IP Subnetting and Related Topics
A Tutorial by Chris Uriarte <chrisjur@cju.com>
Updated April 2001
First and foremost, it’s
important to understand that every IP address has a binary number
equivalent. We use the binary
equivalents to compute subnet information.
It’s very important that you are comfortable with simple binary math,
especially binary addition and converting decimal number to their binary
equivalents.
For example, the IP address
206.20.36.1 has a binary equivalent of:
11001110.
00010100. 00100100.00000001
(11001110 represents 206;
00010100 represents 20; 00100100 represents 36; 00000001 represents 1)
We say that each IP address
is composed four groups of eight bits, ranging from 00000000 to 11111111
(binary). Therefore, IP addresses fall
into the range:
00000000.00000000.00000000.00000000
to 11111111.11111111.11111111.11111111
(binary)
or the decimal equivalent:
0.0.0.0
to 255.255.255.255
(in reality, we don’t
actually assign IP addresses starting or ending with 0 or 255 to hosts…you’ll
learn a bit more later).
There are three general
classes of IP address blocks:
· Class
A - supports 16+ million hosts on each network
· Class
B - supports 65,000+ hosts on each networks
· Class
C - supports 254 hosts on each network
Organizations can be
assigned classes of IP addresses based on their needs. For example, an organization can be allotted
the IP address block of 206.20.36.* (where * represents any valid number),
which includes the IP addresses 206.20.36.0 to 206.20.36.255 (256 IP addresses
total). The IP block 206.20.36.* is
considered a Class C network.
As another example, a
company may be allotted the IP address block 206.20.*.*, which includes the IP
addresses 206.20.0.0 to 206.20.255.255 (65K+ addresses total). 206.20.*.* is considered a class B network.
Although a Class C network
contains a total of 256 IP addresses (206.20.36.0 to 206.20.36.255, for
example), there are actually only 254 IP addresses that can be assigned to
hosts on the network. This is because
there are 2 special IP addresses in each network that cannot be assigned
to hosts.
·
The Network Address –
is the first address on a subnet and is essentially used to identify the
network (think of it as the “name” of network). In the Class C network 206.20.36.*, 206.20.36.0 is the network
address.
·
The Broadcast Address –
is the last IP address on a subnet and represents an “all hosts” address,
utilized to send packets to every host on a subnet. In the Class C network 206.20.36.*, 206.20.36.255 is the
broadcast address.
Therefore, given a subnet
that contains a total of N IP addresses, the total number of IP
addresses you can assign to hosts is N-2.
A subnet is a portion
of a network that shares a common address component with other portions of the
network. On TCP/IP networks, subnets are defined as all devices whose IP
addresses have the same prefix. For example, all devices with IP addresses that
start with 206.20.36. would be part of the same subnet. Dividing a network,
such as a Class B or Class C network, into subnets is useful for security and
performance reasons, as well as for reasons of practicality.
As noted before, a Class B
network contains a total of 65K+ IP addresses, while a Class C network contains
254 IP addresses. Since IP addresses
must be assigned to organizations in blocks, what happens if a an organization
requires only 500 IP addresses??- too many IP addresses for a Class C network,
but far too little addresses to justify the use of an entire Class B
network. This is a prime example of why
we use bubnetting. In this example,
we can divide a Class B network into smaller blocks, or subnets, to accommodate
the need of 500 addresses.
IP networks are divided into
subnets using a subnet mask. A
subnet mask is used to determine what subnet an IP address belongs to. An IP
address has two components: the network address and the host address. For example,
consider the IP address 206.20.36.1. Assuming this is part of a Class B
network, the first two numbers (206.20) represent the Class B network
address, and the second two numbers (36.1) identify a particular
host on this network. Subnetting
enables the network administrator to further divide the host portion of the
address into two or more subnets.
The combination of a network
address (explained earlier) and a subnet mask tell us exactly the IP addresses
contained within a subnet. For example,
the network address 206.30.36.0 with a subnet mask of 255.255.255.0 tells us
that the IP addresses in this subnet are 206.20.36.0 to 206.20.36.255. Given the fact that we cannot assign the
first address in the block (the network address) or the last address (the
broadcast address) to hosts, the useable IP addresses in this subnet are
206.20.36.1 to 206.20.36.254. The next
step is to explain how we actually calculate subnets and subnet masks.
A. Given an IP address and a subnet mask, determine its associated network address.
Determining a subnet’s
network address from an IP address and a subnet mask is quite simple. We simply execute the following steps:
1. Convert both the IP address and subnet mask
to their binary equivalents. Line each
digit up so they evenly match on paper.
