The simplest number system
You're used to decimal, the base-10 system with ten digits (0–9). Binary works exactly the same way, except it has only two digits: 0 and 1. That's it. Every binary number — no matter how large — is built from those two symbols.
A single binary digit is called a bit (short for "binary digit"). It's the smallest unit of data in computing: one bit can represent exactly two things — on or off, true or false, yes or no. Group bits together and they can represent anything: numbers, letters, colors, sound.
Place value works the same as decimal
In decimal, each position is worth ten times the one to its right: ones, tens, hundreds (1, 10, 100…). In binary, each position is worth two times the one to its right — the powers of two:
| Position (right → left) | Place value | Power of two |
|---|---|---|
| 1st | 1 | 2⁰ |
| 2nd | 2 | 2¹ |
| 3rd | 4 | 2² |
| 4th | 8 | 2³ |
| 5th | 16 | 2⁴ |
| 6th | 32 | 2⁵ |
| 7th | 64 | 2⁶ |
| 8th | 128 | 2⁷ |
To read a binary number, multiply each digit by its place value and add everything up. Take 1011:
| Digit | × Place value | = Result |
|---|---|---|
| 1 | × 8 | = 8 |
| 0 | × 4 | = 0 |
| 1 | × 2 | = 2 |
| 1 | × 1 | = 1 |
8 + 0 + 2 + 1 = 11. So 1011 in binary is 11 in decimal. The method never changes: digit × place value, then sum.
Counting in binary
Watch what happens as you count from 0 to 10 — notice how each column "rolls over" just like an odometer:
| Decimal | Binary |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
| 8 | 1000 |
| 9 | 1001 |
| 10 | 1010 |
The pattern: with n bits you can represent 2ⁿ different values. One bit gives 2 values (0–1), four bits give 16 (0–15), and eight bits give 256 (0–255).
Why only 0 and 1?
It's not a mathematical limitation — it's a hardware one. Inside a chip, a transistor is either switched on (current flows) or off (no current). Distinguishing two states is easy and reliable even with electrical noise, heat and manufacturing imperfections. A system with ten voltage levels would need extremely precise, expensive circuitry; a two-level system just needs "clearly on" vs "clearly off". Binary is the sweet spot where physics meets practicality.
Eight bits grouped together are called a byte — the standard chunk computers use to store a single character of text, among other things. You'll meet bytes properly in our bits vs bytes guide.
Try it yourself
Type any binary number and watch it convert instantly, with the full step-by-step working shown.
Key takeaways
- Binary is base 2: every number is built from just the digits 0 and 1.
- A single binary digit is called a bit — the smallest unit of data.
- Each position is worth double the previous one (1, 2, 4, 8, 16…).
- To convert, multiply each digit by its place value and add the results.
- Computers use binary because transistors naturally have two states: on and off.
- Eight bits make a byte; n bits can represent 2ⁿ values.
Frequently asked questions
Why do computers use binary instead of decimal?
Computer hardware works with two physical states — a transistor switched on or off, a high or low voltage. Binary maps perfectly onto those two states, which makes circuits simple, fast and reliable.
What is a bit?
A bit is a single binary digit — one 0 or one 1. It is the smallest unit of data in computing. Eight bits grouped together form a byte.
How do I read the binary number 10110?
Work from right to left, multiplying each digit by its place value: 0×1 + 1×2 + 1×4 + 0×8 + 1×16 = 0 + 2 + 4 + 0 + 16 = 22.
What is the largest number 8 bits can hold?
255. Eight 1s (11111111) equal 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. In general, n bits can represent 2^n different values, from 0 to 2^n − 1.