1. IP v4 Subnetting
IPV4
IP Address Subnetting
Made Easier
“I HOPE”
By
Bill Donahue MS, CCNA, CCDA
Solutions Design Engineer
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2. IP v4 Subnetting
1.0 Introduction
IP v4 was developed in technical time a long time ago when it looked to have an
unlimited supply of addresses available. With the ever increasing usage in IP addresses
we have been waging a war ever since in order to preserve what little space is left. One of
the techniques to optimize addresses is called subnetting. Network engineers must have a
good understanding on how this is accomplished well beyond the use of a subnetting
calculator. The goal of this whitepaper is to help simplify this using techniques I have
learned from my years as both a Network Design Engineer and Faculty at ITT Tech.
I will cover some of the basics that you should already have an understanding of
and then review the technique that I have refined from my Cisco training and other
classes on the subject. I will try to keep it on the lighter side so that you can easily read
through.
2.0 Binary – Decimal or how do I count
We as humans are used to counting by 10. Computers as computers are used to
counting by 2. What engineers as the translators must be able to do is convert them back
and forth with ease. No I am not going to spend any time explaining how the decimal
system operates, if you do not understand this then STOP reading this paper now. Binary
does require a little practice.
Some of the basics definitions include:
Bit – a single numerical value in binary either 1 or 0
Byte – Eight bits and a key value in the IP Addressing scheme that you must know
In IP v4 Addressing understanding what the values are is key. In the Binary system just
as in the decimal system the values increase from right to left with the Most Significant
Bit being on the left. The difference is the Binary the powers increase by 2 not 10.
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So a byte with its eight bits would have the following values
27 26 25 24 23 22 21 20
What does this mean - each bit in the respective bit position starting from the right if it is
a 1 will mean 2 raised to that power in that bit position and knowing the first 7 or being
able to right them down like I have to do before any calculation is key.
Here is a handy chart showing the decimal values of the above numbers
27 = 128
26 = 64
25 = 32
24 = 16
23 = 8
22 = 4
21 = 2
20 = 1
When doing any conversions of a byte value I would recommend writing these numbers
across the top of a piece of paper and then filling in the respective decimal value for each
“1” in the byte for the bit position. Add them all up and you have your decimal equivalent
to the Binary value. Reversing our trend here and going from decimal to binary is just as
easy except we use subtraction and start on the left or with the most significant bit and
keep subtracting the decimal value and reducing our number until we reach zero. Seeing
is believing so let’s go over some examples of this so that you understand this very
important IP addressing step.
2.1 Binary to Decimal
DO NOT TRY TO DO THIS IN YOUR HEAD MISTAKES WILL HAPPEN
Let’s try this byte value 10101010 and convert it to decimal Remember the first part of
this is to put the eight bit place values down on the top of the paper like this:
128 64 32 16 8 4 2 1
You can then insert the binary number below and in each bit position that is a 1 we add
the decimal value up to come up with a total lets see what happens on the next page.
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4. IP v4 Subnetting
Remember our byte value is 10101010 so
128 64 32 16 8 4 2 1
1 0 1 0 1 0 1 0
Gives us - 128 + 32 + 8 + 2 = 170 in decimal
A couple more examples
10110111 in binary
128 64 32 16 8 4 2 1
1 0 1 1 0 1 1 1
128 + 32 + 16 + 4 + 2 + 1 = 183
11111111 in binary
128 64 32 16 8 4 2 1
1 1 1 1 1 1 1 1
128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255.
****** This is actually an extremely important value to know – IF ALL BITS are 1
then the value is 255, you will see later why this is an important value to memorize.
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2.2 Decimal to Binary
Now let’s reverse direction and go from decimal to binary values again we want
to have our scale across the paper and let’s start with 188 as a decimal value that we want
to convert to binary. We start by subtracting the highest value and repeating until we are
at 0.
