1. Decimal Review 10 5 10 4 10 3 10 2 10 1 10 0 100,00010,0001,000100101 Decimal ~ Base 10 number system 10 different numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Based on the powers of 10 (see handout) 1, 10, 100, 1000, 10000, 100000, …

2. Decimal Example 2657= 2000 + 600 + 50 + 7 = 2*1000 + 6*100 + 5*10 + 7*1 = 2*10 3 + 6*10 2 + 5*10 1 + 7*10 0 Place the corresponding digits in the decimal chart for the number: 830157

3. Binary! Counting with 1s and 0s

4. Binary Base 2 number system 2 different numbers: 0, 1 Based on the powers of 2 (see handout) 1, 2, 4, 8, 16, 32, … 2525 2424 23232 2121 2020 32168421

5. Example 1011 2 = 1*2 3 + 0*2 2 + 1*2 1 + 1*2 0 = 1*8 + 0*4 + 1*2 + 1*1 = 8 + 2 + 1 = 11 10 Place the corresponding digits in the binary chart for the number: 001101 What is it in decimal (base 10)?

6. Examples 1) Draw the powers of 2 table 2) Place the following numbers in the table 3) Determine the decimal version! 00011 2 = ? 01111 2 = ? 101011 2 = ?

7. ON-OFF-ON-ON 1 0 1 1

8. Haha! "There are only 10 types of people in the world: Those who understand binary, and those who don't"

9. Decimal  Binary

10. Review Each binary digit (bit) is a power of 2... 2727 2626 2525 2424 23232 2121 2020 1286432 168421...

11. Decimal  Binary 1. Write out the powers of 2 2. Subtract the largest power of 2 that is less than your number 3. Make note of which power of 2 you subtracted with a 1 (unused powers of 2 will be 0) 4. Subtract the next largest power of 2 from the result that you have 5. Repeat until you reach 0 6. Build your binary number from the 1s and 0s that you have placed

12. Examples 15 10 = ? 49 10 = ?... 2727 2626 2525 2424 23232 2121 2020 1286432 168421...

13. Convert the following from decimal to binary 8 10 = ? 25 10 = ? 83 10 = ?