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Real Networkers don’t use Decimal! Part 1.

Binary & Interpreting IP Addresses

October 19, 2004

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Understanding Binary

Computers, networks and network addressing schemes use the binary number system.

Number systems are based on “powers of” the base number.

Binary is based on powers of 2. The powers of 2 table is a powerful tool for

network designers.

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Counting in Binary

0

1

10

11

100

101

110

111

1000

1001

1010

1011

1100

1101

1110

1111

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Powers of 2power decimal binary

0 1 1

1 2 10

2 4 100

3 8 1000

4 16 10000

5 32 100000

6 64 1000000

7 128 10000000

8 256 100000000

9 512 1000000000

10 1,024 10000000000

11 2,048 100000000000

12 4,096 1000000000000

13 8,192 10000000000000

14 16,384 100000000000000

15 32,768 1000000000000000

16 65,536 10000000000000000

2POWER Example

23 = 8 decimal

= 1000 binary

Notice 3 zeros.

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Powers of 2, continued

power decimal binary

17 131,072 100000000000000000

18 262,144 1000000000000000000

19 524,288 10000000000000000000

20 1,048,576 100000000000000000000

21 2,097,152 1000000000000000000000

22 4,194,304 10000000000000000000000

23 8,388,608 100000000000000000000000

24 16,777,216 1000000000000000000000000

25 33,554,432 10000000000000000000000000

26 67,108,864 100000000000000000000000000

27 134,217,728 1000000000000000000000000000

28 268,435,456 10000000000000000000000000000

29 536,870,912 100000000000000000000000000000

30 1,073,741,824 1000000000000000000000000000000

31 2,147,483,648 10000000000000000000000000000000

32 4,294,967,296 100000000000000000000000000000000

32 0’s

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Conversion from Binary to Decimal

Decimal value is determined by the total value of bits.

Each bit position value is some power of 2

position

value

2147483648

1073741824

536870912

268435456

134217728

67108864

33554432

16777216

8388608

4194304

2097152

1048576

524288

262144

131072

65536

32768

16384

8192

4096

2048

1024

512

256

128

64

32

16

8 4 2 1

power 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

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Conversion sample 1

1101101101 Add the value of each bit position containing a one.

position 1 1 0 1 1 0 1 1 0 1

value

2147483648

1073741824

536870912

268435456

134217728

67108864

33554432

16777216

8388608

4194304

2097152

1048576

524288

262144

131072

65536

32768

16384

8192

4096

2048

1024

512

256

128

64

32

16

8 4 2 1

power 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

= 512 + 256 + 64 + 32 + 8 + 4 + 1 = 877

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Conversion sample 2

11011011011101101101 Add the value of each bit position containing a one.

position 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1

value

2147483648

1073741824

536870912

268435456

134217728

67108864

33554432

16777216

8388608

4194304

2097152

1048576

524288

262144

131072

65536

32768

16384

8192

4096

2048

1024

512

256

128

64

32

16

8 4 2 1

power 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

= 524288 + 262144 + 65536 + 32768 + 8192 + 4096 + 1024 + 512 + 256 + 64 + 32 + 8 + 4 + 1 = 898,925

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Key Points of IP addressing

32 bits addressing allows 4,294,967,295 possible addresses.

Not feasible to keep track of 4.3 trillion routes to individual hosts.

Separating the address into Network Bits and Host bits allows a single network address to summarize information for many hosts. 00101100011110111010110001111011

Network Bits Host bits

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Identifying networks A network address represents a way to connect

to many hosts. One Class A network address connects 16,777,215 hosts One Class C network connects 255 hosts.

Network addresses are identified by setting the host bits to 0 in an IP Address.

11011110 00100001 00000100 00000000 is a Class C network

11011110 00100001 00000100 00100100 is a host on that network

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Three types of IP addresses Network Address: Host bits all 0’s Broadcast Address: Host bits all 1’s Host Address: at least one 0 & one 1

11011110 00100001 00000100 00000000 is a network address.

11011110 00100001 00000100 11111111 is the broadcast address for that network.

11011110 00100001 00000100 00100100 is a host address on that network.

All 0’s

All 1’s

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Address Ranges

32 bits on every device 10101100 01111011 10101100 01111011

Class A: 8 network bits, 24 host bits, starts 0… 00101100 01111011 10101100 01111011

Class B: 16 network bits, 16 host bits, starts 10… 10101100 01111011 10101100 01111011

Class C: 24 network bits, 8 host bits, starts 110… 11001100 01111011 10101100 01111011

Does this address identify a host or a network?