128 64 32 16 8 4 2 1
Starting with 188 we subtract 128 leaving 60 then we subtract 32 because 64 does not fit
and we repeat all the way to zero – here it is using basic arithmetic
188 – 128 = 60
60 – 32 = 28
28 – 16 = 12
12 – 8 = 4
4–4=0
Now putting in our “1” values we get
128 64 32 16 8 4 2 1
1 0 1 1 1 1 0 0
Another example lets try 207
207 – 128 = 79
79 – 64 = 15
15 – 8 = 7
7–4=3
3–2=1
1 -1 = 1
Gives us 11001111 as seen below
128 64 32 16 8 4 2 1
1 1 0 0 1 1 1 1
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3.0 IP v4 Basics
IP version 4 consists of 32 bits broken down into four groups of 8 bits (byte)
separated by a period. These bits are then written down as a decimal equivalent number
so that humans can read. Hence the reason why we as engineers must be able to convert
back and forth. Try reading the following same value and figure which is easier to
understand
10100011.11111111.00000001.11001100 in binary or
163.255.1.204 in decimal
As you can see the second value is much easier to understand. Now what does this
number mean not much unless you understand a key point. That is, some of this number
represents a network address and some of this number represents a host address. Where
this separation takes place is of critical importance and can change via subnetting so lets
work through the steps to get there.
3.1 Basic IP Address Classes
In the world of IPV4 there are 4 classes of IP addresses that network people need
to be concerned with (in reality there are 5 classes). For simplicity they are Class A-D
and experimental 5th class (Class E). These are referred to as the Classful boundary and
separate the network portion and host portions of the network. It is this boundary that we
are manipulating with subnetting to adjust our line of demarcation to allocate more or less
hosts.
These classes are broken down based on address numbering in the first byte as follows
Decimal Range Binary Value Host Bits
Class A – 0 – 126 0xxxxxxx 24
Class B – 128-191 10xxxxxx 16
Class C – 192-223 110xxxxx 8
Class D - 224-240 1110xxxx (Multicasting)
Note: you may notice that there is no 127 value listed between the Class A and B
addresses. That is because the value is reserved for Loopback purposes and cannot be
used for general network addressing.
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3.2 Public vs. Private
Our IPV4 addresses are separated into two general categories of addresses these
are Public and Private. What exactly does this mean – preserved IPV4 addresses and
security?
A Public IP Address is a Registered address range assigned to a company that will be
allowed to traverse the internet and can only be used to address a specific Layer 3 device.
A Private IP Address is an Unregistered address range that a company can use internally
to assign IP Addresses to its Layer 3 devices and with the use of Network Address
Translation saves valuable IPV4 address space. These addresses are not routable over the
IP Network. This also provides a level of security as the internal device is not truly seen
from the outside world.
Private addresses include space out of each class as follows:
Class A – 10.0.0.0 to 10.255.255.255
Class B – 172.16.0.0 to 172.31.255.255
Class C – 192.168.0.0 to 192.168.255.255
See RFC 1918 for a detailed explanation
3.3 CIDR notation
In the world of subnetting we need a mask to match with the IP Address to help
us define which portion of the address is network and which portion is host. There are
two types of masks one for humans and one for computers.
For Computers we will transmit the mask with the IP address using the same format as
the address itself with the difference being we will assign 1’s to the network and 0’s to
the host. One critical thing to remember is that the network values start on the left and
MUST continue sequentially to the right
As an example let’s use our address from before:
10100011.11111111.00000001.11001100 in binary or
163.255.1.204 in decimal
Assuming standard addressing and the value of 163 in the first byte we have a Class B
address and the network portion would be the first 2 bytes or 16 bits. If we subnet by just
one bit we would need to let the network know that we have done this by transmitting the
mask with it. It would look like this:
10100011.11111111.00000001.11001100 mask = 11111111.11111111.10000000.0000000
163.255.1.204 in decimal mask 255.255.128.0
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Lots of writing so we use CIDR notation for humans and it represents exactly the same
information just in a more easily read format. The binary would remain the same but the
decimal value would look like this:
163.255.1.204 /17
The /17 tells the user that the first 17 bits are network bits with the e value of one. If you
look at the binary representation you will see that they match.