We usually place the IP address above the subnet mask. If either 8-bit block does not contain 8
digits, you must pad the front of the 8-bit block with zeros until the block
becomes 8 digits. Given the IP address
206.20.36.1 and a subnet mask of 255.255.255.0, we have:
IP
Address: 11001110.00010100.00100100.00000001
Subnet
Mask: 11111111.11111111.11111111.11111111
2. Now apply the Bitwise AND operation
on each corresponding digit in the IP Address and Subnet Mask. The Bitwise AND operation is a function that
compares two numbers and returns true, or 1, if both numbers are true. In the binary number world, the Bitwise AND
operation produces results according to the chart below:
|
Number 1 |
Number 2 |
Bitwise AND Result |
|
0 |
0 |
0 |
|
0 |
1 |
0 |
|
1 |
0 |
0 |
|
1 |
1 |
1 |
So,
for this example, we compare each digit in the IP address with the digit
directly below it in the subnet mask.
If they are both 1, the Bitwise AND result is 1.
|
IP Address: |
11001110.00010100.00100100.00000001 |
|
Subnet Mask: |
11111111.11111111.11111111.00000000 |
|
Bitwise AND Result: |
11001110.00010100.00100100.00000000 |
3. Finally, convert the Bitwise AND result to
from Binary to Decimal format. The
example above, gives us the address of 206.20.36.0, which is the network
address associated with our IP address and subnet mask above.
|
Example A: Given an
IP address of 192.168.14.95 and a subnet mask of 255.255.255.192, what is the
network address associated with this subnet? 1. Convert 192.168.14.95 (IP Address) and
255.255.255.192 (Subnet Mask) to binary: IP: 11000000.10101000.00001110.01011111 Mask: 11111111.11111111.11111111.11000000 2. Perform the Bitwise AND operation between
the corresponding digits in each address: IP: 11000000.10101000.00001110.01011111 Mask: 11111111.11111111.11111111.11000000 Bit. AND:
11000000.10101000.00001110.01000000 3. Convert the Bitwise AND result into
decimal format to its decimal equivalent of
192.168.14.64 – this is the network address. |
B. Given an IP address or Network Address and a subnet mask, determine the usable IP addresses in the subnet.
This scenario is commonly
encountered when you know the IP address and subnet mask of a host on the
network, but are unsure of what IP addresses you can assign to other hosts on
your network.
There are several ways to
figure out subnet IP address ranges in a Class C network through manual
calculations and table lookups. I will
demonstrate both methods.
First, let’s examine the
manual procedure, which, again, utilizes simple binary arithmetic:
1. First, convert each IP address (or network address) into their binary forms. Line each digit up so they evenly match on paper, as we did earlier. Remember, if either 8-bit block does not contain 8 digits, you must pad the front of the 8-bit block with zeros until the block becomes 8 digits. Given the IP address 192.168.14.95 and a subnet mask of 255.255.255.192, we have:
IP
Address: 11000000.10101000.00001110.01011111
Subnet
Mask: 11111111.11111111.11111111.11000000
2. Given the IP address and subnet comparison
above, we now need to break the IP address bits into a host portion and
a network portion. You will
notice that every subnet mask begins with a series of 1’s. The IP address’s bits that correspond to
(i.e. are directly above) the subnet mask’s 1’s are part of the network
portion of the address – these are the bits that are common to all hosts in
this particular subnet. The IP
address’s bits that correspond to the 0’s in the subnet mask are part of the
host portion of the address – these are the bits that uniquely identify each
host in the subnet.
In
the example above, I have separated the host portion of the addresses from the
network portion. The network portion
appears in blue, while the host portion appears
in red.
IP
Address: 11000000.10101000.00001110.01011111
Subnet
Mask: 11111111.11111111.11111111.11000000
3. Next, we want to figure out exactly how
many IP addresses are in each subnet of this Class C. To do this, we count the number of bits contained in the host
portion of our address. In the address
above, the “magic number” is 6, since we have 6 host bits. We now compute 2 to the 6th power
to determine how many IP addresses are in each subnet:
26
= 64
Therefore,
each subnet in this class C contains 64 IP addresses.
In
addition, it is now easy to compute just how many subnets are contained in this
Class C, given the subnet mask above.
Common sense tells you that if there are 256 IP addresses in a Class C
block, you must have (4) blocks of 64 IP addresses. However, you can also count the number of bits in the subnet
portion after the last decimal point in the IP address, or subtract your
“magic number” above, 6, from 8 (8 – 6 = 2).
Now we raise 2 to the 2nd power to get the number 4, which
represents the number of subnets in the class C. You may start to notice a pattern here: if you extend the network portion of the
address (make the subnet mask larger), you increase the number of subnets in a
class C, but decrease the number of IP addresses in each subnet. For example, if we extend the subnet mask
one additional bit in the example above, this class C will contain 23,
or 8, subnets of 32 hosts.
