CCENT (ICND1)ManagementNetworking 101

How to count in Binary

The first and most important thing to understand when it comes to networking is binary. Without the fundamental understanding of binary and how it works, it would be very difficult to understand IP addresses, and without an understanding of IP addresses, it’s impossible to understand networking.

So what is binary?
Binary is a number system based on a Base 2 system. If you remember your school days when you were taught how to count, more than likely your teacher explained how the Base 10 number systems worked. The 10 base number system allows numbers 0 – 9 to be placed under the correct column to be able to represent any possible number. In the table below, we can see the base 10 up to the power of 3 (1000).

 10base

 

So if we wanted to represent the number ‘3062’ we would have to place each number under the correct column

 10baseexample

In the above diagram, we had to represent the number ‘3062’ or more precisely, 3 x 1000’s, 0 x 100’s, 6 x 10’s, 2 X 1’s (3000+0+60+2 = 3062)

Binary on the other hand, is not based on a base 10 number system, it’s based on a base 2. This means 2 things to us. Firstly, the ‘numbers’ we can place under each column can only be 0 or 1 (also known as “Off” and “On”). Secondly, our columns look much different.

 2base

So let’s say we wanted to represent the number ‘56’ in binary.

2baseexample

Since we can only place a ‘0’ or ‘1’ into our column, it really becomes a question of, do I need one of these values to make my number?

If I select yes ‘1’ under column 128, the number would obviously be larger than 56. This means, I don’t need a ‘128’ and also don’t need a ’64’ so I place a ‘0’ under each of those columns. I do however need a ’32’ so I place a ‘1’ under that column. I also need a ’16’ and a ‘8’ and I don’t need any of the other numbers. IMPORTANT NOTE : You MUST place zero’s under the last columns as they are place holders!.

What I now have is a yes ‘1’ under the columns 32, 16, 8 (1x 32, 1×16, 1×8,0x4,0x2,0x1 = 32+16+8+0+0+0 = 56)

The first zero’s in our column can be removed, so 56 can also be written in binary as 111000

One thought on “How to count in Binary

Leave a Reply

Your email address will not be published. Required fields are marked *