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Address Ranges

Class D: Multicast, starts 1110… 11100110 01111011 10101100 01111011

224.0.0.5 and 224.0.0.6 are used by OSPF

Class E: Reserved, starts 1111… 11110100 01111011 10101100 01111011

Classes D & E are not important in CCNA1.

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Address Ranges in Decimal

Class A 1.0.0.0 - 126.0.0.0 (127 is local loopback)

Class B 128.0.0.0 - 191.255.0.0

Class C 192.0.0.0 - 223.255.255.0

Class D 224.0.0.0 - 239.255.255.255

Class E 240.0.0.0 - 247.255.255.255

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Special Address Ranges

Private Class A

10.0.0.0 - 10.255.255.255

Private Class B

172.16.0.0 - 172.31.255.255

Private Class C

192.168.0.0 - 192.168.255.255

Local Loopback

127.0.0.0 - 127.255.255.255

Automatic Private IP

Addressing 169.254.0.0 - 169.254.255.255

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Notation Scheme

IP: 32 bit binary number for all addresses. 10101100011110111010110001111011

Reading and writing 32 bits of binary is too hard!

Converting all 32 bits to Decimal is too tedious

Break 32 bits into 4 groups of 8 bits called octets

Dotted Decimal notation converts octets to decimal

A notation scheme is merely a way of representing the bits in an address, it is for convenience – networking is based on the bits not the notation!

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Sample Address in bits

Without breaking it down into octets 10101100011110110010110001111000

1 0 1 0 1 1 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0

2147483648

1073741824

536870912

268435456

134217728

67108864

33554432

16777216

8388608

4194304

2097152

1048576

524288

262144

131072

65536

32768

16384

8192

4096

2048

1024

512

256

128

64

32

16

8 4 2 1

31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

= 2,893,753,464 too hard to do correctly

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Sample Address, dotted decimal

Same address using octets 10101100.01111011.00101100.01111000

easy to add up each octet 128 + 32 + 8 +4 ● 64 + 32 + 16 + 8 + 2 + 1

● 32 + 8 + 4 ● 64 + 32 +16 +8 = 172.123.44.120 in dotted decimal notation

position 1 0 1 0 1 1 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0

value128

64

32

16

8 4 2 1 128

64

32

16

8 4 2 1 128

64

32

16

8 4 2 1 128

64

32

16

8 4 2 1

power 7 6 5 4 3 2 1 0 7 6 5 4 3 2 1 0 7 6 5 4 3 2 1 0 7 6 5 4 3 2 1 0

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Sample Address Network & Host Bits

Begins 10… so it is a Class B address with the first 16 bits representing the network.

10101100.01111011.00101100.01111000 172.123.44.120 in dotted decimal. This is the 00101100.01111000 host on the 10101100.01111011 network.

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Subnetting begins!

In A, B, & C networks, boundary between network and host bits always on an octet boundary. 10101100.01111011.00101100.01111000

Subnetting: some host bits are converted to subnet bits. 10101100.01111011.00101100.01111000 172.123.44.120

One octet may have both subnet & host bits.

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How many subnets?

10101100 01111011 00100000 00000000 has three subnet bits.

Represents just one subnet. When 3 bits are used for subnetting, how many

possible subnets may be created? Lets list them.

Subnet # Bits Subnet # Bits

0 000 4 100

1 001 5 101

2 010 6 110

3 011 7 111

8 subnets Notice that when the bits are converted from binary to decimal, you get the subnet number!

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Possible subnets in Binary

3 bits are borrowed in a Class B network SN# 0: 10101100 01111011 000 00000 00000000 SN# 1: 10101100 01111011 001 00000 00000000 SN# 2: 10101100 01111011 010 00000 00000000 SN# 3: 10101100 01111011 011 00000 00000000 SN# 4: 10101100 01111011 100 00000 00000000 SN# 5: 10101100 01111011 101 00000 00000000 SN# 6: 10101100 01111011 110 00000 00000000 SN# 7: 10101100 01111011 111 00000 00000000

Subnet number is decimal of subnet bits

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Possible subnets in Dotted Decimal

3 bits are borrowed from a class B network SN# 0: 172.123.0.0 SN# 1: 172.123.32.0 SN# 2: 172.123.64.0 SN# 3: 172.123.96.0 SN# 4: 172.123.128.0 SN# 5: 172.123.160.0 SN# 6: 172.123.192.0 SN# 7: 172.123.224.0

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Some Addresses on a Subnet

10101100 01111011 00100000 00000001 (172.123.32.1) and

10101100 01111011 00100010 00000000 (172.123.34.0) are both hosts on the

10101100 01111011 00100000 00000000 (172.123.32.0 ) network.

