001 and 100101 to
base 10 numbers.
8 + 0 + 2 + 1 = 11
32 + 16 + 0 + 0 + 2 + 1 = 51
32 + 0 + 0 + 4 + 0 + 1 = 37
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4. Convert these base 10 numbers into binary numbers:
5 = 4 + 1
12 = 8 + 4
23 = 16 + 4 + 2 + 1
77 = 64 + 8 + 4 + 1
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5. Unit 7
Number Systems and Bases
You have finished viewing:
Binary and Base 10
Return to front slide
Presentation 1 Binary and Base 10
Presentation 2 Adding Binary Numbers
Presentation 3 Subtracting Binary Numbers
Presentation 4 Binary Multiplication
Presentation 5 Examples in Base 5
Presentation 6 Examples in Base 7

6. Unit 7
Number Systems and Bases
Adding Binary Numbers

7. Key results with binary numbers
Calculate, using these binary numbers
1 + 0 = 1
1 + 1 = 10
1 + 1 + 1 = 10
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1 0 1
+ 1 1
1 0 0 0
1 1 1
+ 1 0 1
1 1 0 0
1 0 1 1
+ 1 0 1
1 0 0 0 0
1 1 1 1
+ 1 1 0 1
1 1 1 0 0
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8. Unit 7
Number Systems and Bases
You have finished viewing:
Adding Binary Numbers
Return to front slide
Presentation 1 Binary and Base 10
Presentation 2 Adding Binary Numbers
Presentation 3 Subtracting Binary Numbers
Presentation 4 Binary Multiplication
Presentation 5 Examples in Base 5
Presentation 6 Examples in Base 7

9. Unit 7
Number Systems and Bases
Subtracting Binary Numbers

10. Key results with binary numbers
Calculate, using these binary numbers
1 - 0 = 1
10 - 1 = 1
11 - 1 = 10
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1 1 1
- 1 0 1
1 0
1 1 0 1 1
- 1 0 1 0
1 0 0 0 1
1 0 1 1
- 1 0 1
1 0 0
1 0 0 1
- 1 1
1 1 0
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1 1 1 0
- 1 1 1
1 1 1
1 0 0 1 1
- 1 0 1 0
1 0 0 1
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11. Unit 7
Number Systems and Bases
You have finished viewing:
Subtracting Binary Numbers
Return to front slide
Presentation 1 Binary and Base 10
Presentation 2 Adding Binary Numbers
Presentation 3 Subtracting Binary Numbers
Presentation 4 Binary Multiplication
Presentation 5 Examples in Base 5
Presentation 6 Examples in Base 7

12. Unit 7
Number Systems and Bases
Binary Multiplication

13. Calculate, using these binary numbers
1 1 0
x 1 1
1 1 0 0
1 1 0
1 1 0 1 0
1 1 1
x 1 1
1 1 1 0
1 1 1
1 0 1 0 1
1 1 0 1
x 1 1 0
1 1 0 1 0 0
1 1 0 1 0
1 1 0 1 1 1 0
1 1 1 1
x 1 1 0
1 1 1 1 0 0
1 1 1 1 0
1 0 1 1 0 1 0
1 1 0 1
X 1 0 1
1 1 0 1 0 0
1 1 0 1
1 1 0 0 0 0 1
1 0 1 1 0
x 1 1 1
1 0 1 1 0 0 0
1 0 1 1 0 0
1 0 1 1 1
1 0 0 1 1 0 1 1
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14. Unit 7
Number Systems and Bases
You have finished viewing:
Binary Multiplication
Return to front slide
Presentation 1 Binary and Base 10
Presentation 2 Adding Binary Numbers
Presentation 3 Subtracting Binary Numbers
Presentation 4 Binary Multiplication
Presentation 5 Examples in Base 5
Presentation 6 Examples in Base 7

15. Unit 7
Number Systems and Bases
Examples in Base 5

16. Convert the base 5 numbers 124 and 1223 into base 10.
Convert 152 from base 10 to base 5.
25 + 10 + 4 = 39
125 + 50 + 10 + 3 = 188
152 = 125 + 25 + 2
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17. Carry out the following base 5 calculations
4 1
+ 2 2
1 1 3
1 2
x 2 4
2 4 0
1 0 3
3 4 3
1 0 4 3
+ 1 2 3
1 2 2 4
1 4 4
x 2 3
3 4 3 0
1 0 4 2
1 0 0 2 2??
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18. Unit 7
Number Systems and Bases
You have finished viewing:
Examples in Base 5
Return to front slide
Presentation 1 Binary and Base 10
Presentation 2 Adding Binary Numbers
Presentation 3 Subtracting Binary Numbers
Presentation 4 Binary Multiplication
Presentation 5 Examples in Base 5
Presentation 6 Examples in Base 7

19. Unit 7
Number Systems and Bases
Examples in Base 7

20. Convert 164 from base 7 to base 10
Convert 142 from base 10 to base 7
Carry out the following calculations in base 7:
49 + 42 + 4 = 95???? ?? ??
142 = (2 x 49) + (6 x 7) + (2 x 1)
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1 4
+ 2 3
4 0
3 4
x 1 2
3 4 0
1 0 1
4 4 1
4 6
x 3 4
2 0 4 0
2 5 3
2 3 2 2
1 4 3
+ 2 2 5
4 0 1?? ??
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21. Unit 7
Number Systems and Bases
You have finished viewing:
Examples in Base 7
Return to front slide
Presentation 1 Binary and Base 10
Presentation 2 Adding Binary Numbers
Presentation 3 Subtracting Binary Numbers
Presentation 4 Binary Multiplication
Presentation 5 Examples in Base 5
Presentation 6 Examples in Base 7