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 to Binary
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!