Binary Lesson 10 Powers of 2 Base Ten

Binary Lesson 10 Powers of 2

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

Base Ten 147 Hundreds place Number of hundreds 10^2 Ones place Number of ones 10^0 Tens place Number of tens 10^1

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

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

Dividing n n n 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^(2 -1) SUBTRACT exponents when dividing

Binary 1 0 0 1 8 s 2^3 4 s 2^2 2 s 2^1 1 s 2^0

Base Two n Binary Numbers n Each place has one of these values: n 01 n 11 =1*2+1=3 n Or 1*2^1 + 2^0

Base Two 101 Fours place Number of fours 2^2 Ones place Number of ones 2^0 Twos place Number of twos 2^1

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

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

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

Powers of 2 n n n n n 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 n n n 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 n n n How many addresses are available in a /24 network? 32 bits in the IPv 4 addresses 24 network bits 32 - 24 = 8 host bits # of host addresses = 2^8 = 256 n (Including network and broadcast)

Network Sizes n n n How many addresses are available in a /16 network? 32 bits in the IPv 4 addresses 16 network bits 32 - 16 = 16 host bits # of host addresses = 2^16 = 65, 536 n (Including network and broadcast)

Network Sizes n n n How many addresses are available in a /19 network? 32 bits in the IPv 4 addresses 19 network bits 32 - 19 = 13 host bits # of host addresses = 2^13 = 8, 192 n (Including network and broadcast)

Subnetting n n n Start with the 192. 168. 100. 0/24 network Subnet it into /25 subnets How many subnets are there? n n 2 ^ (25 - 24) = 2^1 = 2 How many addresses in each subnet? # host bits = 32 - 25 = 7 n # addresses = 2^7 = 128 n n (including network and broadcast)

Subnetting n n n Start with the 147. 144. 0. 0/16 network Subnet it into /18 subnets How many subnets are there? n n 2 ^ (18 - 16) = 2^2 = 4 How many addresses in each subnet? # host bits = 32 - 18 = 14 n # addresses = 2^14 = 16, 384 n n (including network and broadcast)

Powers of 2 i. Clicker Questions

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

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

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

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

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

The 192. 168. 0. 0/24 network is divided into /28 subnets. How many subnets are there? A. B. C. D. E. 2 4 8 16 Something else

The 147. 144. 0. 0/16 network is divided into /24 subnets. How many subnets are there? A. B. C. D. E. 16 64 256 1, 024 Something else

The 147. 144. 0. 0/16 network is divided into /30 subnets. How many subnets are there? A. B. C. D. E. 1, 024 8, 192 16, 384 32, 768 Something else

The 172. 16. 0. 0/13 supernet combines several /16 classful subnets. How many subnets does it contain? A. B. C. D. E. 2 4 8 16 Something else

How many addresses are in the 10. 0/24 subnet? A. B. C. D. E. 64 256 2, 048 32, 768 Something else

How many addresses are in the 172. 16. 64. 0/20 subnet? A. B. C. D. E. 1, 024 2, 048 4, 096 8, 192 Something else

How many addresses are in the 147. 144. 192. 0/18 subnet? A. B. C. D. E. 1, 024 2, 048 4, 096 8, 192 Something else