Binary To Decimal Calculator - Mathematical Calculations & Solutions
How It Works
Enter Binary
Input binary number (0s and 1s)
Convert
Apply binary to decimal conversion
Common Examples
Binary To Decimal Calculator
What
Convert binary numbers (base 2) to decimal numbers (base 10) instantly.
Why
Essential for computer science, programming, digital electronics, and mathematics education.
Applications
Programming, computer science education, digital systems, and data representation.
Calculation Examples
| Input | Formula | Result | Use Case |
|---|---|---|---|
| 101₂ | 1×2² + 0×2¹ + 1×2⁰ | 5₁₀ | Basic 3-bit conversion |
| 1010₂ | 1×2³ + 0×2² + 1×2¹ + 0×2⁰ | 10₁₀ | 4-bit binary number |
| 1111₂ | 1×2³ + 1×2² + 1×2¹ + 1×2⁰ | 15₁₀ | Maximum 4-bit value |
| 11111111₂ | Σ(1×2ⁱ) for i=0 to 7 | 255₁₀ | 8-bit byte maximum |
Frequently Asked Questions
How does binary to decimal conversion work?
Enter a binary number (containing only 0s and 1s) and the calculator converts it to decimal using positional notation where each digit represents a power of 2.
What is a valid binary number?
A binary number contains only digits 0 and 1. Examples: 101, 1010, 11111111. No spaces, letters, or other digits are allowed.
Is this conversion accurate?
Yes, the calculator uses the standard binary to decimal conversion algorithm (parseInt with base 2) ensuring 100% accurate results.
Can I use this for learning computer science?
Absolutely! This calculator is perfect for students learning number systems, computer science fundamentals, and digital electronics.
What is the conversion formula?
The formula is: Decimal = Σ(digit × 2^position). Each binary digit is multiplied by 2 raised to its position power, then all results are summed.
What's the maximum binary number I can convert?
JavaScript can handle very large binary numbers. Practically, you can convert binary numbers up to 53 bits (JavaScript's safe integer limit).
Why learn binary to decimal conversion?
Understanding binary is fundamental in computer science, programming, and digital electronics. It's how computers represent and process all data internally.