IP Sub-Netting

In this article, we will learn how to subnet and make subnetting an easy task.

The table below summarizes the possible network numbers, the total number of each type, and the number of hosts in each Class A, B, and C network.

	Default subnet mask	Range
Class A	255.0.0.0 (/8)	1.0.0.0 – 126.255.255.255
Class B	255.255.0.0 (/16)	128.0.0.0 – 191.255.255.255
Class C	255.255.255.0 (/24)	192.0.0.0 – 223.255.255.255

Table 1 – Default subnet mask & range of each class

Class A addresses begin with a 0 bit. Therefore, all addresses from 1.0.0.0 to 126.255.255.255 belong to class A (1=0000 0001; 126 = 0111 1110).
The 0.0.0.0 address is reserved for default routing and the 127.0.0.0 address is reserved for loopback testing so they don’t belong to any class.
Class B addresses begin with a 1 bit and a 0 bit. Therefore, all addresses from 128.0.0.0 to 191.255.255.255 belong to class B (128=1000 0000; 191 =1011 1111).
Class C addresses begin with two 1 bits and a 0 bit. Class C addresses range from 192.0.0.0 to 223.255.255.255 (192 = 1100 0000; 223 = 1101 1111).

Class D & E are used for Multicast and Research purposes and we are not allowed to subnet them so they are not mentioned here.

Note: The number behind the slash notation (/) specifies how many bits are turned on (bit 1). For example:

+ “/8″ equals “1111 1111.0000 0000.0000 0000.0000 0000″ -> 8 bits are turned on (bit 1)
+ “/12″ equals “1111 1111.1111 0000.0000 0000.0000 0000″ -> 12 bits are turned on (bit 1)
+ “/28″ equals “1111 1111.1111 1111.1111 1111.1111 0000″ -> 28 bits are turned on (bit 1)
+ “/32″ equals “1111 1111.1111 1111.1111 1111.1111 1111″ -> 32 bits are turned on (bit 1) and this is also the maximum value because all bits are turned on.

The slash notation (following with a number) is equivalent to a subnet mask. If you know the slash notation you can figure out the subnet mask and vice versa. For example, “/8″ is equivalent to “255.0.0.0″; “/12″ is equivalent to “255.240.0.0″; “/28″ is equivalent to “255.255.255.240″; “/32″ is equivalent to “255.255.255.255″.

The Network & Host parts of each class by default

From the “default subnet mask” shown above, we can identify the network and host part of each class. Notice that in the subnet mask, bit 1 represents for Network part while bit 0 presents for Host part (255 equals to 1111 1111 and 0 equals to 0000 0000 in binary form).

What is “subnetting”?

When changing a number in the Network part of an IP address we will be in a different network from the previous address. For example, the IP address 11.0.0.1 belongs to class A and has a default subnet mask of 255.0.0.0; if we change the number in the first octet (a block of 8 bits, the first octet is the leftmost 8 bits) we will create a different network. For example, 12.0.0.1 is in a different network from 11.0.0.1. But if we change a number in the Host part, we are still in the same Network. For example, 11.1.0.1 is in the same network of 11.0.0.1.

The problem here is if we want to create 300 networks how can we do that? In the above example, we can only create different networks when changing the first octet so we can create a maximum of 255 networks because the first octet can only range from 1 to 255 (in fact it is much smaller because class A only range from 1 to 126). Now we have to use a technique called “subnetting” to achieve our purpose.

“Subnetting” means we borrow some bits from the Host part to add to the Network part. This allows us to have more networks than using the default subnet mask. For example, we can borrow some bits in the next octet to make the address 11.1.0.1 belong to a different network from 11.0.0.1.

How to subnet?

Do you remember that I said “in the subnet mask, bit 1 represents for Network part while bit 0 presents for Host part”? Well, this also means that we can specify how many bits we want to borrow by changing how many bit 0 to bit 1 in the subnet mask.

Let’s come back to our example with the IP 11.0.0.1, we will write all numbers in binary form to reveal what a computer really sees in an IP address.