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4.0 Subnetting
Let’s get into the heart of subnetting. I will start with a brief step – by – step
outline and then using an example I will go into detailed instructions as they pertain to
each step. Many of the technical aspects were covered in the previous sections of this
white paper.
4.1 Step – by – Step Overview
This may seem a little confusing but as you will see in the detailed steps it is fairly simple
if you go one step at a time. I would also like to acknowledge Cisco with their use of the
demarcation line which makes this process much simpler.
Step 1 – Write down the 128 64 32 16 8 4 2 1 conversion table at the top of a
blank piece of paper
Step 2 – Using the Subnet Mask figure out which byte we are working with
Step 3 – Using the Conversion table from step 1 convert the working byte to
binary
Step 4 – Insert the mask below the binary converted number
Step 5 – Draw a line of demarcation separating the network and host portions of
the address
Step 6 – Multiply down the mask and address
Step 7 – Convert back to decimal this is now your network number network
number
Step 8 – Now change all host bits to the right of the demarcation line in step 5 to
“1”s.
Step 9 – Convert back to decimal and you now have your broadcast address.
Step 10 – Then add 1 to the network address and you now have your 1 st host
address in this subnet
Step 11 – Subtract 1 from the broadcast address and you have the last host in the
subnet
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4.2 Class C Subnetting example
We will start with a Class C address as an example. This is the simplest one to do since
all the manipulation takes place in the right most byte.
193.200.175.188 /28
Step 1 – Write down the 128 64 32 16 8 4 2 1 conversion table at the top of a
blank piece of paper. Since I am doing this as an example I will be carrying the
items down throughout each step.
128 64 32 16 8 4 2 1
Step 2 – Using the Subnet Mask figure out which byte we are working with. In
this example the /28 would put us in the 4th byte (188) since each period
represents eight bit positions and we are counting over to the 28th position.
Step 3 – Using the Conversion table from step 1 convert the working byte to
binary.
So using what we learned earlier we do our subtraction and fill in under our
conversion chart, 1s where we can subtract and 0s where we cannot
188 – 128 = 60
60 – 32 = 28
28 – 16 = 12
12 – 8 = 4
4–4=0
128 64 32 16 8 4 2 1
1 0 1 1 1 1 0 0
Step 4 – Insert the mask below the binary converted number
/28 would be 4 bits into the byte
128 64 32 16 8 4 2 1
1 0 1 1 1 1 0 0
1 1 1 1 0 0 0 0
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Step 5 – Draw a line of demarcation separating the network and host portions of
the address. This is very important do not skip this simple step.
128 64 32 16 8 4 2 1
1 0 1 1 1 1 0 0
1 1 1 1 0 0 0 0
NETWORK PORTION HOST PORTION
Step 6 – Multiple down the mask and address
128 64 32 16 8 4 2 1
1 0 1 1 1 1 0 0
1 1 1 1 0 0 0 0
1 0 1 1 0 0 0 0
Step 7 – Convert back to decimal this is now your network number
Converting 10110000 back to decimal gives us a value of 176 since we are
working in the 4th bytes and the original number given was 193.200.175.188 /28
The network number associated with the original IP Address is
193.200.175.176
Step 8 – Now change all host bits to the right of the demarcation line in step 5 to
“1”s.
128 64 32 16 8 4 2 1
1 0 1 1 1 1 0 0
1 1 1 1 0 0 0 0
1 0 1 1 1 1 1 1
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Step 9 – Convert back to decimal and you now have your broadcast address.
Converting 10111111 back to decimal gives us a value of 191. Since we are
working in the 4th bytes and the original number given was 193.200.175.188 /28
The broadcast address associated with the original IP Address is
193.200.175.191
Step 10 – Then add 1 to the network address and you now have your 1 st host
address in this subnet.
