Binary to Decimal Formula Explained, With Examples
Every binary to decimal result comes from one formula. Once you understand what goes into it, you can sanity-check any figure you are given, whether by an employer, a bank, a teacher or another website.
The formula
Sum each bit × 2^position.
What each input means
- Binary number: the value you enter in the calculator.
Example
For example, with these inputs:
- Binary number: 10011100
the calculator returns:
- Decimal: 156
Why it matters
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.
Each formula has assumptions built in. Area formulas assume flat shapes, volume formulas assume regular solids and statistical measures assume the data you enter is the data you want to describe. Knowing the assumptions helps you pick the right tool.
Calculators are best used to check working rather than replace it, especially for exams where method marks count. Work the problem by hand first, then confirm with the calculator.
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.
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.
Use the Binary to Decimal Converter to plug in your own numbers.
Run your own numbers: Binary to Decimal Converter