Real Networkers don

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Real Networkers dont 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 2
2POWER Example 23 8 decimal 1000
binary Notice 3 zeros.
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Powers of 2, continued
32 0s
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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

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Conversion sample 1

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

• 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.

• 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. 001011000111101110101
  10001111011

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 0s
• Broadcast Address Host bits all 1s
• 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 0s
All 1s
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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
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Special Address Ranges
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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

• 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

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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.

• 8 subnets

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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

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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

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Why a mask is necessary

• A 32 bit address may be interpreted many ways.
• 10101100 01111011 00101100 01111000
• 172.123.44.120/16 (no subnet)
• 10101100 01111011 00101100 01111000
• 172.123.44.120/19 (subnetted using 3 bits)
• 10101100 01111011 00101100 01111000
• 172.123.44.120/21 (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 10101100.01111011.00101100.0111100
  0
• Binary Mask 11111111.11111111.00000000.00000000
• Dotted Decimal Address 172.123.44.120
• Dotted Decimal Mask 255.255.0.0

• 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 1s 19

• 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

• 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 11111111.11111111.11110
  000.00000000
• 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 of
• Address 172.123.44.120 10101100 01111011
  00101100 01111000
• Mask 255.255.240.0 or /20 11111111.11111111.1111
  0000.00000000
• Apply the mask
• 10101100 01111011 00101100 0111100011111111.1111
  1111.11110000.0000000010101100 01111011 00100000
  00000000
• Network Address 172.123.32.0

AND
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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 1s
• 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

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Interpreting IP Addresses

• To get the network address from a specific host
  address and mask.
• Convert Address and Mask to binary
• AND the Address and Mask to get the Network
  Address
• 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.
• Convert Network Address and Mask to binary
• Use the Mask to identify the network and host
  bits
• Copy the network bits from the Network Address
  and make the remaining host bits all 1s.
• Convert to dotted decimal.

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HAPPY NETWORKING!