Base/Number System Converter
Instantly convert between binary, decimal, hexadecimal, and octal number systems. Essential tool for programmers, students, and math enthusiasts.
Number System Converter
Enter a value in any number system and instantly convert it to all other systems. Supports binary (base-2), decimal (base-10), hexadecimal (base-16), and octal (base-8).
Convert Between Number Systems
Number Systems Overview
Different number systems are used in computing and mathematics for various purposes. Here's a quick overview of each:
Uses only 0 and 1
The fundamental language of computers. Each digit is called a "bit".
- Base: 2
- Digits: 0, 1
- Example: 1011₂
- Used in: Digital circuits, computer memory
Our everyday number system
The standard system for denoting integer and non-integer numbers.
- Base: 10
- Digits: 0-9
- Example: 255₁₀
- Used in: Everyday counting, finance
Compact representation of binary
Used as a human-friendly representation of binary values.
- Base: 16
- Digits: 0-9, A-F
- Example: FF₁₆
- Used in: Programming, memory addresses
Three binary digits per octal digit
Less common today but still used in some computing applications.
- Base: 8
- Digits: 0-7
- Example: 377₈
- Used in: Unix file permissions
How to Use the Base Converter
Follow these simple steps to convert between number systems:
Input the number you want to convert in the "Input Value" field. Make sure it's valid for the selected base:
- Binary: Only 0 and 1 digits
- Decimal: Digits 0-9
- Hexadecimal: Digits 0-9 and A-F (case insensitive)
- Octal: Digits 0-7
Choose the base system of your input number from the dropdown menu:
- Binary - Base-2 system
- Decimal - Base-10 system
- Hexadecimal - Base-16 system
- Octal - Base-8 system
Select which number systems you want to convert to by checking the boxes:
- Uncheck systems you don't need
- Check all for complete conversion
- Results appear instantly after conversion
- You can copy results with one click
Examine your conversion results:
- Each result shows the value in the target base
- Click the copy button to copy any result
- Use "Clear All" to reset the converter
- Try different numbers to practice conversions
Common Conversion Examples
Here are some common conversions between number systems for reference:
| Decimal | Binary | Hexadecimal | Octal | Notes |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | Zero in all systems |
| 1 | 1 | 1 | 1 | One in all systems |
| 10 | 1010 | A | 12 | Decimal ten |
| 15 | 1111 | F | 17 | Max single hex digit |
| 16 | 10000 | 10 | 20 | Base of hexadecimal |
| 255 | 11111111 | FF | 377 | Max 8-bit value |
| 1024 | 10000000000 | 400 | 2000 | 1 Kilobyte in bytes |
| 4096 | 1000000000000 | 1000 | 10000 | 4KB memory page |
Real-World Applications
Computer Programming
- Hexadecimal: Used for memory addresses, color codes (RGB), and debugging
- Binary: Direct manipulation of bits and bytes
- Octal: File permission codes in Unix/Linux systems
- Bitwise operations: AND, OR, XOR, and shift operations
Digital Electronics & Networking
- IP addresses: Sometimes represented in hex (IPv6)
- MAC addresses: Hexadecimal format (e.g., 00:1A:2B:3C:4D:5E)
- Error detection: Checksums and CRCs often use hex representation
- Digital circuits: Binary is fundamental to all digital logic
Quick Reference Tables
Binary-Hex Table
Each hex digit = 4 binary digits
| Hex | Binary |
|---|---|
| 0 | 0000 |
| 1 | 0001 |
| 2 | 0010 |
| 3 | 0011 |
| 4 | 0100 |
| 5 | 0101 |
Powers of Two
Essential for binary calculations
| Power | Decimal | Binary |
|---|---|---|
| 2⁰ | 1 | 1 |
| 2¹ | 2 | 10 |
| 2² | 4 | 100 |
| 2³ | 8 | 1000 |
| 2⁴ | 16 | 10000 |
| 2⁵ | 32 | 100000 |
Hex Digits
Hexadecimal digit values
| Hex | Decimal |
|---|---|
| 0-9 | 0-9 |
| A/a | 10 |
| B/b | 11 |
| C/c | 12 |
| D/d | 13 |
| E/e | 14 |
| F/f | 15 |