We're used to counting with ten digits, from 0 to 9. This is the decimal system, and it's been the foundation of human mathematics for centuries. But computers think differently. They operate in a world with only two digits: 0 and 1. This is the binary system.

Imagine a light switch. It can be in one of two states: on or off. There's no in-between. Computers are built on millions of tiny electronic switches called transistors. Each one can be either on (representing 1) or off (representing 0). This simple on-off logic is why binary is the native language of every digital device you've ever used.

Each of these 0s and 1s is called a bit, short for "binary digit." By stringing bits together, computers can represent incredibly complex information, from numbers and letters to images and sounds. A single bit isn't very useful, but a group of them can be.

So how can just two digits represent a number like 2, or 10, or 437? The secret is place value. It's a concept you already know from the decimal system, also called base-10.

In a number like 437, the '7' is in the ones place ($10^0$), the '3' is in the tens place ($10^1$), and the '4' is in the hundreds place ($10^2$). Each position is ten times more valuable than the one to its right. So, 437 is really $(4 \times 100) + (3 \times 10) + (7 \times 1)$.

Binary, or base-2, works the same way, but each place value is a power of two instead of a power of ten. Instead of a ones, tens, and hundreds place, binary has a ones place ($2^0$), a twos place ($2^1$), a fours place ($2^2$), an eights place ($2^3$), and so on.

Let's look at the binary number 1011. To find its decimal value, we just add up the place values that have a '1'.

• There's a 1 in the eights place ($2^3$).
• There's a 0 in the fours place ($2^2$).
• There's a 1 in the twos place ($2^1$).
• There's a 1 in the ones place ($2^0$).

So, the calculation is $8 + 0 + 2 + 1 = 11$. The binary number 1011 is equal to the decimal number 11.

This system might seem clunky for humans, but it's perfect for computers. The logic is simple and direct, which allows for incredibly fast and reliable calculations. Every single operation a computer performs, from loading a webpage to running a game, is broken down into millions of these simple binary steps.