Now you can clearly see that the subnet mask will decide which is the Network part, which is the Host part. By borrowing 8 bits, our subnet mask will be like this:

After changing the second octet of the subnet mask from all “0″ to all “1″, the Network part is now extended. Now we can create new networks by changing number in the first or second octet. This greatly increases the number of networks we can create. With this new subnet mask, IP 11.1.0.1 is in different network from IP 11.0.0.1 because “1″ in the second octet now belongs to the Network part.

So, in conclusion we “subnet” by borrowing bit “0″ in the Host portion and converting them to bit “1″. The number of borrowed bits is depended on how many networks we need.

Note: A rule of borrowing bits is we can only borrow bit 0 from the left to the right without skipping any bit 0. For example, you can borrow like this: “1111 1111. 1100 0000.0000 0000.0000 0000″ but not this: “1111 1111. 1010 0000.0000 0000.0000 0000″. In general, just make sure all your bit “1″s are successive on the left and all your bit “0″s are successive on the right.

Calculate how many networks and hosts-per-subnet

In our example, you may raise a question: “when we borrow 8 bits, how many sub-networks and how many hosts per sub-network do it create?”

Note: From now, we will call sub-networks “subnets”. This term is very popular so you should be familiar with it.

How many new subnets?

Because we can change any bit in the second octet to create a new subnet, each bit can be “0″ or “1″ so with this subnet mask (255.255.0.0) we can create 2⁸ more subnets. From here we can deduce the formula to calculate the newly created subnets. Suppose n is the number of bits we borrow:

The number of newly created subnets = 2n

In our example, we borrow 8 bits so we will have 2ⁿ = 2⁸ = 256 subnets!

How many hosts per subnet?

The number of hosts per subnet is depended on the Host part, which is indicated by the “0″ part of the subnet mask. So suppose k is the number of bits “0″ in the subnet mask. The formula to calculate the number of hosts is 2^k. But notice that with each subnet, there are two addresses we can’t assign for hosts because they are used for network address & broadcast address. Thus we must subtract the result to 2. Therefore the formula should be:

The number of hosts per subnet = 2k – 2

In our example, the number of bit “0″ in the subnet mask 255.255.0.0 (in binary form) is 16 so we will have 2^k – 2 = 2¹⁶ – 2 = 65534 hosts-per-subnet!

Some other examples

Well, practice makes perfect so we should have some more exercises to be familiar with them. But remember that this is only the beginning in your journey to become a subnetting guru :)

Exercise 1

Your company has just been assigned the network 4.0.0.0. How many subnets and hosts-per-subnet you can create with a subnet mask of 255.255.255.0?

(Please try to solve by yourself before reading the solution ^^)

Solution

First of all you have to specify which class this network belongs to. According to Table 1, it belongs to class A (simply, class A ranges from 1 to 126) and its default subnet mask is 255.0.0.0. Therefore if we use a subnet mask of 255.255.255.0, it means we borrowed 16 bits (to convert from 0 to 1).

255.0.0.0 = 1111 1111.0000 0000.0000 0000.0000 0000
255.255.255.0 = 1111 1111.1111 1111.1111 1111.0000 0000

Now use our above formulas to find the answers:

The number of newly created subnets = 2¹⁶ = 65536 (with 16 is the borrowed bits)
The number of hosts per subnet = 2⁸ – 2 = 254 (with 8 is the bit “0″s left in the 255.255.255.0 subnet mask)

Exercise 2

Your company has just been assigned the network 130.0.0.0. How many subnets and hosts-per-subnet you can create with a subnet mask of 255.255.128.0?

(Please try to solve by yourself before reading the solution ^^)

Solution

130.0.0.0 belongs to class B with the default subnet mask of 255.255.0.0. But is the subnet mask of 255.255.128.0 strange? Ok, let’s write all subnet masks in binary:

255.255.128.0 = 1111 1111.1111 1111.1000 0000.0000 0000

This is a valid subnet because all bit “1″s and “0″s are successive. Comparing to the default subnet mask, we borrowed only 1 bit:

255.255.0.0 = 1111 1111.1111 1111.0000 0000.0000 0000

Therefore:

The number of newly created subnets = 2¹ = 2 (with 1 is the borrowed bits)
The number of hosts per subnet = 2¹⁵ – 2 = 32766 (with 15 is the bit “0″s left in the 255.255.128.0 subnet mask)

Exercise 3

Your company has just been assigned the network 198.23.16.0/28. How many subnets and hosts-per-subnet you can create with a subnet mask of 255.255.255.252?

