How Computers Store Data (Binary)

Everything is numbers

Open a photo, play a song, send a message — to you they feel completely different. But deep inside a computer, they are all the same thing: long strings of 0s and 1s. This system of just two symbols is called binary, and understanding it unlocks how computers really work.

In an earlier lesson you may have learned that a program is a set of instructions a computer follows. Now we'll look at how the computer stores the data those instructions work on.

Why only 0 and 1?

A computer is built from billions of tiny switches. A switch has exactly two states: off or on. There is no "half on." This is the key idea — it is easy and reliable for a machine to tell the difference between off and on, but very hard to tell apart, say, ten different brightness levels without making mistakes.

So engineers gave the two states two symbols:

• Off → 0
• On → 1

Because there are only two symbols, we call it binary ("bi" means two). Everything a computer stores must be built out of these two states. That sounds limiting, but as you'll see, you can represent anything with enough 0s and 1s.

Bits and bytes

Each single 0 or 1 is called a bit, short for binary digit. One bit on its own can only say two things, like yes/no or off/on. That isn't much. So computers group bits together.

Eight bits grouped together make a byte. With 8 bits, you can make 256 different patterns (from 00000000 to 11111111). That's enough to cover every letter, digit, and punctuation mark you might type. Bytes are the basic building block of computer storage, which is why we measure memory in kilobytes, megabytes, and gigabytes — thousands, millions, and billions of bytes.

Counting in binary

Our everyday number system uses ten digits (0–9). It's called base 10, probably because we have ten fingers. Each position in a number is worth ten times the one to its right: ones, tens, hundreds, thousands.

Binary works the same way, but each position is worth two times the one to its right. So instead of ones, tens, and hundreds, the positions are ones, twos, fours, eights, and so on — the powers of 2.

Let's read the binary number 101:

Position value	4	2	1
Binary digit	1	0	1

We add up the positions where there is a 1: that's the 4 and the 1. So 101 in binary equals 4 + 0 + 1 = 5.

Here's another, 1101:

Position value	8	4	2	1
Binary digit	1	1	0	1

Add the positions with a 1: 8 + 4 + 0 + 1 = 13.

To count up in binary, you do the same thing as in base 10 — when a column "fills up," you carry to the next. Watch the first few numbers:

0  = 0
1  = 1
2  = 10
3  = 11
4  = 100
5  = 101
6  = 110
7  = 111
8  = 1000

Notice how each time we run out of room, a new column appears on the left, just like going from 9 to 10 in normal counting.

Storing letters

Computers store numbers naturally, but how do they store the letter A? The trick is simple: give every letter a number, then store that number in binary.

There's an agreed-upon code for this called ASCII. In ASCII:

• Capital A is 65, which in binary is 01000001.
• Capital B is 66 → 01000010.
• A space is 32 → 00100000.

So the word "HI" is stored as two bytes: H (72) and I (73), or 01001000 01001001. As long as every computer agrees on the same code, they can swap text perfectly. Modern computers use a bigger code called Unicode so they can store every alphabet on Earth, plus emoji 😀 — but the idea is the same: a letter is just a number, and a number is just binary.

Storing pictures and sounds

The same trick stretches to pictures and sounds:

• 🖼️ Pictures are grids of tiny dots called pixels. Each pixel's colour is stored as numbers — usually how much red, green, and blue it has, each from 0 to 255. Three numbers per pixel, all in binary, and you have a photo.
• 🔊 Sounds are stored by measuring the height of a sound wave thousands of times per second and saving each measurement as a number.

Whether it's a selfie, a song, or a sentence, the recipe is always: turn it into numbers, then store the numbers in binary.

The same bits, different meanings

Here's a brain-twister. The byte 01000001 is the number 65, the letter A, and part of a colour, all at once. How does the computer know which one you mean?

It depends on the context the program sets. A word processor reading that byte expects a letter, so it shows "A." A calculator expects a number, so it shows 65. The bits don't change — the program decides how to read them. This is why the same data can be reused in clever ways, and it's also why opening a photo file in a text editor shows nonsense: the program is reading picture bits as if they were letters. Spotting mix-ups like this is a real part of debugging.

Try it yourself

Practise thinking like a computer:

• 🔢 Convert these binary numbers to normal numbers: 10, 110, 1001, 1111. (Answers: 2, 6, 9, 15.)
• ✍️ Write your age in binary. Find the biggest power of 2 that fits, subtract it, and repeat. For example, 12 = 8 + 4, so 1100.
• 💡 Try a "binary fingers" trick: each finger is a bit (1, 2, 4, 8, 16...). Raising fingers in the right pattern lets you count past 1,000 on two hands!
• 🔤 Using ASCII (A = 65, B = 66, ...), work out the number for the first letter of your name, then convert it to binary.

Once you see that everything is just 0s and 1s underneath, the whole digital world starts to make sense — every app, game, and message is binary in disguise.