© 2010 Cisco Systems, Inc. All rights reserved. 1 Network Math.
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Transcript of © 2010 Cisco Systems, Inc. All rights reserved. 1 Network Math.
© 2010 Cisco Systems, Inc. All rights reserved. 1
Network Math
2© 2010 Cisco Systems, Inc. All rights reserved.
Decimal Numbers AKA
BASE 10 Numbers
3© 2010 Cisco Systems, Inc. All rights reserved.
Decimal numbers are based on 10 digits:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Decimal Number Format
Ten Millions Millions
Hundred thousands
Tenthousands Thousands Hundreds Tens Ones
10,000,000 1,000,000 100,000 10,000 1,000 100 10 1
4© 2010 Cisco Systems, Inc. All rights reserved.
Example:
7,469
7000 + 400 + 60 + 9 = 7469
Decimal Number Format
Thousands Hundreds Tens Ones
7 4 6 9
X 1000 X 100 X 10 X 1
7000 400 60 9
5© 2010 Cisco Systems, Inc. All rights reserved.
Place holders for each digit are based on a power of 10
Decimal Number Format
Ten Millions Millions
Hundred thousands
Tenthousands Thousands Hundreds Tens Ones
10,000,000 1,000,000 100,000 10,000 1,000 100 10 1
107 106 105 104 103 102 101 100
6© 2010 Cisco Systems, Inc. All rights reserved.
Example:
7,469
TOTAL7469
Decimal Number Format is a Base 10 Format
Thousands Hundreds Tens Ones
7 4 6 9
X 103 X 102 X 101 X 100
7000 400 60 9
7© 2010 Cisco Systems, Inc. All rights reserved.
Binary Numbers AKA
Base 2 Numbers
8© 2010 Cisco Systems, Inc. All rights reserved.
Binary numbers are based on 2 digits: 0 & 1
Place holders for each digit are based on a power of 2
Binary (BASE 2) Number Format
27 26 25 24 23 22 21 20
9© 2010 Cisco Systems, Inc. All rights reserved.
Binary numbers are based on 2 digits: 0 & 1
The decimal value of each place in a binary number can be calculated by raising 2 to the appropriate power:
20 = 1
Binary (BASE 2) Number Format
1
27 26 25 24 23 22 21 20
10© 2010 Cisco Systems, Inc. All rights reserved.
Binary numbers are based on 2 digits: 0 & 1
The decimal value of each place in a binary number can be calculated by raising 2 to the appropriate power:
21 = 2
Binary (BASE 2) Number Format
2 1
27 26 25 24 23 22 21 20
11© 2010 Cisco Systems, Inc. All rights reserved.
Binary numbers are based on 2 digits: 0 & 1
The decimal value of each place in a binary number can be calculated by raising 2 to the appropriate power:
22 = 4
Binary (BASE 2) Number Format
4 2 1
27 26 25 24 23 22 21 20
12© 2010 Cisco Systems, Inc. All rights reserved.
Binary numbers are based on 2 digits: 0 & 1
The decimal value of each place in a binary number can be calculated by raising 2 to the appropriate power:
23 = 8
Binary (BASE 2) Number Format
8 4 2 1
27 26 25 24 23 22 21 20
13© 2010 Cisco Systems, Inc. All rights reserved.
Binary numbers are based on 2 digits: 0 & 1
The decimal value of each place in a binary number can be calculated by raising 2 to the appropriate power:
24 = 16
Binary (BASE 2) Number Format
16 8 4 2 1
27 26 25 24 23 22 21 20
14© 2010 Cisco Systems, Inc. All rights reserved.
Binary numbers are based on 2 digits: 0 & 1
The decimal value of each place in a binary number can be calculated by raising 2 to the appropriate power:
25 = 32
Binary (BASE 2) Number Format
32 16 8 4 2 1
27 26 25 24 23 22 21 20
15© 2010 Cisco Systems, Inc. All rights reserved.
Binary numbers are based on 2 digits: 0 & 1
The decimal value of each place in a binary number can be calculated by raising 2 to the appropriate power:
26 = 64
Binary (BASE 2) Number Format
64 32 16 8 4 2 1
27 26 25 24 23 22 21 20
16© 2010 Cisco Systems, Inc. All rights reserved.
Binary numbers are based on 2 digits: 0 & 1
The decimal value of each place in a binary number can be calculated by raising 2 to the appropriate power:
27 = 128
Binary (BASE 2) Number Format
128 64 32 16 8 4 2 1
27 26 25 24 23 22 21 20
17© 2010 Cisco Systems, Inc. All rights reserved.
