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

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 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

5. Unit 7 Number Systems and Bases You have finished viewing: Binary and Base 10 Return to front slide Presentation 1Binary and Base 10 Presentation 2Adding Binary Numbers Presentation 3Subtracting Binary Numbers Presentation 4Binary Multiplication Presentation 5Examples in Base 5 Presentation 6Examples 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 ? ? ? ? ? ? 101 +11 1000 111 +101 1100 1011 +101 10000 1111 +1101 11100 ? ? ? ? ? ? ? ?

8. Unit 7 Number Systems and Bases You have finished viewing: Adding Binary Numbers Return to front slide Presentation 1Binary and Base 10 Presentation 2Adding Binary Numbers Presentation 3Subtracting Binary Numbers Presentation 4Binary Multiplication Presentation 5Examples in Base 5 Presentation 6Examples 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 ? ? ? ? ? ? 111 -101 10 11011 -1010 10001 1011 -101 100 1001 -11 110 ? ? ? ? ? ? 1110 -111 111 10011 -1010 1001 ? ? ? ? ? ?

11. Unit 7 Number Systems and Bases You have finished viewing: Subtracting Binary Numbers Return to front slide Presentation 1Binary and Base 10 Presentation 2Adding Binary Numbers Presentation 3Subtracting Binary Numbers Presentation 4Binary Multiplication Presentation 5Examples in Base 5 Presentation 6Examples in Base 7

12. Unit 7 Number Systems and Bases Binary Multiplication

13. Calculate, using these binary numbers 110 x11 1100 110 11010 111 x11 1110 111 10101 1101 x110 110100 11010 1101110 1111 x110 111100 11110 1011010 1101 X101 110100 1101 1100001 10110 x111 1011000 101100 10111 10011011 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

14. Unit 7 Number Systems and Bases You have finished viewing: Binary Multiplication Return to front slide Presentation 1Binary and Base 10 Presentation 2Adding Binary Numbers Presentation 3Subtracting Binary Numbers Presentation 4Binary Multiplication Presentation 5Examples in Base 5 Presentation 6Examples 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 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

17. Carry out the following base 5 calculations 41 +22 113 12 x24 240 103 343 1043 +123 1224 144 x23 3430 1042 10022 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

18. Unit 7 Number Systems and Bases You have finished viewing: Examples in Base 5 Return to front slide Presentation 1Binary and Base 10 Presentation 2Adding Binary Numbers Presentation 3Subtracting Binary Numbers Presentation 4Binary Multiplication Presentation 5Examples in Base 5 Presentation 6Examples 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) ? ? ? ? ? ? 14 +23 40 34 x12 340 101 441 46 x34 2040 253 2322 143 +225 401 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

21. Unit 7 Number Systems and Bases You have finished viewing: Examples in Base 7 Return to front slide Presentation 1Binary and Base 10 Presentation 2Adding Binary Numbers Presentation 3Subtracting Binary Numbers Presentation 4Binary Multiplication Presentation 5Examples in Base 5 Presentation 6Examples in Base 7