1. Binary Lesson 10 Powers of 2

2. Base Ten The number 147 means The number 147 means 1 x 100 + 4 x 10 + 7 1 x 100 + 4 x 10 + 7

3. Base Ten 1 4 71 4 71 4 71 4 7 Ones place Number of ones 10^0 Tens place Number of tens 10^1 Hundreds place Number of hundreds 10^2

4. Exponential Notation 10^1 = 10 10^2 = 10 x 10 = 100 10^3 = 10 x 10 x 10 = 1,000 10^4 = 10 x 10 x 10 x 10 = 10,000 10^4 = 10^1 x 10^1 x 10^1 x 10^1 = 10^(1+1+1+1) ADD Exponents when multiplying

5. Exponential Notation 10^6 = 1,000,000 = 1,000 x 1,000 = 10^3 x 10^3 = 10^(3+3) = 10^(2+2+2) = 10^2 x 10^2 x 10^2 = 100 x 100 x 100

6. Dividing If I have 100 pennies and I divide them into 10 equal piles, how many are in each pile? 100 / 10 = 10 In exponential notation, this becomes 10^2 / 10^1 = 10^1 = 10^(2-1) SUBTRACT exponents when dividing

7. Binary 1 0 0 11 0 0 11 0 0 11 0 0 1 8s 2^3 4s 2^2 2s 2^1 1s 2^0

8. Base Two Binary Numbers Binary Numbers Each place has one of these values: Each place has one of these values: 0 1 0 1 11 = 1 * 2 + 1 = 3 11 = 1 * 2 + 1 = 3 Or 1*2^1 + 2^0 Or 1*2^1 + 2^0

9. Base Two 1 0 11 0 11 0 11 0 1 Ones place Number of ones 2^0 Twos place Number of twos 2^1 Fours place Number of fours 2^2

10. Exponential Notation 2^1 = 2 2^2 = 2 x 2 = 4 2^3 = 2 x 2 x 2 = 8 2^4 = 2 x 2 x 2 x 2 = 16 2^4 = 2^1 + 2^1 + 2^1 + 2^1 = 2^(1+1+1+1) ADD Exponents when multiplying

11. Exponential Notation 2^6 = 2 x 2 x 2 x 2 x 2 x 2 2^6 = 2^1 x 2^1 x 2^1 x 2^1 x 2^1 x 2^1 = 2^(1+1+1+1+1+1) = 2^(3+3) = 2^3 x 2^3 = 8 x 8 = 64 = 2^2 x 2^2 x 2^2

12. Powers of 2 2^8 = 256 2^7 = 128 2^6 = 64 2^5 = 32 2^4 = 16 2^3 = 8 2^2 = 4 2^1 = 2 2^0 = 1

13. Powers of 2 2^16 = 65,536 2^15 = 32,768 2^14 = 16,384 2^13 = 8,192 2^12 = 4,096 2^11 = 2,048 2^10 = 1,024 2^9 = 512 2^8 = 256

14. Dividing If I have 256 pennies and I divide them into 4 equal piles, how many are in each pile? 256 / 4 = 64 In exponential notation, this becomes 2^8 / 2^2 = 2^(8-2) = 2^6 SUBTRACT exponents when dividing

15. Network Sizes How many addresses are available in a /24 network? 32 bits in the IPv4 addresses 24 network bits 32 - 24 = 8 host bits # of host addresses = 2^8 = 256 (Including network and broadcast)

16. Network Sizes How many addresses are available in a /16 network? 32 bits in the IPv4 addresses 16 network bits 32 - 16 = 16 host bits # of host addresses = 2^16 = 65,536 (Including network and broadcast)

17. Network Sizes How many addresses are available in a /19 network? 32 bits in the IPv4 addresses 19 network bits 32 - 19 = 13 host bits # of host addresses = 2^13 = 8,192 (Including network and broadcast)

18. Subnetting Start with the 192.168.100.0/24 network Subnet it into /25 subnets How many subnets are there? 2 ^ (25 - 24) = 2^1 = 2 How many addresses in each subnet? # host bits = 32 - 25 = 7 # addresses = 2^7 = 128 (including network and broadcast)

19. Subnetting Start with the 147.144.0.0/16 network Subnet it into /18 subnets How many subnets are there? 2 ^ (18 - 16) = 2^2 = 4 How many addresses in each subnet? # host bits = 32 - 18 = 14 # addresses = 2^14 = 16,384 (including network and broadcast)

20. Powers of 2 iClicker Questions

21. What is 100 x 1000 x 100? A.10^5 B.10^6 C.10^7 D.10^8 E.Something else

22. What is 100 x 1000 / 10? A.10^3 B.10^4 C.10^5 D.10^6 E.Something else

23. What is 2^5? A.8 B.16 C.32 D.64 E.Something else

24. What is 2^10? A.128 B.512 C.1024 D.4096 E.Something else

25. What is 2^15? A.1,024 B.8,192 C.16,384 D.65,536 E.Something else

26. The 192.168.0.0/24 network is divided into /28 subnets. How many subnets are there? A.2 B.4 C.8 D.16 E.Something else

27. The 147.144.0.0/16 network is divided into /24 subnets. How many subnets are there? A.16 B.64 C.256 D.1,024 E.Something else

28. The 147.144.0.0/16 network is divided into /30 subnets. How many subnets are there? A.1,024 B.8,192 C.16,384 D.32,768 E.Something else

29. The 172.16.0.0/13 supernet combines several /16 classful subnets. How many subnets does it contain? A.2 B.4 C.8 D.16 E.Something else

30. How many addresses are in the 10.0.0.0/24 subnet? A.64 B.256 C.2,048 D.32,768 E.Something else

31. How many addresses are in the 172.16.64.0/20 subnet? A.1,024 B.2,048 C.4,096 D.8,192 E.Something else

32. How many addresses are in the 147.144.192.0/18 subnet? A.1,024 B.2,048 C.4,096 D.8,192 E.Something else