💡 Binary: 0-1 | Decimal: 0-9 | Octal: 0-7 | Hex: 0-9, A-F | Valid digits only | Supports up to 64-bit numbers
📖 How to Use This Binary Converter
1
Enter the number - Type or paste the number you want to convert.
2
Select the source base - Choose from Binary (base-2), Decimal (base-10), Octal (base-8), or Hexadecimal (base-16).
3
Select the target base - Choose the number system you want to convert to.
4
Get instant results - The converted value appears automatically.
💻 Understanding Number Systems
A number system (or base) defines how many unique digits are used to represent numbers. Each position in a number represents a power of the base.
- Binary (Base-2): Uses digits 0 and 1. The fundamental language of computers.
- Decimal (Base-10): Uses digits 0-9. The standard number system for everyday use.
- Octal (Base-8): Uses digits 0-7. Used as shorthand for binary (3 bits = 1 octal digit).
- Hexadecimal (Base-16): Uses digits 0-9 and A-F. Used in programming, memory addresses, and colors.
📊 Conversion Methods
Step 1: Convert to Decimal
Multiply each digit by (base^position) and sum.
Example: Binary 1011₂ = 1×8 + 0×4 + 1×2 + 1×1 = 11₁₀
Step 2: Convert from Decimal to Target Base
Repeatedly divide by target base, read remainders backwards.
💡 Common Conversions
- Binary to Decimal: 1010₂ = 10₁₀
- Decimal to Binary: 25₁₀ = 11001₂
- Hexadecimal to Decimal: FF₁₆ = 255₁₀
- Octal to Binary: 17₈ = 1111₂
- Hexadecimal to Binary: A3₁₆ = 1010 0011₂
❓ FAQ
Why do computers use binary?
Computers use binary because electronic circuits have two stable states: on (1) and off (0).
What is the difference between octal and hexadecimal?
Octal uses base-8 (digits 0-7). Hexadecimal uses base-16 (digits 0-9, A-F). Hex is more common in computing.
How do I convert decimal to binary quickly?
Use the 'divide by 2' method: repeatedly divide by 2, recording remainders. Read remainders from last to first.
What is the largest number this converter can handle?
This converter supports up to 64-bit numbers (18,446,744,073,709,551,615 in decimal).
What are valid hexadecimal digits?
Hexadecimal digits are 0-9 and A-F (case-insensitive). A=10, B=11, C=12, D=13, E=14, F=15.