IPv4

Internet Protocol version 4

What you will know after reading this post:

• What is the purpose of IPs
• How many parts make up a valid IPv4 address
• What the valid range of an IPv4 address is
• What an octet is
• How to do binary math for IPv4 addresses
• How IP addresses increment

IPv4 stands for Internet Protocol version 4. It helps information travel from one device to another. The most commonly used analogy is a mailing address. Just like you have a home mailing address, your devices use IP addresses as their mailing address. An IPv4 address always has four parts. Each part is separated by a dot or period.

Note: The version does not correspond with how many parts.

Valid

127.0.0.1

Not Valid

127.1

127.0.1

127.0.0.0.1

Each part of an IP address has the same range of numbers, from 0 to 255. This means there are a total of 256 possible numbers that each part of an IP can have.

Valid

127

1

0

255

Not Valid

-1

333

256

277

Each part of an IPv4 address is also known as an octet, so there are four octets in an address.

octet . octet . octet . octet

What does octet mean? We can look at the prefix of the word, which is “oct.” This makes me think of things like an octagon or (my favorite) an octopus. All three of these things refer to something with eight - eight sides, eight angles, and eight legs. In the case of IPv4, eight bits.

Valid Octet

00000000

11111111

01010101

10101010

11001010

Not Valid

01010101010101

55555

111

0

01010102

One bit is the smallest form of data. It is a binary value. Like octet has oct as a prefix, binary has bi as a prefix, meaning two. This is why a bit is usually either a 1 or a 0, but can also be viewed as on/off, true/false, yes/no, etc. There is a component of a computer that translates these 1s and 0s into higher and lower levels of electricity or signals used to communicate with other devices.

Ben Eater has a great video on this in action, showing how voltages represent bits that are eventually turned into human-readable information (and all of the details in between).

The image below summarizes what we’ve covered so far.

Alright, so we mentioned above that each part, or octet, has a valid decimal number range of 0-255 and 8 bits. Let’s dive a little deeper into what this means for an IPv4 address. It means there are 8(bits) x 4(parts) = 32 bits total in every IPv4 address.

octet 1 . octet 2 . octet 3 . octet 4

11111111 . 00000000 . 10101010 . 11010110

_ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ = 32 bits total

But how do we get from an IPv4 address like 127.0.0.1 to all 32 bits and vice versa? That’s where binary math comes in, and it’s easier than it sounds! As we do binary math, you might find it helpful to picture a panel of 8 light switches. Each switch connects to a light bulb. Each light bulb will have a different number drawn on it, representing the decimal number value given to that bit.

If the light switch is on, that means the bit is set to 1, and we should use the number that light bulb is set to. If the light switch is off, that means the bit is set to 0, and we should skip the number on that light bulb.

Let’s start with the number 0. The number 0 has an octet of all 0s. This means every switch is turned off, and there are no numbers to add together.

0 -> 00000000 -> off off off off off off off off

Let’s fill out the rest of the values for each bit. Do you see a pattern with the values?

Now we know which bit position in an octet has what value. When only one bit is set to on, that octet is equal to that number.

NOTE: To easily remember all the numbers you need in order, just start from 1 on the right side and double the number each time until you have all eight.

Lastly, what about all the numbers between those bit values, like 3, 5, 7, 127, and all the others? Isn’t the range of numbers supposed to be 0-255? That’s what is so interesting about binary math for IPv4. You only need to figure out which numbers combined get the value you need. If you need a 3, you “add” or turn on the bits for 1 and 2. This means that the last two bits will be set to 1 or on -> 00000011 = 3. We know 4 is 00000100, so what about 5? Well, 4 + 1 is 5, so 00000101 = 5.

127 -> _ + 64 + 32 + 16 + 8 + 4 + 2 + 1 -> off on on on on on on on -> 01111111

Let’s look at some more examples.

Decimal to binary

33 -> _ + _ + 32 + _ + _ + _ + _ + 1 -> off off on off off off off on -> 00100001

76 -> _ + 64 + _ + _ + 8 + 4 + _ + _ -> off on off off on on off off -> 01001100

231 -> 128 + 64 + 32 + _ + _ + 4 + 2 + 1 -> on on on off off on on on -> 11100111

196 -> 128 + 64 + _ + _ + _ + _ + 2 + _ -> on on off off off off on off -> 11000010

255 -> 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 -> on on on on on on on on -> 11111111

Binary to decimal

00010111 -> off off off on off on on on -> _ + _ + _ + 16 + _ + 4 + 2 + 1 -> 23

00110000 -> off off on on off off off off -> _ + _ + 32 + 16 + _ + _ + _ + _ -> 48

11001000 -> on on off off on off off off -> 128 + 64 + _ + _ + 8 + _ + _ + _ -> 200

01110111 -> off on on on off on on on -> _ + 64 + 32 + 16 + _ + 4 + 2 + 1 -> 119

01000011 -> off on off off off off on on -> _ + 64 + _ + _ + _ + _ + 2 + 1 -> 67

To close, I have a challenge for you. Can you find your phone’s or computer’s IP address? What is it in binary? Also, don’t forget to quiz yourself below and practice with the binary math worksheet linked below!