How to Calculate Binary to Decimal: A Step-by-Step Guide
Converts binary to decimal.
These calculations come up in school, at work and in daily life, from PSLE and O-Level practice to measuring a room for new flooring. Doing them by hand builds understanding, and a calculator lets you check the answer instantly.
What you need
- Binary number
Step by step
- Enter the binary number.
- The results update as you type, or press Calculate.
- Read the decimal first, then the supporting figures below it.
The formula
Sum each bit × 2^position.
Worked example
For example, with these inputs:
- Binary number: 10011100
the calculator returns:
- Decimal: 156
Practical tips
- For exam work, show your method; marks are often given for working, not just the answer.
- Write down the formula before plugging numbers in; it prevents mixing up variables.
- Estimate the answer roughly first so you can spot a result that is clearly wrong.
- Check your answer by working backwards from the result.
Background
These calculations appear throughout the Singapore syllabus, from primary school percentages and fractions to secondary school algebra and geometry. Understanding the formula makes problem sums easier because you can recognise which quantity is missing.
Rounding is a common source of small errors. Keep full precision during intermediate steps and round only the final answer to the number of decimal places or significant figures the question asks for.
A quick mental estimate before calculating is a powerful check. If a room's floor area comes out at 4,000 square metres or a percentage comes out above 100% when it should not, you know to look again.
Related calculations
- Standard Deviation Calculator: Measures how spread out a list of numbers is.
- Weighted Average Calculator: Calculates averages where items count differently, like weighted exam components.
- GCD (HCF) Calculator: Finds the highest common factor.
- LCM Calculator: Finds the lowest common multiple.
Want to skip the arithmetic? The free Binary to Decimal Converter does all of this instantly and updates as you type.
Run your own numbers: Binary to Decimal Converter