Binary Numbers
Computers use the binary system of ones and zeros, because circuits have two states, on and off.
▶ Interact
Play with the controls to see the idea in action.
📘 Learn
Computers use the binary system of ones and zeros, because circuits have two states, on and off.
- Each place is a power of two
- 1011 in binary is 11 in decimal
- A bit is one binary digit
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Binary Numbers?
Within Computer Science, which covers algorithms, programming, data, networks, hardware and safe, responsible use of technology, this topic explains Binary Numbers. Computing topics explain how software, hardware and data work, with diagrams and models that show each step in order.
Check that you can explain Binary Numbers in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Binary Numbers helps you design, test and explain programs, websites and systems, from small projects to exam questions.
Binary Numbers in detail
Computers use binary, a base-2 number system with only two digits, 0 and 1, because their circuits have two states: off and on. Each binary digit is called a bit, and eight bits make a byte. Place values double from the right: 1, 2, 4, 8, 16, 32, 64, 128.
So 1011 in binary means 8 + 0 + 2 + 1 = 11 in decimal. All data, whether numbers, text, images or sound, is stored in binary form. With n bits, you can represent 2ⁿ different values, so 8 bits give 256 values (0–255). Binary is the foundation of how computers work.
How the interactive helps you understand Binary Numbers
Watch the binary display in the interactive. Use any sliders or buttons it offers to change the values and see how the binary display responds.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Binary Numbers.
Real-life uses and examples
- Trace through a process that uses Binary Numbers to check what it does step by step.
- Recognise Binary Numbers in an app or device you use every day.
- Apply Binary Numbers when you design a small program, website or spreadsheet.
Common mistakes to avoid
- Testing only the normal case and forgetting the edge cases.
- Using the term without being able to say what the computer actually does.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Binary Numbers
What is Binary Numbers?
Computers use the binary system of ones and zeros, because circuits have two states, on and off.
What are the most important points about Binary Numbers?
The main points are: Each place is a power of two; 1011 in binary is 11 in decimal; A bit is one binary digit.
Why is Binary Numbers useful?
Understanding Binary Numbers helps you design, test and explain programs, websites and systems, from small projects to exam questions.
How can I practise Binary Numbers?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Binary Numbers?
Related topics in Computer Science include Binary Arithmetic, Compression, Algorithms.