Free Online Hex Converter Tool
Convert hexadecimal numbers to decimal, binary, and octal formats instantly. Our advanced hex converter supports all major number system conversions with step-by-step explanations.
How Hex Conversion Works
Step-by-Step Conversion Process
Number system conversion follows mathematical principles based on positional notation. Each digit position represents a power of the base number.
Hexadecimal to Decimal Conversion:
- Start from the rightmost digit (position 0)
- Multiply each digit by 16 raised to its position power
- Sum all the results to get the decimal value
Example: Hex 2F = (2 × 16¹) + (15 × 16⁰) = 32 + 15 = 47 decimal
Decimal to Hexadecimal Conversion:
- Divide the decimal number by 16
- Record the remainder (0-15, where 10-15 become A-F)
- Repeat with the quotient until it becomes 0
- Read the remainders in reverse order
Example: 47 ÷ 16 = 2 remainder 15(F), 2 ÷ 16 = 0 remainder 2, so 47 = 2F hex
About This Hex Converter
Our comprehensive hex converter tool provides instant, accurate conversions between hexadecimal, decimal, binary, and octal number systems. Whether you're a programmer, student, or digital electronics enthusiast, this tool simplifies complex number system conversions.
Key Features:
- Multi-format Support: Convert between hex, decimal, binary, and octal
- Real-time Validation: Instant feedback on input format
- Step-by-step Explanations: Learn how conversions work
- Mobile-friendly Interface: Works perfectly on all devices
- Copy & Share: Easy sharing of conversion results
- No Registration Required: Free to use without signup
How to Use the Hex Converter
- Enter Your Number: Type the number you want to convert in the input field
- Select Input Format: Choose whether your input is hexadecimal, decimal, binary, or octal
- Click Convert: Press the "Convert" button to see results in all formats
- View Results: See your number converted to all supported formats
- Share Results: Use the share buttons to send results to others
- Reset: Click "Reset" to clear all fields and start over
Input Examples:
- Hexadecimal: FF, 1A2B, CAFE, DEAD
- Decimal: 255, 6699, 51966, 57005
- Binary: 11111111, 1101000101011, 1100101011111110
- Octal: 377, 15053, 145376, 157055
Conversion Formulas
Base Conversion Formula:
From Base-n to Decimal:
Result = Σ(digit × base^position)
Where position starts from 0 (rightmost digit)
Specific Conversion Examples:
Hexadecimal (Base 16) to Decimal:
A2F₁₆ = (10×16²) + (2×16¹) + (15×16⁰) = 2560 + 32 + 15 = 2607₁₀
Binary (Base 2) to Decimal:
1011₂ = (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = 8 + 0 + 2 + 1 = 11₁₀
Octal (Base 8) to Decimal:
745₈ = (7×8²) + (4×8¹) + (5×8⁰) = 448 + 32 + 5 = 485₁₀
Use Cases & Applications
Programming & Software Development:
- Memory Addresses: Converting memory locations in debugging
- Color Codes: Converting hex color values (#FF0000) to RGB
- Binary Operations: Working with bitwise operations and flags
- ASCII Values: Converting character codes between formats
Digital Electronics:
- Circuit Design: Converting logic states and addresses
- Microcontroller Programming: Setting register values
- Digital Signal Processing: Converting sample values
- Hardware Interface: Communication protocol values
Computer Science Education:
- Learning Number Systems: Understanding different bases
- Algorithm Study: Analyzing computational complexity
- Data Representation: How computers store information
- Network Programming: IP addresses and subnet calculations
Conversion Examples
| Hexadecimal | Decimal | Binary | Octal |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| F | 15 | 1111 | 17 |
| 10 | 16 | 10000 | 20 |
| FF | 255 | 11111111 | 377 |
| 100 | 256 | 100000000 | 400 |
| CAFE | 51966 | 1100101011111110 | 145376 |
Frequently Asked Questions
What is hexadecimal?
Hexadecimal (hex) is a base-16 number system that uses 16 distinct symbols: 0-9 and A-F. It's commonly used in computing and digital electronics because it provides a more human-friendly representation of binary data, where each hex digit represents exactly 4 binary digits.
Why use hexadecimal in programming?
Hexadecimal is widely used in programming because it's more compact than binary (each hex digit represents 4 binary digits) and easier to read than long binary strings. It's commonly used for memory addresses, color codes in web design, and representing binary data in a more human-readable format.
How do you convert hex to decimal?
To convert hex to decimal, multiply each digit by 16 raised to its position power (starting from 0 on the right) and sum the results. For example, hex 2F = (2 × 16¹) + (15 × 16⁰) = 32 + 15 = 47 decimal.
What are the hex digits A-F equivalent to?
In hexadecimal, A=10, B=11, C=12, D=13, E=14, and F=15 in decimal. These letters are used because hex needs 16 distinct symbols (0-15), and using A-F extends beyond the 10 decimal digits (0-9).
Can I convert negative numbers?
Yes, our converter supports negative numbers. For negative hex numbers, simply include the negative sign (-) before the hex value. The converter will handle the sign appropriately across all number systems.
What's the maximum number I can convert?
Our converter can handle very large numbers, supporting up to 15 digits in most formats. For extremely large numbers, the precision may be limited by JavaScript's number handling capabilities, but it covers virtually all practical use cases.
Is this hex converter free to use?
Yes, our hex converter is completely free to use. There are no registration requirements, no usage limits, and no hidden fees. You can perform unlimited conversions and access all features without any cost.
Does the converter work offline?
Once the page is loaded, the conversion calculations are performed locally in your browser using JavaScript. However, you need an internet connection to initially load the page and access the latest features and updates.