What address type is 10101100 01111011 01100010 00000000 (172.123.98.0) ?

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The Formula!

3 bits can provide for 8 possible subnets, 4 bits can provide for 16 possible subnets.

What is the rule?

# of Possible Subnets = 2Number of subnet bits

borrowed 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

number of

subnets

4194304

2097152

1048576

524288

262144

131072

65536

32768

16384

8192

4096

2048

1024

512

256

128

64

32

16

8 4 2 1

The Powers of 2 table again!

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Why a mask is necessary

A 32 bit address may be interpreted many ways.

10101100 01111011 00101100 01111000172.123.44.120/16 (no subnet)

10101100 01111011 00101100 01111000172.123.44.120/19 (subnetted using 3 bits)

10101100 01111011 00101100 01111000172.123.44.120/21 (subnetted using 5 bits)

IP address is meaningless without a mask!

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Masking Subnet mask: every network bit is 1 and every

host bit is 0. Binary Address: 10101100.01111011.00101100.01111000

Binary Mask: 11111111.11111111.00000000.00000000

Dotted Decimal Address: 172.123.44.120 Dotted Decimal Mask: 255.255.0.0

position 1 1 1 1 1 1 1 1

value 128

64

32

16

8 4 2 1

This is the default mask of a class B network.

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Masking a 3 bit Subnet Network, Subnet, & Host Bits Binary Address: 10101100 01111011 00101100 01111000

Binary Mask: 11111111.11111111.11100000.00000000

Prefix:11111111.11111111.111 count 1’s 19

position 1 1 1 0 0 0 0 0

value 128

64

32

16

8 4 2 1

Dotted Decimal Address: 172.123.44.120 Dotted Decimal Mask: 255.255.224.0 Prefix: /19

The mask does not distinguish between network and subnetwork bits!

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Masking a 4 bit Subnet Network, Subnet, & Host Bits Binary Address: 10101100 01111011 00101100 01111000

Binary Mask: 11111111.11111111.11110000.00000000

position 1 1 1 1 0 0 0 0

value 128

64

32

16

8 4 2 1

Dotted Decimal Address: 172.123.44.120 Dotted Decimal Mask: 255.255.240.0 Prefix: /_ _

Only 9 possible mask values: 0, 128, 192, 224, 240, 248, 252, 254 and 255

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How many subnet bits?

A mask has only network and host bits. The number of subnet bits must be

calculated.

Number of subnet bits =

Number of actual mask network bits –

Number of default (class) mask network bits

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Example Subnet bits calculation.

Address: 172.123.44.120 10101100 01111011 00101100 01111000

Mask: 255.255.240.0 or /20 11111111.11111111.11110000.00000000

Address begins 10… so it is a Class B address which has a /16 default mask.

20 mask bits – 16 default mask bits =

4 subnet bits

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How a Mask works.

The IP address and the mask are ANDed to determine the network address.

0 AND 0 = 0

0 AND 1 = 0

1 AND 0 = 0

1 AND 1 = 1 The mask acts as a filter which keeps only

the network bits, sets all others to 0.

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Sample Mask Application

What is the network address ofAddress: 172.123.44.120 10101100 01111011 00101100 01111000

Mask: 255.255.240.0 or /20 11111111.11111111.11110000.00000000

Apply the mask:10101100 01111011 00101100 0111100011111111.11111111.11110000.0000000010101100 01111011 00100000 00000000

Network Address: 172.123.32.0

AND

Applying a Mask to an IP address leaves the network address!

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Determining the Broadcast Address for a network Start with a network address and mask

10101100 01111011 00100000 00000000 (172.123.32.0)

11111111.11111111.11110000.00000000 (255.255.240.0)

Apply the mask; network bits remain unchanged! 10101100 01111011 0010

Set all host bits to 1’s 1111 11111111

Put them together and you have the broadcast address 10101100 01111011 00101111 11111111 172.23.47.255 is the broadcast address for the

172.123.32.0 /20 network

The mask is necessary!

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Interpreting IP Addresses

To get the network address from a specific host address and mask.

1. Convert Address and Mask to binary

2. AND the Address and Mask to get the Network Address

3. Convert the Network Address to decimal

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Determining a Broadcast address

To get the broadcast address from a specific network address and mask.

1. Convert Network Address and Mask to binary

2. Use the Mask to identify the network and host bits

3. Copy the network bits from the Network Address and make the remaining host bits all 1’s.

4. Convert to dotted decimal.

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HAPPY NETWORKING!HAPPY NETWORKING!