Binary to Decimal Converter
Convert binary numbers (base-2) to decimal (base-10) and vice-versa
Common Conversions
About Binary
Binary (base-2) is the fundamental language of computers. It uses only two digits, 0 and 1, to represent all data and instructions. Each position represents a power of 2.
- Used in digital electronics
- Foundation of boolean logic
- Represents ON/OFF states
How to Convert
To convert binary to decimal, multiply each digit by 2 raised to the power of its position (starting from right at 0) and sum the results.
(1 × 2²) + (0 × 2¹) + (1 × 2⁰) = 4 + 0 + 1 = 5
How to Convert Binary to Decimal Manually
Converting binary to decimal is all about understanding Powers of 2. Each digit in a binary number represents a power of 2, starting from the rightmost digit which is 20.
Step-by-Step Guide:
Let's convert the binary number 1011 to decimal.
| Binary Digit | 1 | 0 | 1 | 1 |
|---|---|---|---|---|
| Position | 3 | 2 | 1 | 0 |
| Power of 2 | 23 = 8 | 22 = 4 | 21 = 2 | 20 = 1 |
| Calculation | 1 × 8 | 0 × 4 | 1 × 2 | 1 × 1 |
| Result | 8 | 0 | 2 | 1 |
Total: 8 + 0 + 2 + 1 = 11
How to Use Binary To Decimal Converter
- Input Data: Enter or paste your binary (zeros and ones) or decimal number into the input field.
- Process: Click the "Convert" button. The tool will automatically validate your input.
- View Results: See the precise conversion instantly. You can copy the result or see the calculation steps.
- Swap Mode: Use the swap button to switch between Binary-to-Decimal and Decimal-to-Binary modes.
Common Use Cases
Professional Use
Essential for developers working with low-level programming, networking (IP addresses), and digital electronics design.
Education
Great for computer science students learning number systems. Use it to verify your manual calculations and understand the math.
Digital Systems
Understanding how data is stored in memory, color codes, and bitwise operations.
Everyday Tasks
Quickly translate binary jokes or decode binary messages found in CTFs and puzzles.