binary lesson 10 powers of 2. base ten the number 147 means the number 147 means 1 x 100 + 4 x 10 +...
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Binary Lesson 10Binary Lesson 10Powers of 2Powers of 2
Base TenBase Ten
The number 147 meansThe number 147 means 1 x 100 + 4 x 10 + 71 x 100 + 4 x 10 + 7
Base TenBase Ten
11 44 77
Ones placeNumber of ones
10^0
Tens placeNumber of tens
10^1
Hundreds placeNumber of hundreds
10^2
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
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
BinaryBinary
11 00 00 11
8s2^3
4s2^2
2s2^1
1s2^0
Base TwoBase Two
Binary NumbersBinary Numbers Each place has one of these Each place has one of these
values:values: 0 10 1
11 = 1 * 2 + 1 = 311 = 1 * 2 + 1 = 3 Or 1*2^1 + 2^0Or 1*2^1 + 2^0
Base TwoBase Two
11 00 11
Ones placeNumber of ones
2^0
Twos placeNumber of twos
2^1
Fours placeNumber 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^(1+1+1+1) 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^(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
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 32 - 24 = 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 32 - 16 = 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 32 - 19 = 13 host bits # of host addresses = 2^13 = 8,192
(Including network and broadcast)
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)
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)
Powers of 2Powers of 2iClicker QuestionsiClicker Questions
What is 100 x 1000 x 100?What is 100 x 1000 x 100?
A.A. 10^5 10^5
B.B. 10^610^6
C.C. 10^710^7
D.D. 10^810^8
E.E. Something elseSomething else
What is 100 x 1000 / 10?What is 100 x 1000 / 10?
A.A. 10^3 10^3
B.B. 10^410^4
C.C. 10^510^5
D.D. 10^610^6
E.E. Something elseSomething else
What is 2^5?What is 2^5?
A.A. 88
B.B. 1616
C.C. 3232
D.D. 6464
E.E. Something elseSomething else
What is 2^10?What is 2^10?
A.A. 128128
B.B. 512512
C.C. 10241024
D.D. 40964096
E.E. Something elseSomething else
What is 2^15?What is 2^15?
A.A. 1,0241,024
B.B. 8,1928,192
C.C. 16,38416,384
D.D. 65,53665,536
E.E. Something elseSomething else
The 192.168.0.0/24 network is The 192.168.0.0/24 network is divided into /28 subnets. How divided into /28 subnets. How
many subnets are there?many subnets are there?
A.A. 22
B.B. 44
C.C. 88
D.D. 1616
E.E. Something elseSomething else
The 147.144.0.0/16 network is The 147.144.0.0/16 network is divided into /24 subnets. How divided into /24 subnets. How
many subnets are there?many subnets are there?
A.A. 1616
B.B. 6464
C.C. 256256
D.D. 1,0241,024
E.E. Something elseSomething else
The 147.144.0.0/16 network is The 147.144.0.0/16 network is divided into /30 subnets. How divided into /30 subnets. How
many subnets are there?many subnets are there?
A.A. 1,0241,024
B.B. 8,1928,192
C.C. 16,38416,384
D.D. 32,76832,768
E.E. Something elseSomething else
The 172.16.0.0/13 supernet The 172.16.0.0/13 supernet combines several /16 classful combines several /16 classful subnets. How many subnets subnets. How many subnets
does it contain?does it contain?
A.A. 22
B.B. 44
C.C. 88
D.D. 1616
E.E. Something elseSomething else
How many addresses are in the How many addresses are in the 10.0.0.0/24 subnet?10.0.0.0/24 subnet?
A.A. 6464
B.B. 256256
C.C. 2,0482,048
D.D. 32,76832,768
E.E. Something elseSomething else
How many addresses are in the How many addresses are in the 172.16.64.0/20 subnet?172.16.64.0/20 subnet?
A.A. 1,0241,024
B.B. 2,0482,048
C.C. 4,0964,096
D.D. 8,1928,192
E.E. Something elseSomething else
How many addresses are in the How many addresses are in the 147.144.192.0/18 subnet?147.144.192.0/18 subnet?
A.A. 1,0241,024
B.B. 2,0482,048
C.C. 4,0964,096
D.D. 8,1928,192
E.E. Something elseSomething else