IP addresses

The Internet Protocol (IP) describes how two computers can communicate with each other, and it's used by every computer on the Internet.

Each computer has an IP address, just like homes and companies have mail addresses.

When a computer sends a message to another computer, it specifies the recipient's address and also makes sure to include its own address, so that the second computer can reply.

In the IP v4 protocol, IP addresses look like this:

🔍Try visiting that IP in your browser. Where does it go?

Each IP address is split into 4 numbers, and each number can range from 0 to 255:

We write those numbers in decimal, but to the computer, they're represented with bits, like so:

Each number can represent $2^8$‍ values, thanks to the 8 bits. That's also why we often call them "octets."

Overall, that's $2^{32}$‍ possible values: $4,294,967,296$‍ possible IPv4 addresses.

That's a lot! But remember, in the beginning, we said there are more than 4 billion devices connected to the Internet? Well, we're reaching the limit of possible IP addresses. It's time for plan B.

Back when they invented the Internet, they didn't anticipate how popular it'd become and they thought that 4 billion would be plenty.

That's what led to the IPv6 protocol, a new addressing scheme. Here's an IPv6 address:

Notice the letters in those numbers, like d and b in 0db8? Those are hexadecimal numbers, which means that the IPv6 address is much longer than it looks. Let's do some math to see exactly how much longer.

There are 8 hexadecimal numbers, and each number is 4 digits long. The highest value for each number is $\text{FFFF}$‍, since $\text{F}$‍ is the highest digit in hexadecimal. Thus, the highest address would look like:

What's $\text{FFFF}$‍ in decimal?

Each $\text{F}$‍ represents 15 in decimal, so that's $(15\times 4096)+(15\times 256)+(15\times 16)+(15\times 1)$‍: a grand total of $65,535$‍.

We can also calculate that based on the bit representation of $\text{FFFF}$‍. Each hexadecimal digit $\text{F}$‍ corresponds to $1111$‍ in binary, so that results in these 16 bits:

As we discuss in Binary numbers, the highest number that can be represented by $n$‍ binary digits is $2^n-1$‍. That means the binary number above is $2^{16}-1$‍, which once again equals $65,535$‍.

Each 4-digit hexadecimal number can range between $0$‍ and $65,535$‍, so each number can represent $65,536$‍ unique values—and there are 8 of them!

In total, each IP v6 address is represented by 128 bits, so there are $2^{128}$‍ possible IP v6 addresses. That's 340 undecillion:

🤔 Imagine a world where we have that many Internet connected devices. What does that look like? How could that much Internet make the world better?

Many addressing schemes are hierarchical, like phone numbers:

We can break that into 4 parts:

The hierarchy makes it easier for the telephone system to efficiently send calls to the right lines.

IP addresses are also hierarchical. The first sequence of bits identifies the network, and the final bits identify the individual node in the network.

Consider this IP address:

We can break that into 2 parts:

Network administrators can break IP addresses into further subnets (subnetworks) as needed, for easier routing.

Starting with this IP address:

That could break down into 3 parts:

In actuality, addresses are typically split in the middle of the octets. The first 16 bits might route to all of UMich, the next 2 bits route to a specific UMich school, and the final 14 bits route to individual computers.

IP addresses use this hierarchical addressing scheme to make routing messages easier from place to place. Once a message gets to the network, then the network can take care of sending it to the individual node.

One way to find out your computer's IP address is by searching Google for "IP address". Google knows your IP address, since your computer sends a message to the Google computers as soon as it loads google.com.

Your IP address might be different tomorrow than it is today. Each ISP has a range of addresses they can assign, and they might give you a different one of those addresses each time they see your computer pop up on the network. That's called a "dynamic" IP address.

Switching to a different Wi-Fi network will definitely give you a new IP address, since each Wi-Fi provider has its own range of addresses that it can give out.

Computers that act as servers, like the computers that power Google.com, often have "static" IP addresses. That makes it easier for computers to quickly send search requests to the Google servers. If you tried out the IP address above, you hopefully found yourself on the Google homepage.