Binary numbers are based on 2 digits: 0 & 1
The decimal value of each place in a binary number can be calculated by raising 2 to the appropriate power:
27 = 128
Binary (BASE 2) Number Format
128 64 32 16 8 4 2 1
27 26 25 24 23 22 21 20
18© 2010 Cisco Systems, Inc. All rights reserved.
8-BIT BINARY NUMBERS
What do 8-bit binary numbers look like? They will use the digits 0 and 1
They will be 8 bits long
19© 2010 Cisco Systems, Inc. All rights reserved.
8-BIT BINARY NUMBERS
Here are some examples of 8-bit binary numbers.
00000101
10101010
11001100
11100111
20© 2010 Cisco Systems, Inc. All rights reserved.
8-BIT BINARY NUMBERS
There are 256 combinations of 8-bit binary numbers:
Smallest: 00000000
Largest: 11111111
21© 2010 Cisco Systems, Inc. All rights reserved.
What is the decimal value of the smallest 8-bit binary number? 00000000
Since zero is a factor when multiplying each place value, there are 8 zeros to add together:
0+0+0+0+0+0+0+0 = 0 converted to Base 10
8-BIT BINARY NUMBERS
0 0 0 0 0 0 0 0
128 64 32 16 8 4 2 1
0x128=0 0x64=0 0x32=0 0x16=0 0x8=0 0x4=0 0x2=0 0x1=0
27 26 25 24 23 22 21 20
22© 2010 Cisco Systems, Inc. All rights reserved.
What is the decimal value of the largest 8-bit binary number? 11111111
Since each place value is multiplied by 1, the 8 place values are added together:
128+64+32+16+8+4+2+1=255 converted to Base 10
8-BIT BINARY NUMBERS
1 1 1 1 1 1 1 1
128 64 32 16 8 4 2 1
1x128=128 1x64=64 1x32=32 1x16=16 1x8=8 1x4=4 1x2=2 1x1=1
27 26 25 24 23 22 21 20
23© 2010 Cisco Systems, Inc. All rights reserved.
What is the decimal value of this 8-bit binary number? 00000101
Each zero factor will result in a zero value when multiplying the place value, but the factors of 1 will be added together:
0+0+0+0+0+4+0+1 = 5 converted to Base 10
8-BIT BINARY NUMBERS
0 0 0 0 0 1 0 1
128 64 32 16 8 4 2 1
0x128=0 0x64=0 0x32=0 0x16=0 0x8=0 1x4=0 0x2=0 1x1=0
27 26 25 24 23 22 21 20
24© 2010 Cisco Systems, Inc. All rights reserved.
What is the decimal value of this 8-bit binary number? 10101010
Each zero factor will result in a zero value when multiplying the place value, but the factors of 1 will be added together:
128+0+32+0+8+0+2+0 = 170 converted to Base 10
8-BIT BINARY NUMBERS
1 0 1 0 1 0 1 0
128 64 32 16 8 4 2 1
1x128=128 0x64=0 1x32=32 0x16=0 1x8=8 0x4=0 1x2=2 0x1=0
27 26 25 24 23 22 21 20
25© 2010 Cisco Systems, Inc. All rights reserved.
What is the decimal value of this 8-bit binary number? 11001100
Each zero factor will result in a zero value when multiplying the place value, but the factors of 1 will be added together:
= converted to Base 10
8-BIT BINARY NUMBERS
1 1 0 0 1 1 0 0
128 64 32 16 8 4 2 1
27 26 25 24 23 22 21 20
26© 2010 Cisco Systems, Inc. All rights reserved.
What is the decimal value of this 8-bit binary number? 11100111
Each zero factor will result in a zero value when multiplying the place value, but the factors of 1 will be added together:
= converted to Base 10
8-BIT BINARY NUMBERS
1 1 1 0 0 1 1 1
128 64 32 16 8 4 2 1
27 26 25 24 23 22 21 20
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CONVERSIONS Binary to Decimal Decimal to Binary
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Remember the decimal values for each placeholder in an 8-bit binary number:
Converting from Binary to Decimal and
Converting from Decimal to Binary utilize this
These conversions will be necessary numerous times!
IMPORTANT TO REMEMBER!
128 64 32 16 8 4 2 1
29© 2010 Cisco Systems, Inc. All rights reserved.
30© 2010 Cisco Systems, Inc. All rights reserved.
