Binary to Decimal Converter

Convert binary numbers to decimal instantly with step-by-step explanations. Perfect for students, programmers, and anyone learning computer science fundamentals.

✓ Instant Conversion ✓ Step-by-Step Guide ✓ Educational Examples ✓ Input Validation

🔢 Binary to Decimal Converter

Enter a binary number to see its decimal equivalent

Maximum 32 bits supported
Enter binary number above
Quick Input:

⚡ Quick Examples

1010
Binary
10
Decimal
11111111
Binary
255
Decimal
1100100
Binary
100
Decimal
10000000
Binary
128
Decimal

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📊 Powers of 2 Reference

Position Power Value
02⁰1
12¹2
22²4
32³8
42⁴16
52⁵32
62⁶64
72⁷128

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💡 Conversion Tips

💡
Each binary digit represents a power of 2
💡
Rightmost digit is 2⁰ (1), next is 2¹ (2), etc.
💡
Only use digits 0 and 1 in binary
💡
Add up all positions where digit is 1
✓
Example: 101 = 4 + 0 + 1 = 5

🔢 Common Binary Numbers

0 → 0
1 → 1
10 → 2
11 → 3
100 → 4
101 → 5
110 → 6
111 → 7
1000 → 8
1111 → 15

🎯 Features

⚡
Instant Conversion
Real-time binary to decimal
📚
Step-by-Step
Detailed calculation process
👁️
Visualization
Visual binary breakdown
✓
Input Validation
Ensures valid binary input

Understanding Binary to Decimal Conversion

🧮 How Binary Works

Binary is a base-2 number system that uses only two digits: 0 and 1. Each position in a binary number represents a power of 2, starting from 2⁰ (1) on the right and increasing as you move left.

To convert binary to decimal, multiply each binary digit by its corresponding power of 2, then add all the results together. Only positions with a '1' contribute to the final sum.

📖 Conversion Example

Binary: 1011
Position 3: 1 × 2³ = 1 × 8 = 8
Position 2: 0 × 2² = 0 × 4 = 0
Position 1: 1 × 2¹ = 1 × 2 = 2
Position 0: 1 × 2⁰ = 1 × 1 = 1
Total: 8 + 0 + 2 + 1 = 11

Frequently Asked Questions

What is binary and why is it important?

Binary is the fundamental number system used by computers. All digital data is stored and processed in binary format, making it essential for understanding computer science, programming, and digital electronics.

How do I convert binary to decimal manually?

Start from the rightmost digit (position 0). Multiply each binary digit by 2 raised to its position number. Add all the results where the binary digit is 1. For example: 101₂ = (1×2²) + (0×2¹) + (1×2⁰) = 4 + 0 + 1 = 5₁₀

What's the largest binary number I can convert?

This tool supports up to 32-bit binary numbers. The largest 32-bit binary number is 11111111111111111111111111111111, which equals 4,294,967,295 in decimal.

Can I enter invalid characters in the binary input?

No, the tool validates input and only accepts 0s and 1s. If you enter any other characters, you'll see an error message prompting you to use only binary digits.

Why do computers use binary instead of decimal?

Computers use binary because it's easier to represent electronically with two states: on (1) and off (0). This corresponds to electrical switches, transistors, and magnetic states, making binary the most efficient system for digital processing.

How is this tool useful for programming?

Understanding binary conversion is crucial for bitwise operations, memory management, data structures, and low-level programming. It helps in debugging, optimization, and understanding how data is stored and manipulated in computer systems.