Hexadecimal ↔ Decimal Converter
Convert between hexadecimal (base-16) and decimal (base-10) number systems instantly. Essential tool for programmers, web developers, and anyone working with color codes, memory addresses, or low-level programming.
Hexadecimal ↔ Decimal Converter
Convert between hexadecimal (base-16) and decimal (base-10) number systems
Use digits 0-9 and letters A-F. Optional 0x prefix accepted.
Quick Examples
Hexadecimal Reference
Hex Digits
Powers of 16
How to Use the Hexadecimal Converter
Master hex-decimal conversion with our comprehensive guide
1Choose Conversion Direction
Select whether you want to convert:
- Hex to Decimal: Convert base-16 to base-10
- Decimal to Hex: Convert base-10 to base-16
- Both directions: See both representations
- Real-time: Conversion happens as you type
2Enter Your Number
Input the number in the appropriate format:
- Hexadecimal: Use digits 0-9 and letters A-F
- Decimal: Standard base-10 numbers
- With/without prefix: 0x optional for hex
- Case insensitive: A-F or a-f both work
3View Results
See the conversion with detailed breakdown:
Breakdown: (15×16¹) + (15×16⁰) = 240 + 15 = 255
4Copy and Apply
Use the converted values in your projects:
- • Copy hex values for CSS color codes
- • Use decimal values for programming calculations
- • Apply in memory address calculations
Understanding Hexadecimal Numbers
Learn the fundamentals of base-16 number system
Hexadecimal is a base-16 number system that uses sixteen distinct symbols: 0-9 to represent values zero to nine, and A-F (or a-f) to represent values ten to fifteen. Each position represents a power of 16, making it extremely useful in computing and digital systems.
Hexadecimal Digits
Position Values
Conversion Examples & Practice
Step-by-step examples to master hex-decimal conversion
Hex to Decimal Examples
Example 1: Simple Conversion
Example 2: Two Digits
Example 3: Larger Number
Decimal to Hex Examples
Example 1: Division Method
Example 2: Larger Number
Example 3: Powers of 16
Real-World Applications
Discover how hexadecimal is used across different fields
Web Development
CSS color codes use hexadecimal format. #FF0000 represents pure red, #00FF00 is green, and #0000FF is blue. Understanding hex makes color manipulation much easier.
Memory Addresses
Computer memory addresses are typically displayed in hexadecimal. It's more compact than decimal and aligns with byte boundaries, making debugging and low-level programming easier.
Programming
Hexadecimal is used for bit manipulation, color values, Unicode characters, and representing binary data in a more readable format. Essential for systems programming.
Cryptography
Hash functions, encryption keys, and digital signatures are often represented in hexadecimal format. It provides a readable way to display binary cryptographic data.
File Formats
Many file formats use hexadecimal values for headers, metadata, and binary data representation. Hex editors display file contents in hexadecimal for analysis.
Hardware Design
Digital circuit design, microcontroller programming, and hardware debugging often use hexadecimal for register values, instruction codes, and configuration settings.
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Frequently Asked Questions
Common questions about hexadecimal number conversion
Why is hexadecimal used in computing?
Hexadecimal provides a compact way to represent binary data. Each hex digit represents exactly 4 binary digits (bits), making it much more readable than long binary strings. It's also aligned with byte boundaries (8 bits = 2 hex digits), which is fundamental to computer architecture.
What's the largest hex number this converter can handle?
Our converter can handle very large hexadecimal numbers, limited mainly by JavaScript's number precision (up to about 15-16 significant digits). For most programming and web development tasks, this range is more than sufficient. For cryptographic applications requiring larger numbers, specialized libraries would be needed.
Do I need the "0x" prefix for hexadecimal numbers?
No, the "0x" prefix is optional in our converter. It's commonly used in programming languages to indicate hexadecimal numbers (like 0xFF for 255), but our tool recognizes hex numbers with or without this prefix. The converter will automatically detect the format.
How do hex color codes work?
Hex color codes use 6 hexadecimal digits: two for red, two for green, and two for blue (RGB). For example, #FF0000 is pure red (FF=255 for red, 00=0 for green and blue). Each color component ranges from 00 (0) to FF (255), giving 16.7 million possible colors.
Can I convert negative numbers to hexadecimal?
Hexadecimal representation of negative numbers depends on the context. In programming, negative numbers are often represented using two's complement notation with a fixed bit width. Our basic converter handles positive integers. For negative numbers, you'd typically work with the absolute value and handle the sign separately.
What's the relationship between hex and binary?
Hexadecimal and binary have a direct relationship: each hex digit represents exactly 4 binary digits. For example, hex F equals binary 1111, hex A equals binary 1010. This makes hex an excellent shorthand for binary numbers, which is why it's so popular in programming and computer science.
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