Bits, bytes, and how devices get addresses

Counting with switches instead of fingers

You have ten fingers, so counting to ten is easy. A computer chip doesn't have fingers — it has millions of tiny electrical switches that can only be on or off. Nothing in between. Networking, at its very bottom, is entirely about turning those on/off switches into numbers, and those numbers into addresses.

We call one switch a bit (binary digit): 0 for off, 1 for on. Group 8 bits together and you get a byte, which can represent $2^8 = 256$ different patterns — enough to represent, say, every letter of the alphabet plus punctuation, or a color's brightness level, or (as you'll see) one piece of an IP address.

Turning switches into numbers

In the number system you grew up with (decimal), each digit position is worth a power of 10: ones, tens, hundreds. Binary works identically, just with powers of 2:

$\underbrace{1}_{2^7=128} \; \underbrace{0}_{2^6=64} \; \underbrace{1}_{2^5=32} \; \underbrace{1}_{2^4=16} \; \underbrace{0}_{2^3=8} \; \underbrace{0}_{2^2=4} \; \underbrace{1}_{2^1=2} \; \underbrace{0}_{2^0=1}$

Read left to right, this byte is 10110010. To convert it to the decimal number you're used to, add up the powers of 2 wherever there's a 1:

$128 + 32 + 16 + 2 = 178$

So 10110010 in binary is 178 in decimal. This exact conversion — binary bytes turning into the familiar decimal numbers you'll see in an IP address like 192.168.1.178 — is something you'll use constantly once we reach subnetting later in this course.

How many addresses fit in $n$ bits?

Each additional bit doubles how many distinct patterns you can represent, because each new bit can independently be 0 or 1 for every existing pattern:

$\text{total addresses} = 2^n$

• 8 bits → $2^8 = 256$ addresses (0 through 255)
• 32 bits → $2^{32} = 4{,}294{,}967{,}296$ addresses — about 4.3 billion
• 48 bits → $2^{48} \approx 281$ trillion addresses

Keep those three numbers in mind — they are, respectively, roughly the size of one IPv4 "octet," the size of the entire IPv4 address space, and the size of the MAC address space you're about to meet.

Two addresses for one device: MAC vs IP

Every device that talks on a network actually carries two different addresses, and mixing them up is one of the most common beginner confusions in networking.

MAC address — think of it as your fingerprint. It's a 48-bit number burned into your network card at the factory (AA:BB:CC:DD:EE:FF, written in hexadecimal, base 16, where each pair of digits is one byte). It never changes no matter where you take the device, and it only matters to devices on the same local network — a MAC address means nothing to a computer on the other side of the world. IP address — think of it as your postal address. A 32-bit number (for IPv4), like 192.168.1.10, split into four bytes ("octets") separated by dots for readability. Unlike a fingerprint, your postal address changes when you move — and similarly, your IP address changes depending on which network you've connected to (your home Wi-Fi hands out a different IP than the coffee shop's Wi-Fi does).

Why do we need both? Because delivering a letter needs two different kinds of information: the postal service needs your address to route it toward your city and street (that's the IP address's job — routing across networks), but once the mail truck is on your exact street, the mail carrier needs to know which specific mailbox is yours (that's the MAC address's job — final delivery on the local network). You'll see exactly how a device discovers which MAC address belongs to which IP address (a process called ARP) in the Data Link Layer module.

Common mistakes

1. Thinking IP addresses are permanent. Most home and mobile IP addresses are handed out temporarily (via a protocol called DHCP) and can change every time you reconnect.
2. Confusing address length with address "importance." A 48-bit MAC isn't "better" than a 32-bit IP — they solve two entirely different jobs, at two different layers.
3. Miscounting available addresses. A common trap: $2^{32}$ is not "32 billion," it's about 4.3 billion — always compute the power, don't estimate it.

Summary

Everything a network sends is ultimately just bits — on/off switches — grouped into bytes and interpreted as numbers using powers of 2 instead of powers of 10. Every device needs two separate addresses: a permanent, factory-set MAC address for delivery within its local network, and a temporary, location-dependent IP address for routing across networks. The next module goes underneath both of these, into how those bits are actually turned into electrical signals or radio waves on a real wire or through the air.