Number Base Converter
Convert numbers between binary, octal, decimal, and hexadecimal bases. Supports real-time conversion with validation and formatted output.
Number Input
Decimal (Base 10)
Decimal is the standard base-10 system using digits 0-9.
Example: 123₁₀ = 1×10² + 2×10¹ + 3×10⁰ = 100 + 20 + 3 = 123₁₀
Conversion Results
Binary (Base 2)2
—
Uses digits: 0, 1
Octal (Base 8)8
—
Uses digits: 0-7
Decimal (Base 10)10
—
Uses digits: 0-9
Hexadecimal (Base 16)16
—
Uses digits: 0-9, A-F
Number Base Reference
| Decimal | Binary | Octal | Hexadecimal |
|---|---|---|---|
| 0 | 0000 | 0 | 0 |
| 1 | 0001 | 1 | 1 |
| 2 | 0010 | 2 | 2 |
| 3 | 0011 | 3 | 3 |
| 4 | 0100 | 4 | 4 |
| 5 | 0101 | 5 | 5 |
| 6 | 0110 | 6 | 6 |
| 7 | 0111 | 7 | 7 |
| 8 | 1000 | 10 | 8 |
| 9 | 1001 | 11 | 9 |
| 10 | 1010 | 12 | A |
| 11 | 1011 | 13 | B |
| 12 | 1100 | 14 | C |
| 13 | 1101 | 15 | D |
| 14 | 1110 | 16 | E |
| 15 | 1111 | 17 | F |
About Number Base Converter
The Number Base Converter transforms numbers between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) number systems. Essential for programming, computer science, and digital electronics.
Supported Number Bases:
- Binary (Base 2): Uses digits 0 and 1, fundamental in computing
- Octal (Base 8): Uses digits 0-7, common in Unix permissions
- Decimal (Base 10): Standard human counting system using 0-9
- Hexadecimal (Base 16): Uses 0-9 and A-F, common in programming
Key Features:
- Real-time Conversion: Instant conversion as you type
- Input Validation: Ensures valid characters for each base
- Formatted Output: Grouped digits for better readability
- Quick Switching: Convert results to different input bases
- Copy Functions: Copy individual results or all conversions
- Reference Tables: Built-in conversion tables and examples
Use Cases:
- Programming: Convert between number systems in code
- Computer Science: Understand binary and hexadecimal representations
- Digital Electronics: Work with binary and hex values
- System Administration: Convert Unix file permissions (octal)
- Web Development: Convert color codes and memory addresses
- Debugging: Analyze binary data and memory dumps
- Education: Learn number system concepts and conversions
Number System Applications:
- Binary: CPU instructions, digital circuits, boolean logic
- Octal: Unix file permissions, some assembly languages
- Decimal: Human-readable numbers, user interfaces
- Hexadecimal: Memory addresses, color codes, checksums
Conversion Methods:
- To Decimal: Multiply each digit by base raised to position power
- From Decimal: Repeatedly divide by target base, collect remainders
- Between Non-Decimal: Convert through decimal as intermediate
- Binary to Hex: Group binary digits in sets of 4
- Binary to Octal: Group binary digits in sets of 3
Programming Examples:
- Colors: #FF0000 (hex) = 255,0,0 (RGB decimal)
- Permissions: 755 (octal) = 111101101 (binary)
- Memory: 0x1000 (hex) = 4096 (decimal)
- Flags: 0b1010 (binary) = 10 (decimal)
Tips:
- Use binary for understanding bit operations and flags
- Use hexadecimal for memory addresses and color codes
- Use octal for Unix file permissions and some legacy systems
- Group digits for better readability (4 for hex/binary, 3 for octal)
- Validate input characters match the selected base
- Practice with powers of 2 for quick mental conversions
Common Ranges:
- 8-bit: 0-255 (decimal), 0-FF (hex), 0-377 (octal)
- 16-bit: 0-65535 (decimal), 0-FFFF (hex)
- 32-bit: 0-4294967295 (decimal), 0-FFFFFFFF (hex)