In this section I will look at converting decimals to binary, hexadecimal and also look
at the operation called “and”.
These skills are important to learn when you start dealing with IP addresses.
If you career starts taking you more towards the networking side of things, understanding
how to convert numbers between different formats becomes essential to creating and managing
a network.
In computing you have switches which can either be set to on or off.
This gives you 2 possible values.
To allow you to represent larger numbers computers group these switches together.
The most common one you will deal with is a byte which is 8 bits.
A byte has a value of 0 to 255.
To convert a decimal to a binary I use the following table.
Each bit in the table has a value assigned to it.
You can see, going from right to left the first value has a 1 in the first position.
The second position has a value of 2.
Twice the previous value.
The 3 position has a value of 4.
As you can see the value doubles in each position until the final value of 128.
If I take a random number, say 174 and wanted to convert it into binary I would do the following.
First I would go to bit 8 and work out if 174 is greater or equal to 128.
If 174 is greater than 128, which it is, the result is a 1.
I would than subtract 128 from 174 and place the result, 46 in the next column.
The next column has a value of 64.
46 is not greater than 64 so the result is no and gets a value of 0.
I now move 46 to the next column and compare it with its value of 32.
46 is greater than 32 so I place a one in this column and subtract 32 from 46 to give
me 14.
I keep following the same procedure throughout the table.
You will notice that when I get to the second last column the value 2 equals the column
value.
In this case the value is equal to the column value and thus the result is still a one.
All columns after this will equal zero since there is no remainder to subtract from the
column value.
This gives us a binary value of 1 0 1 0 1 1 1 0.
Using this method you can quickly and easily covert any decimal number into a binary number.
With IP version 6, hexadecimal is used in the IP address so you need to have an understanding
of it in order to master IP version 6.
If I were to take an IP version 4 address and convert to hexadecimal I would do the
following.
First of all I would convert the numbers into binary using the previously shown method.
Once the numbers are in binary they are easier to work with.
The next step is to divide the binary into groups of four.
Dividing the bits up like this gives each group of 4 bits 16 different possible values.
Hexadecimal uses 16 values and thus that is where hexadecimal gets it’s name from.
It is a simple matter to convert these values into decimal values.
As you can see each group of 4 bits has been given a value between 0 and 15.
Once you have this value you can use this table to determine the hexadecimal value.
As you can see the first value 12 and gets a value of C. Values between 0 and 9 get the
same value so therefore the values in the example 0, 9, 1, 1 and 3 all get the same
values.
It is not till we get to far right you see the value 14 will get the value of E and the
value 10 will get the value of A. Certain IP version 6 addresses have IP version 4 addresses
imbedded in them.
It is important to understand how to covert decimal to hexadecimal to understand IP version
6 addresses.
Slide 4 Once you start working with more than one
network, it is important to understand how the “and” operator works.
Consider this table.
When comparing two bits, if both bits are 1 the result is a one.
You will notice that in all other cases the results is zero.
All it takes is one or both bits to be zero and the result it zero.
If you have trouble understanding this, think of the “and” operator as a multiplication
operator instead.
1 times 1 is 1.
1 times 0 is 0.
0 times 1 is 0 and 0 times 0 is 0.
Why is the “and” operator important?
Later in the course you will learn the “and” operator is used to determine the destination
of a packet.
Consider this small network.
If a computer sends data over the network to a server, the computer needs to determine
if the data is to be sent directly to the server or the data needs to be sent via a
router.
If the server is on the same network as the client it sends it directly to the server.
If the server is on anther network the client computer sends the data to a router.
By using the “and” operator, your computer can work out where to send the data.
Later on in the course this process will be explained in more detail.
This has been a short induction to converting decimals.
If you don’t work a great deal with the networking side, you may want to consider
using the windows calculator to convert decimals to hexadecimal and binary for you.
Just remember to switch the calculator to scientific mode first.
Before sitting for your exam, check the exam requirements.
A lot of the exams will allow you to use the windows calculator in the exam.
If you are planning to sit any Cisco exams, you need to have an excellent understanding
of how to covert decimals.
Cisco don’t give you a calculator in the exam to help you and believe me you need to
do the math fast.
Lastly if you need more practice there are a lots of resources on the internet.
When I was first learning networking I used a web site called learn to subnet dot com.
This is a great little site that will help you understand how to convert decimals to
binary and also how to subnet.
I will cover subnetting in more detail later in the course so don’t worry if you don’t
understand it yet.
For the present just make sure you understand the basics of binary and hexadecimal.
If you don’t understand how to covert values you can also cheat for the moment and use
the windows calculator.