193.200.175.176 network
Plus 1 193.200.175.177 first subnet host
Step 11 – Subtract 1 from the broadcast address and you have the last host in the
subnet
193.200.175.191 broadcast
Minus 1 193.200.175.190 last subnet host
Following the above steps on IP Address 193.200.175.188 /28 we end up with
193.200.175.176 Network Address
193.200.175.177 First Subnet Host
193.200.175.190 Last Subnet Host
192.200.175.191 Broadcast Address
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4.3 Class B Subnetting example
We will start with a Class C address as an example. This is the simplest one to do since
all the manipulation takes place in the right most byte. The MOST IMPORTANT thing to
remember when working with Class B subnetting is to not forget that even though we are
working with the 3rd byte the 4th byte will need to be manipulated to all 0’s for Network
Address and all 1’s for Broadcast address
173.200.195.108 /19
Step 1 – Write down the 128 64 32 16 8 4 2 1 conversion table at the top of a
blank piece of paper. Same as before
128 64 32 16 8 4 2 1
Step 2 – Using the Subnet Mask figure out which byte we are working with. In
this example the /19 would put us in the 3rd byte (195) since each period
represents eight bit positions and we are counting over to the 19th position.
Step 3 – Using the Conversion table from step 1 convert the working byte to
binary.
So using what we learned earlier we do our subtraction and fill in under our
conversion chart, 1s where we can subtract and 0s where we cannot
195 – 128 = 67
67 – 64 = 3
3 -2 = 1
1 -1 = 0
128 64 32 16 8 4 2 1
1 1 0 0 0 0 1 1
Step 4 – Insert the mask below the binary converted number
/19 would be 3 bits into the byte
128 64 32 16 8 4 2 1
1 1 0 0 0 0 1 1
1 1 1 0 0 0 0 0
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Step 5 – Draw a line of demarcation separating the network and host portions of
the address. This is very important do not skip this simple step. Also do not forget
that the 4th byte will need to be made all 0’s for the network or all 1’s for the
broadcast
128 64 32 16 8 4 2 1
1 1 0 0 0 0 1 1
1 1 1 0 0 0 0 0
NETWORK PORTION HOST PORTION
Step 6 – Multiple down the mask and address
128 64 32 16 8 4 2 1
1 1 0 0 0 0 1 1
1 1 1 0 0 0 0 0
1 1 0 0 0 0 0 0
Step 7 – Convert the answer back to decimal this is now your network number
Converting 11000000 back to decimal gives us a value of 192 since we are working in
the 3rd bytes and the original number given was 173.200.195.108 /19
The network number associated with the original IP Address is
173.200.192.0
REMEMBER: The forth byte is also all 0’s for the network number
Step 8 – Now change all host bits to the right of the demarcation line in step 5 to
“1”s. This will also include the 4th byte
128 64 32 16 8 4 2 1
1 1 0 0 0 0 1 1
1 1 1 0 0 0 0 0
1 1 0 1 1 1 1 1
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Step 9 – Convert back to decimal and you now have your broadcast address.
Converting 11011111 back to decimal gives us a value of 223. Since we are
working in the 3rd bytes and the original number given was 173.200.195.108 /19
Remember that the 1’s carry into the 4th byte
The broadcast address associated with the original IP Address is
173.200.223.255
Step 10 – Then add 1 to the network address and you now have your 1 st host
address in this subnet.
173.200.192.0 network
Plus 1 173.200.192.1 first subnet host
Step 11 – Subtract 1 from the broadcast address and you have the last host in the
subnet
173.200.223.255 broadcast
Minus 1 173.200.223.254 last subnet host
Following the above steps on IP Address 173.200.195.108 /19 we end up with
173.200.192.0 Network Address
173.200.192.1 First Subnet Host
173.200.223.254 Last Subnet Host
173.200.223.255 Broadcast Address
173.200.224.0
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References
1. Cisco CCNA TV – Cisco.com
2. CCNA ICND Exam Certification Guide by Wendell Odom
3. Some of my students at ITT Tech that said – “hey this way may be easier”
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