Binary Lesson 10 Powers of 2

Base Ten The number 147 means The number 147 means 1 x x x x

Base Ten Ones place Number of ones 10^0 Tens place Number of tens 10^1 Hundreds place Number of hundreds 10^2

Exponential Notation 10^1 = 10 10^2 = 10 x 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^( ) ADD Exponents when multiplying

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

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

Binary s 2^3 4s 2^2 2s 2^1 1s 2^0

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

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

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^( ) ADD Exponents when multiplying

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^( ) = 2^(3+3) = 2^3 x 2^3 = 8 x 8 = 64 = 2^2 x 2^2 x 2^2

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

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

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

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

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

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

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

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

Powers of 2 iClicker Questions

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

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

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

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

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

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

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

The /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

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

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

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

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