How to Calculate Decimal to Binary: A Step-by-Step Guide

Updated 5 Oct 2026 in Math & Geometry

Converts a base-10 number to binary, octal and hex.

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

• Decimal number

Step by step

1. Enter the decimal number.
2. The results update as you type, or press Calculate.
3. Read the binary first, then the supporting figures below it.

The formula

Repeatedly divide by the base and read the remainders upwards.

Worked example

For example, with these inputs:

• Decimal number: 156

the calculator returns:

• Binary: 10011100
• Octal: 234
• Hexadecimal: 9C

A second example

Now change the inputs to:

• Decimal number: 195

the calculator returns:

• Binary: 11000011
• Octal: 303
• Hexadecimal: C3

Practical tips

• For exam work, show your method; marks are often given for working, not just the answer.
• Estimate the answer roughly first so you can spot a result that is clearly wrong.
• Use brackets to make the order of operations explicit.
• Check your answer by working backwards from the result.

Background

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.

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.

In everyday life the same maths shows up in discounts, recipe scaling, renovation measurements and comparing prices per unit. Being comfortable with it saves money and avoids costly measuring mistakes.

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 Decimal to Binary Converter does all of this instantly and updates as you type.

Run your own numbers: Decimal to Binary Converter