Binary Arithmetic
Binary arithmetic follows the same rules as decimal, adding digits column by column and carrying when the total reaches two.
▶ Interact
Play with the controls to see the idea in action.
📘 Learn
Binary arithmetic follows the same rules as decimal, adding digits column by column and carrying when the total reaches two.
- 1 plus 1 equals 10 in binary
- Overflow occurs when a result is too large
- Shifting left doubles a number
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Binary Arithmetic?
Within Computer Science, which covers algorithms, programming, data, networks, hardware and safe, responsible use of technology, this topic explains Binary Arithmetic. 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 Arithmetic in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Binary Arithmetic helps you design, test and explain programs, websites and systems, from small projects to exam questions.
Binary Arithmetic in detail
Binary addition follows simple rules: 0 + 0 = 0, 0 + 1 = 1, 1 + 1 = 10 (0 carry 1) and 1 + 1 + 1 = 11 (1 carry 1). Add column by column from the right, carrying as in decimal addition. If the result needs more bits than are available, an overflow error occurs.
A binary shift moves bits left or right: a left shift multiplies by 2 and a right shift divides by 2, for each place shifted. Negative numbers can be shown using two's complement. Computers carry out all calculations using binary arithmetic in the ALU with logic gates.
How the interactive helps you understand Binary Arithmetic
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 Arithmetic.
Real-life uses and examples
- Trace through a process that uses Binary Arithmetic to check what it does step by step.
- Recognise Binary Arithmetic in an app or device you use every day.
- Apply Binary Arithmetic 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 Arithmetic
What is Binary Arithmetic?
Binary arithmetic follows the same rules as decimal, adding digits column by column and carrying when the total reaches two.
What are the most important points about Binary Arithmetic?
The main points are: 1 plus 1 equals 10 in binary; Overflow occurs when a result is too large; Shifting left doubles a number.
Why is Binary Arithmetic useful?
Understanding Binary Arithmetic helps you design, test and explain programs, websites and systems, from small projects to exam questions.
How can I practise Binary Arithmetic?
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 Arithmetic?
Related topics in Computer Science include Compression, Algorithms, Decomposition and Abstraction.