Unit 7 Number Systems and Bases Presentation 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

Unit 7 Number Systems and Bases Binary and Base 10

Convert the binary numbers 1011, 11001 and 100101 to base 10 numbers. ? 8 + 0 ? + 2 ? + 1 ? = 11 ? ? + 16 ? + 0 ? + ? 2 + ? 1 = 51 ? 32 ? + ? 0 + 0 ? + ? 4 + 0 ? + 1 ? = 37 ? 32

Convert these base 10 numbers into binary numbers: 5 = 4 + 1 12 = 8 + 4 23 = 16 + 4 ? + 2 + 1 77 = 64 + 8? + 4 + 1 ? ? ? ? ?

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

Unit 7 Number Systems and Bases Adding Binary Numbers

Key results with binary numbers 1 + 0 = 1? ? 1 + 1 = 10 Calculate, using these binary numbers 1 0 1 + + 1 1 1 + 1 0 1 1 ? 0 0 0 1 ? 1 0 0 1 1 1 1 0 0 ? 0 0 + 1 1 0 1 1 ? 0 0

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

Unit 7 Number Systems and Bases Subtracting Binary Numbers

Key results with binary numbers 1 - 0 = 1? 10 - 1 = 1? ? 11 - 1 = 10 Calculate, using these binary numbers 1 1 1 - - 1 0 1 1 0 - 1 1 1 0 1 1 - 1 0 ? 1 0 1? 1 1 1 0 ? 0 0 1 1 1 0 1 1 ? 0 0 - 1 1 1? 1 0 - 1 0 1 ? 0 0 1

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

Unit 7 Number Systems and Bases Binary Multiplication

Calculate, using these binary numbers 1 1 0 x 1 1 1 x 1 1 0 1 X 1 0 1 1 1 0 1 x 1 1 0 1 ? 1 0 0 1 ? 1 1 0 1 1 ? 0 1 0 0 ? 1 1 1 ? 1 1 0 1 1 ? 0 1 0 ? 1 0 1 1 1 0 ? 0 0 0 1 1 1 0 ? 1 1 1 0 1 1 x 1 1 0 x 1 1 1 ? 1 1 0 0 1? 1 0 0 0 1 ? 1 1 1 0? 1 1 0 0 1 ? 1 0 1? 0 1 1 0 0 1? 1 0 1 1

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

Unit 7 Number Systems and Bases Examples in Base 5

Convert the base 5 numbers 124 and 1223 into base 10. ? + 10 ? + 4 ? = 39 ? 25 ? + 50 ? + 10 ? + ? 3 = 188 ? 125 Convert 152 from base 10 to base 5. 152 = 125 + 2 ? ?

Carry out the following base 5 calculations 4 1 + x 2 2 1 0 4 3 + 1 2 3 1? 1 3 1 2 ? 2 4 1 2 1 4 4 2 4 x 2 3 2? 4 0 3 ? 4 3 0 1? 0 3 1 ? 0 4 2 3? 4 3 1 0 ? 0 2 2

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

Unit 7 Number Systems and Bases Examples in Base 7

Convert 164 from base 7 to base 10 ? + 42 ? + 4 ? = 95 ? 49 Convert 142 from base 10 to base 7 142 = (2 x 49) + (6 x 7) + (2 x 1) ? ? Carry out the following calculations in base 7: 3 4 1 4 + 2 3 ? 4 0 x 1 2 3? 4 0 1? 0 1 4? 4 1 4 6 1 4 3 + 2 2 5 4? 0 1 x 3 4 2 0? 4 0 2? 5 3 2 3? 2 2 ?

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