Binary to Decimal Converter
Free online tool to convert between binary and decimal numbers instantly. Perfect for students, programmers, and anyone learning about number systems.
Binary to Decimal
Decimal Result:
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Decimal to Binary
Binary Result:
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How Binary to Decimal Conversion Works
Converting binary to decimal is all about understanding position values. Each digit in a binary number represents a power of 2, starting from the right:
- Rightmost position: 2⁰ = 1
- Second position: 2¹ = 2
- Third position: 2² = 4
- Fourth position: 2³ = 8
- And so on, doubling each time...
Example: Converting 1011 to Decimal
1 0 1 1
Reading from right to left:
- 1 × 2⁰ = 1 × 1 = 1
- 1 × 2¹ = 1 × 2 = 2
- 0 × 2² = 0 × 4 = 0
- 1 × 2³ = 1 × 8 = 8
Sum: 8 + 0 + 2 + 1 = 11
Result: 1011₂ = 11₁₀
How Decimal to Binary Conversion Works
To convert decimal to binary, we use the "division by 2" method:
- Divide the number by 2
- Write down the remainder (0 or 1)
- Divide the quotient by 2 again
- Repeat until the quotient is 0
- Read the remainders from bottom to top
Example: Converting 13 to Binary
| 13 ÷ 2 = 6 | remainder 1 |
| 6 ÷ 2 = 3 | remainder 0 |
| 3 ÷ 2 = 1 | remainder 1 |
| 1 ÷ 2 = 0 | remainder 1 |
Reading remainders from bottom to top:
Result: 13₁₀ = 1101₂
Common Binary-Decimal Conversions
Here are some frequently used conversions to memorize:
| Decimal | Binary |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 10 | 1010 |
| 15 | 1111 |
| 16 | 10000 |
| 32 | 100000 |
| 64 | 1000000 |
| 100 | 1100100 |
| 128 | 10000000 |
| 255 | 11111111 |
Why Binary Conversion Matters
For Programmers
- Understanding bitwise operations
- Working with binary flags and permissions
- Network programming (IP addresses, subnet masks)
- Debugging at the bit level
For Students
- Computer science fundamentals
- Digital logic and circuits
- Computer architecture courses
- Understanding how computers store data
In Real Life
- RGB color codes (0-255 for each channel)
- File sizes (kilobytes, megabytes based on powers of 2)
- Understanding computer memory (RAM sizes: 4GB, 8GB, 16GB...)
- Appreciating the digital world around you
Learn More About Binary
Want to deepen your understanding of binary? Check out these resources:
- What is a Binary Clock? - Learn about the most fun way to practice binary
- How to Count in Binary - Master binary counting from 0 to 100
- Binary Number System Explained - Deep dive into number bases
- Shop Binesse Binary Clocks - Practice binary every time you check the time!