Binary to Decimal converter
Binary to Decimal converter. Exact conversion factors, worked examples, and privacy-first browser calculation on CalculatorX. Runs locally in your browser.
Enter values to convert.
Formulas
Core equations used by this converter.
How to use
Write powers of 2 under each bit, starting at \(2^0 = 1\) on
Write powers of 2 under each bit, starting at \(2^0 = 1\) on the right.
Multiply each bit by its power.
Multiply each bit by its power.
Add the products.
Add the products.
Example conversions
Common values with formula and result.
Doubling method on `1011₂
Doubling method on `1011₂
Binary to Decimal converter specification
Version 1.1.0 · Engine tested
- Engine tested 1 published cases
- Named expert review Not performed
- Calculation version 1.1.0
- Definition
- **Binary (base 2)** — digits 0 and 1 only; each place is a power of 2. **Decimal (base 10)** — digits 0–9; each place is a power of 10.
- What it calculates
- Convert binary (base 2) to decimal (base 10). Use positional notation: sum each bit × power of 2. Worked examples and conversion table.
- Inputs
- Values required by the selected conversion mode
- Outputs
- Converted result in the target unit or format
- Formula
decimal = d₀·2⁰ + d₁·2¹ + d₂·2² + … + dₙ₋₁·2ⁿ⁻¹- Binary to decimal conversion table
Bit 1 1 1 0 0 1 Power 2⁵ 2⁴ 2³ 2² 2¹ 2⁰ Value 32 16 8 0 0 1 - 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
- Doubling method on `1011₂ → (×2+1)=11
- Validation cases
- Doubling method on `1011₂ → (×2+1)=11
- 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 Binary to Decimal converter update locally in your browser.
Related tools
Frequently asked questions
Key distinctions behind the conversion.
How do you convert using Binary to Decimal converter?
Use decimal = d₀·2⁰ + d₁·2¹ + d₂·2² + … + dₙ₋₁·2ⁿ⁻¹. Example: Doubling method on `1011₂ → (×2+1)=11.
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.