Decimal to Binary converter
Convert decimal (base 10) to binary (base 2). Runs locally in your browser. Free online tool — no sign-up. Clear formulas and worked examples. Try it free.
Enter values to convert.
Formulas
Core equations used by this converter.
How to use
Open the converter
Use the interactive panel at the top of the page.
Enter values
Fill in the required fields for this conversion.
Convert and read the result
Use Convert or let the result update automatically.
Example conversions
Common values with formula and result.
13₁₀` → binary (division)
13₁₀` → binary (division)
13₁₀` → binary (powers)
13₁₀` → binary (powers)
255₁₀` → binary
255₁₀` → binary
13₁₀
13₁₀
Decimal to Binary converter specification
Version 1.1.0 · Engine tested
- Engine tested 4 published cases
- Named expert review Not performed
- Calculation version 1.1.0
- Definition
- **Decimal** — base 10, digits 0–9. **Binary** — base 2, digits 0–1; the native representation for digital hardware.
- What it calculates
- Convert decimal (base 10) to binary (base 2). Use repeated division by 2 and remainders, or subtract powers of 2. Examples and conversion table.
- Inputs
- Values required by the selected conversion mode
- Outputs
- Converted result in the target unit or format
- Formula
13 ÷ 2 = 6 rem 1- Decimal to binary conversion table
Decimal Binary 0 0 1 1 2 10 3 11 4 100 5 101 6 110 7 111 8 1000 9 1001 10 1010 15 1111 - Assumptions
- Conversion runs locally in the browser; values are not uploaded.
- Uses the formulas documented on this page.
- Units
- Formula
- Boundary conditions
- Empty or invalid input yields no valid result.
- Out-of-range values may be rejected by the tool runtime.
- Example
- 13₁₀` → binary (division) → 1101₂
- Validation cases
- 13₁₀` → binary (division) → 1101₂
- 13₁₀` → binary (powers) → 1101₂
- 255₁₀` → binary → 11111111₂
- 13₁₀ → 1101₂
- Sources
- CalculatorX converter runtime
- Standard unit / encoding definitions where applicable
- Calculation version
- 1.1.0
Background
Interpretation and common distinctions.
Use the converter tabs to switch direction when available. Results for Decimal to Binary converter update locally in your browser.
Related tools
Frequently asked questions
Key distinctions behind the conversion.
How do you convert using Decimal to Binary converter?
Use 13 ÷ 2 = 6 rem 1. Example: 13₁₀` → binary (division) → 1101₂.
Can I switch direction?
Open the related reverse converter listed under Related tools.
Does this run online or locally?
Calculation runs locally in your browser. Values are not uploaded.
How precise are the results?
Results follow the formulas on this page. Round to the precision your use case needs.