4. Now that you know that there are 64 hosts in each subnet of class C 192.168.14.* you can begin to make a chart of the subnet blocks in the class C, keeping in mind that the first IP address in a Class C starts with zero:
Subnet
Blocks in Class C 192.168.14.* with subnet mask of 255.255.255.192:
192.168.14.0
to 192.168.14.63
192.168.14.64
to 192.168.14.127
192.168.14.128
to 192.168.14.191
192.168.14.192
to 192.168.14.255
Notice
that we created 4 subnets containing 64 IP addresses in each. Remember, however, that you can only assign
62 of these addresses to hosts, as the first and last IP addresses of the
subnet are the network address and broadcast address, respectively.
Assuming you have a host on the network 192.168.14.95, you can see that it falls into the second subnet in this Class C: 192.168.14.64 to 192.168.14.127. Taking away the network and broadcast addresses, this tells you that you can assign any IP address between 192.168.14.65 and 192.168.14.127 to hosts on your network.
The procedure above
demonstrates the “manual” method used to compute subnet IP address ranges. There are, however, freely available charts
available in books an on the Internet that will map out subnet IP ranges for
each available subnet mask. I have included
a chart at the end of this document.
|
Example B: Given and
IP address of 206.20.36.1 and a subnet mask of 255.255.255.240, what are
valid IP addresses that can be assigned to hosts on this subnet? 1. Convert 206.20.36.1 (IP Address) and
255.255.255.240 (Subnet Mask) to binary: IP: 11001110.00010100.00100100.00000001 Mask: 11111111.11111111.11111111.11110000 2. Separate the addresses into network
portions and host portions: (The network portion is
represented in blue, while the host portion is represented in red) IP: 11001110.00010100.00100100.00000001 Mask: 11111111.11111111.11111111.11110000 3. Determine the number of hosts in the
subnet by counting the number of host bits.
There are 4 host bits in
this address; therefore, there are 24, or 16, IP addresses in each
subnet in this class C. You can now
create a subnet map for the class C 206.20.36.*: 206.20.36.0
to 206.20.36.15 206.20.36.16
to 206.20.36.31 206.20.36.32
to 206.20.36.47 etc.
etc. You can now see that the
given IP address of 206.20.36.1 falls into the first subnet, which contains
the IP addresses 206.20.36.0 to 206.20.36.15. Excluding the network (206.20.36.0) and broadcast
(206.20.36.15) addresses, you can assign any address from 206.20.36.1 to
206.20.36.15 to any host on this subnet. |
|
|
|
|
Valid |
|
|
Number
of hosts per subnetwork |
|
|
|
host numbers |
|
Number
of subnetworks |
|
|
|
|
|
Subnet
Mask |
|
|
|
|
|
255.255.255.128 |
1/2 |
126 |
0 |
1-126 |
|
|
|
|
128 |
129-254 |
|
|
|
|
Valid |
|
|
Number
of hosts per subnetwork |
|
|
|
host numbers |
|
Number
of subnetworks |
|
|
|
|
|
Subnet
Mask |
|
|
|
|
|
255.255.255.192 |
3/4 |
62 |
0 |
1-62 |
|
|
|
|
64 |
65-126 |
|
|
|
|
128 |
129-190 |
|
|
|
|
192 |
193-254 |
|
|
|
|
Valid |
|
|
Number
of hosts per subnetwork |
|
|
|
host numbers |
|
Number
of subnetworks |
|
|
|
|
|
Subnet
Mask |
|
|
|
|
|
255.255.255.224 |
7/8 |
30 |
0 |
1-31 |
|
|
|
|
