Converting Binary and Decimal
Binary is converted to decimal by adding the place values where there is a one, and decimal is converted back by repeated division by two.
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Binary is converted to decimal by adding the place values where there is a one, and decimal is converted back by repeated division by two.
- Place values are 128, 64, 32, 16, 8, 4, 2, 1
- Divide by two and record the remainders
- Eight bits make a byte
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Converting Binary and Decimal?
Within Computer Science, which covers algorithms, programming, data, networks, hardware and safe, responsible use of technology, this topic explains Converting Binary and Decimal. Computing topics explain how software, hardware and data work, with diagrams and models that show each step in order.
Check that you can explain Converting Binary and Decimal in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Converting Binary and Decimal helps you design, test and explain programs, websites and systems, from small projects to exam questions.
Converting Binary and Decimal in detail
To convert binary to decimal, write the place values above each bit and add the values where there is a 1: 1101 = 8 + 4 + 0 + 1 = 13. To convert decimal to binary, use the subtraction method with place values (128, 64, 32 …) or repeated division by 2, reading the remainders from bottom to top.
For 13: 13 ÷ 2 = 6 r1, 6 ÷ 2 = 3 r0, 3 ÷ 2 = 1 r1, 1 ÷ 2 = 0 r1, giving 1101. Check by converting back. Leading zeros pad numbers to a set length, such as 8 bits (00001101). Fluency with conversion is a basic computing skill.
How the interactive helps you understand Converting Binary and Decimal
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 Converting Binary and Decimal.
Real-life uses and examples
- Explain Converting Binary and Decimal to someone new to computing by comparing it to a familiar process.
- Trace through a process that uses Converting Binary and Decimal to check what it does step by step.
- Recognise Converting Binary and Decimal in an app or device you use every day.
Common mistakes to avoid
- Using the term without being able to say what the computer actually does.
- Testing only the normal case and forgetting the edge cases.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Converting Binary and Decimal
What is Converting Binary and Decimal?
Binary is converted to decimal by adding the place values where there is a one, and decimal is converted back by repeated division by two.
What are the most important points about Converting Binary and Decimal?
The main points are: Place values are 128, 64, 32, 16, 8, 4, 2, 1; Divide by two and record the remainders; Eight bits make a byte.
Why is Converting Binary and Decimal useful?
Understanding Converting Binary and Decimal helps you design, test and explain programs, websites and systems, from small projects to exam questions.
How can I practise Converting Binary and Decimal?
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 Converting Binary and Decimal?
Related topics in Computer Science include Text, Images and Sound as Data, Logic Gates, Flowcharts.