(Please try to solve by yourself before reading the solution ^^)

Solution

In this exercise, your company was given a “subnetted” network from the beginning and it is not using the default subnet mask. So we will compare two subnet masks above:

/28 = 1111 1111.1111 1111.1111 1111.1111 0000 (=255.255.255.240)
255.255.255.252 = 1111 1111.1111 1111.1111 1111.1111 1100 (= /30)

In this case we borrowed 2 bits. Therefore:

The number of newly created subnets = 2² = 4 (with 2 is the borrowed bits)
The number of hosts per subnet = 2² – 2 = 2 (with 2 is the bit “0″s left in the 255.255.255.252 subnet mask)

In this exercise I want to go a bit deeper into the subnets created. We learned there are 4 created subnets but what are they? To find out, we should write all things in binary:

Because two subnet masks (/28 & /30) only affect the 4th octet so we don’t care about the first three octets. In the 4th octet we are allowed to change 2 bits (in the green box) of the IP address to create a new subnet. So there are 4 values we can use: 00, 01, 10 & 11. After changing, we convert them back to decimal numbers. We get 4 subnets:

+ First subnet: 198.23.16.0/30 (the 4th octet is 00000000)
+ Second subnet: 198.23.16.4/30 (the 4th octet is 00000100)
+ Third subnet: 198.23.16.8/30 (the 4th octet is 00001000)
+ Fourth subnet: 198.23.16.12/30 (the 4th octet is 00001100)

So how about hosts per subnet? Please notice that all these 4 subnets are successive. So we can deduce the range of these subnets:

+ First subnet: ranges from 198.23.16.0 to 198.23.16.3
+ Second subnet: ranges from 198.23.16.4 to 198.23.16.7
+ Third subnet: ranges from 198.23.16.8 to 198.23.16.11
+ Fourth subnet: ranges from 198.23.16.12 to 198.23.16.15

Let’s analyze the first subnet which ranges from 198.23.16.0 to 198.23.16.3. Notice that all networks (and subnets) have a network address and a broadcast address. In this case, the network address is 198.23.16.0 and the broadcast address is 198.23.16.3 and they are not assignable or usable for hosts. This is the reason why we have to subtract 2 in the formula “The number of hosts per subnet = 2^k – 2″. After eliminating these 2 addresses we have 2 addresses left (which are 198.23.16.1 & 198.23.16.2) as calculated above.

In the previous examples, we have to write all subnet masks and IP addresses in binary numbers to find out the results. It is a boring and time-consuming task. In this part I will show you a shortcut to subnet without using a calculator or rough paper!

Subnetting – The quick & easy way

One important thing we should notice is that a valid subnet mask must have all bit “1″s and “0″s successive, in which bit “1″s must be on the left; bit “0″s must be on the right. Therefore we only have 8 situations:

               

Table 2 – lists all valid subnet masks

This is a very important table to do subnet quickly! Please take some time to learn it by heart. Make sure you remember the right-most bit “1″ position (the least significant bit 1, which are in red in the above table) and their equivalent decimal values.

In most cases, this table is used to quickly convert a number from decimal to binary value without any calculation. For example, you can quickly convert the 4th octet of the subnet mask 255.255.255.248 to 11111000. Or if you are given a subnet of /29 you will know it equals to 255.255.255.248 (by thinking “/24 is the default subnet mask of class C so /29 will have the right-most bit “1″ at 5th position).

Try to practice with these questions:

+ “/28″ in binary form?
+ “255.255.224.0″ in binary form?
+ “255.192.0.0″ in slash notation form?
+ “/26″ in binary form?
+ “255.128.0.0″ in binary form?
+ “248.0.0.0″ in slash notation form?

(Please try to solve by yourself before reading the solution)

Answers:

+ /28 -> 1111 1111.1111 1111.1111 1111.1111 0000
+ 255.255.224.0 -> 1111 1111.1111 1111.1110 0000.0000 0000
+ 255.192.0.0 -> /10
+ /26 -> 1111 1111.1111 1111.1111 1111.1100 0000
+ 255.128.0.0 -> 1111 1111.1000 0000.0000 0000.0000 0000
+ 248.0.0.0 -> /5

How to find out the increment number?