32 |
33-62 |
|
|
|
|
64 |
65-94 |
|
|
|
|
96 |
97-126 |
|
|
|
|
128 |
129-158 |
|
|
|
|
160 |
161-190 |
|
|
|
|
192 |
193-222 |
|
|
|
|
224 |
225-254 |
|
|
|
|
Valid |
|
|
Number
of hosts per subnetwork |
|
|
|
host numbers |
|
Number
of subnetworks |
|
|
|
|
|
Subnet
Mask |
|
|
|
|
|
255.255.255.240 |
15/16 |
14 |
0 |
1-14 |
|
|
|
|
16 |
17-30 |
|
|
|
|
32 |
33-46 |
|
|
|
|
48 |
49-62 |
|
|
|
|
64 |
65-78 |
|
|
|
|
80 |
81-94 |
|
|
|
|
96 |
97-110 |
|
|
|
|
112 |
113-126 |
|
|
|
|
128 |
129-142 |
|
|
|
|
144 |
145-158 |
|
|
|
|
160 |
161-174 |
|
|
|
|
176 |
177-190 |
|
|
|
|
192 |
193-206 |
|
|
|
|
208 |
209-222 |
|
|
|
|
224 |
225-238 |
|
|
|
|
240 |
241-254 |
|
|
|
|
Valid |
|
|
Number
of hosts per subnetwork |
|
|
|
host numbers |
|
Number
of subnetworks |
|
|
|
|
|
Subnet
Mask |
|
|
|
|
|
255.255.255.248 |
31/32 |
6 |
0 |
1-6 |
|
|
|
|
8 |
9-14 |
|
|
|
|
16 |
17-22 |
|
|
|
|
24 |
25-30 |
|
|
|
|
32 |
33-38 |
|
|
|
|
40 |
41-46 |
|
|
|
|
48 |
49-54 |
|
|
|
|
56 |
57-62 |
|
|
|
|
64 |
65-70 |
|
|
|
|
72 |
73-78 |
|
|
|
|
80 |
81-86 |
|
|
|
|
88 |
89-94 |
|
|
|
|
96 |
97-102 |
|
|
|
|
104 |
105-110 |
|
|
|
|
112 |
113-118 |
|
|
|
|
120 |
121-126 |
|
|
|
|
128 |
129-134 |
|
|
|
|
136 |
137-142 |
|
|
|
|
144 |
145-150 |
|
|
|
|
152 |
153-158 |
|
|
|
|
160 |
161-166 |
|
|
|
|
168 |
169-174 |
|
|
|
|
176 |
177-182 |
|
|
|
|
184 |
185-190 |
|
|
|
|
192 |
193-198 |
|
|
|
|
200 |
201-206 |
|
|
|
|
208 |
209-214 |
|
|
|
|
216 |
217-222 |
|
|
|
|
224 |
225-230 |
|
|
|
|
232 |
233-238 |
|
|
|
|
240 |
241-246 |
|
|
|
|
248 |
249-254 |
|
|
|
|
Valid |
|
|
Number
of hosts per subnetwork |
|
|
|
host numbers |
|
Number
of subnetworks |
|
|
|
|
|
Subnet
Mask |
|
|
|
|
|
255.255.255.252 |
63/64 |
2 |
0 |
1-2 |
|
|
|
|
4 |
5-6 |
|
|
|
|
8 |
9-10 |
|
|
|
|
12 |
13-14 |
|
|
|
|
16 |
17-18 |
|
|
|
|
20 |
21-22 |
|
|
|
|
24 |
25-26 |
|
|
|
|
28 |
29-30 |
|
|
|
|
32 |
33-34 |
|
|
|
|
36 |
37-38 |
|
|
|
|
40 |
41-42 |
|
|
|
|
44 |
45-46 |
|
|
|
|
48 |
49-50 |
|
|
|
|
52 |
53-54 |
|
|
|
|
56 |
57-58 |
|
|
|
|
60 |
61-62 |
|
|
|
|
64 |
65-66 |
|
|
|
|
68 |
69-70 |
|
|
|
|
72 |
73-74 |
|
|
|
|
76 |
77-78 |
|
|
|
|
80 |
81-82 |
|
|
|
|
84 |
85-86 |
|
|
|
|
88 |
89-90 |
|
|
|
|
92 |
93-94 |
|
|
|
|
96 |
97-98 |
|
|
|
|
100 |
101-102 |
|
|
|
|
104 |
105-106 |
|
|
|
|
108 |
109-110 |
|
|
|
|
112 |
113-114 |
|
|
|
|
116 |
117-118 |
|
|
|
|
120 |
121-122 |
|
|
|
|
124 |
125-126 |
|
|
|
|
128 |
129-130 |
|
|
|
|
132 |
133-134 |
|
|
|
|
136 |
137-138 |
|
|
|
|
140 |
141-142 |
|
|
|
|
144 |
145-146 |
|
|
|
|
148 |
149-150 |
|
|
|
|
152 |
153-154 |
|
|
|
|
156 |
157-158 |
|
|
|
|
160 |
161-162 |
|
|
|
|
164 |
165-166 |
|
|
|
|
168 |
169-170 |
|
|
|
|
172 |
173-174 |
|
|
|
|
176 |
177-178 |
|
|
|
|
180 |
181-182 |
|
|
|
|
184 |
185-186 |
|
|
|
|
188 |
189-190 |
|
|
|
|
192 |
193-194 |
|
|
|
|
196 |
197-198 |
|
|
|
|
200 |
201-202 |
|
|
|
|
204 |
205-206 |
|
|
|
|
208 |
209-210 |
|
|
|
|
212 |
213-214 |
|
|
|
|
216 |
217-218 |
|
|
|
|
220 |
221-222 |
|
|
|
|
224 |
225-226 |
|
|
|
|
228 |
229-230 |
|
|
|
|
232 |
233-234 |
|
|
|
|
236 |
237-238 |
|
|
|
|
240 |
241-242 |
|
|
|
|
244 |
245-246 |
|
|
|
|
248 |
249-250 |
|
|
|
|
252 |
253-254 |