The Foundation
Every conversation begins with two symbols. Before computers exchange files, authenticate users, request web pages, or transmit packets across the internet, they must first agree on a language.
That language is binary. Every image, every email, every password, every network packet, and every line of code eventually becomes a sequence of zeros and ones.
Before we can understand the conversations taking place across a network, we first need to understand the foundation those conversations are built on.
Computers don't understand letters.
They don't understand numbers.
They understand electrical states.
Off.
On.
Those two states become two symbols:
0
1
Everything else is built from there.
This chart represents a full byte (8 bits).
Each column represents a binary place value (a power of 2). Read from right to left: 1's place, 2's place, 4's place, 8's place, 16's place, 32's place, 64's place, and 128's place.
To get the decimal value: Add up the place values wherever you see a 1.
The "128" Place Matters: A byte has 8 bits. The place values for 7 bits stop at 64 (which only gives us values 0-127). To fully represent a byte, we need the 128 place (2⁷), which gives us 256 possible values (0-255).
The Binary Chart is Infinite: Just like decimal numbers go on forever (ones, tens, hundreds, thousands, millions...), binary place values extend infinitely to the left (1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024...). We stop at 128 here because that's where one byte ends. For larger numbers, we just add more bytes!
That's 128 + 64 + 8 = 200.
If we didn't have the 128 place, we could never represent numbers above 127!
| Decimal | 128 (2⁷) |
64 (2⁶) |
32 (2⁵) |
16 (2⁴) |
8 (2³) |
4 (2²) |
2 (2¹) |
1 (2⁰) |
Binary |
|---|