The increment is the heart of subnetting; if you can find out the increment, you can find all the information to solve a subnetting question. So it is usually the first thing you must find out in a subnetting question.

The increment number is the number specifying how “big” your subnets are. Let’s take an example of the increment number! Did you remember the subnets in “Exercise 3″ in the previous part? By changing bits in the Network part, we found out 4 subnets:

+ First subnet: 198.23.16.0/30 (the 4th octet is 00000000)
+ Second subnet: 198.23.16.4/30 (the 4th octet is 00000100)
+ Third subnet: 198.23.16.8/30 (the 4th octet is 00001000)
+ Fourth subnet: 198.23.16.12/30 (the 4th octet is 00001100)

In this case the increment is 4 (in the 4th octet) because the “difference” between two successive subnets is 4 (from 0 -> 4; from 4 -> 8; from 8 -> 12)

There are 2 popular ways to find out the increment number:

1) Use the formula:

Increment = 256 – x

In which “x” is the first octet (counting from the left) which is smaller than 255 in a subnet mask. For example:

+ In a subnet mask of 255.224.0.0 -> x = 224
+ In a subnet mask of /29 -> x = 248 (because /29 = 255.255.255.248)
+ In a subnet mask of 1111 1111.1111 1100.0000 0000.0000 0000 -> x = 252

In the case you see a subnet mask of 255.255.255.255 (which is very rare in CCNA), x = 255

Note: Also remember which octet “x” belongs to because we have to plus the increment to that octet.

Now let’s solve Exercise 3 again by using this formula:

Exercise 3 one again (with the formula 256 – x):

Your company has just been assigned the network 198.23.16.0/28. How many subnets and hosts-per-subnet you can create with a subnet mask of 255.255.255.252?

The subnet mask is 255.255.255.252 -> x = 252 (x belongs to 4th octet)

Therefore the Increment = 256 – 252 = 4

The initial network 198.23.16.0/28 is also the first subnet, so:
+ The first subnet: 198.23.16.0/30
+ The second subnet: 198.23.16.4/30 because the increment is 4 so we plus the network address with it to get the next network address (0 + 4 = 4)
+ The third subnet: 198.23.16.8/30 (4 + 4 = 8)
+ The fourth subnet: 198.23.16.12/30 (8 + 4 = 12)

Note: We know there are only 4 subnets because we borrow 2 bits.

2) Learn by heart the decimal value of the rightmost bit “1″ in the subnet mask:

Another way to find the increment value is to write “x” in binary: 11110000. Consider the rightmost bit “1″, the decimal value of this bit is the increment value. In this case it equals to 16.

The table below summarizes the decimal values of bit “1″ depending on its position. To use this method, you should learn by heart this table:

Table 3 – How to find out increment based on the “least-significant” (rightmost) bit 1

Now let’s solve Exercise 3 again by using this method:

Exercise 3 one again (with the “decimal value of the rightmost bit 1″ method):

Your company has just been assigned the network 198.23.16.0/28. How many subnets and hosts-per-subnet you can create with a subnet mask of 255.255.255.252?

First use Table 2 to convert 252 to 1111 1100. The decimal value of the rightmost bit “1″ is 4 (according to Table 3) -> The Increment is 4.

After finding out the increment we can deduce 4 subnets it creates.

The initial network 198.23.16.0/28 is also the first subnet, so:
+ The first subnet: 198.23.16.0/30
+ The second subnet: 198.23.16.4/30 because the increment is 4 so we plus the network address with it to get the next network address (0 + 4 = 4)
+ The third subnet: 198.23.16.8/30 (4 + 4 = 8)
+ The fourth subnet: 198.23.16.12/30 (8 + 4 = 12)

Note: We should only choose one method to use and try to practice, practice & practice more with it. Practice until you can solve any subnetting questions within 20 seconds!

Maybe you will ask why 256 can help you find the increment. In fact, by using the formula Increment = 256 – x you are trying to separate the rightmost bit “1″ from other bits:

256 – x = 255 – x + 1

In which “255 – x” will convert all bit “0″s to bit “1″s and all bit “1″s to “0″s while “+1″ part will make our result have only one bit “1″ left. For example, if x = 240 then:

                

So in fact we can say two above methods are the same!