Converting IPv4 to Binary

In IPv4 you have have four octets, each octet is separated by a dot (.). This format is referred as "dotted-decimal" format. The following is an example of a valid IPv4 address in dotted-decimal.

Remember that IPv4 address can technically go from 0.0.0.0 to 255.255.255.255, this will come in handy later.

We can break an IPv4 address into our four octets:

Before we can convert an octet into binary we need to understand Binary. Binary is a "base-2 numeral system", or two to the power of x (2^x). Recall that Binary has two states, 1 is considered on, and 0 is considered off.

For each octet starting on the right you raise 2 to the x (2^x). The first bit (on the far right) would be 2 to the power of 0 (2^0), then 2 to the power of 1 (2^1), then 2 to the power of 2 (2^2) and so on until you have 2 to the power of 7 (2^7).

Lets create a Binary Cheat Sheet:

Which if we calculate those values out we get:

Now let’s take an example were ever one of the bits (8 total) are active (or have a 1 value), the following is binary for "255":

The above binary of 11111111 is 255 because you take the value of each bit with a 1 or an “on” value and add the values together, since 255 contains nothing but `1’s we have:

If you are still confused then lets break it down with another number. Lets try our first octet in the example IPv4 address 198.120.50.6, which would be 198.

First lets create a blank binary placeholder, each "X" represents a bit in the octet:

Second lets take the octet (198) and subtract the largest amount from 2^x power starting from the left side. In this case we can subtract 128 from 198 without getting a negative number.

We can now fill in our blank bits with a 1 because it is active.

Now take your remainder (70) and subtract it by the next largest base-2 power without receiving a negative number. We can do 64:

Since 64 was subtracted we fill in its bit.

Now we have 6, we can not subtract 32, 16 or 8 from 6 so we fill in those bits with a zero.

The next number we can subtract by is 4.

We can fill in that bit with a one:

Finally we have 2 which can be subtracted by 2 for a value of 0.

We can fill in that bit with a one and fill in all remanding bits with zeros because we have no more number to subtract by.

That’s it! Our binary number for 198 is 11000110. If we follow the same procedure as above can find the other 3 octets, they are:

This gives us an IPv4 address of 11000110.01111000.00110010.00000110 in binary, imagine remembering those numbers instead of 198.120.50.6!

Converting Binary back to a valid IPv4 address is as easy as reversing the steps above. Remember each octet is 8 bits, and we once again use our base-2 system.

Single out the ones:

Add up all the bits with a 1 as the value.

Octet 1

Octet 2

Octet 3

Octet 4

And we get 198.120.50.6, easy!

If you wan to learn about IPv6 and subnetting checkout these articles: