Hexadecimal Calculator
Convert between hexadecimal, decimal, binary, and octal with detailed analysis
Number System Conversion
Enter a non-negative decimal number
Conversion Results
Enter a number to convert between number systems
Understanding Hexadecimal Numbers
What is Hexadecimal?
Hexadecimal (base-16) is a number system that uses 16 distinct symbols: 0-9 for values zero to nine, and A-F for values ten to fifteen. It's widely used in computer science and digital systems.
Hexadecimal Digits:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A(10), B(11), C(12), D(13), E(14), F(15)
Example: FF = 15×16¹ + 15×16⁰ = 255 in decimal
Why Use Hexadecimal?
Hexadecimal is commonly used in computing because it represents binary data more compactly. One hexadecimal digit represents exactly four binary digits (bits), making it ideal for memory addresses, color codes, and data representation.
- •Compact: Represents large binary numbers efficiently
- •Alignment: One hex digit = 4 bits, two hex digits = 1 byte
- •Human-readable: Easier to read than long binary strings
- •Standard: Industry standard for many applications
Common Conversions
Decimal to Hexadecimal
255 ÷ 16 = 15 remainder 15 → FF
1024 ÷ 16 = 64 remainder 0 → 400
4096 ÷ 16 = 256 remainder 0 → 1000
Hexadecimal to Binary
A = 1010, F = 1111 → AF = 10101111
FF = 11111111, 00 = 00000000 → FF00 = 1111111100000000
Hexadecimal to Decimal
1A3 = 1×16² + 10×16¹ + 3×16⁰ = 256 + 160 + 3 = 419
FF = 15×16¹ + 15×16⁰ = 240 + 15 = 255
Real-World Applications
Web Development
Color codes
- • HTML color codes (#FF0000)
- • CSS color values
- • RGB color representation
- • Alpha transparency
Computer Memory
Memory addresses
- • Memory locations
- • Pointer values
- • Debug information
- • Register values
Networking
MAC addresses
- • MAC address format
- • IPv6 addresses
- • Network protocols
- • Error codes
Programming
Character encoding
- • Unicode values
- • ASCII codes
- • String literals
- • Escape sequences
Digital Electronics
Hardware design
- • Circuit design
- • Microcontroller code
- • Device registers
- • Firmware development
Security
Cryptography
- • Hash values
- • Encryption keys
- • Digital signatures
- • Security certificates
Number System Comparison
Base Systems
Binary (Base 2)
Digits: 0, 1 | Used in digital circuits
Octal (Base 8)
Digits: 0-7 | Unix file permissions
Decimal (Base 10)
Digits: 0-9 | Everyday counting
Hexadecimal (Base 16)
Digits: 0-9, A-F | Computer systems
Conversion Examples
Number: 255
Binary: 11111111
Octal: 377
Decimal: 255
Hexadecimal: FF
Number: 1024
Binary: 10000000000
Octal: 2000
Decimal: 1024
Hexadecimal: 400
Quick Reference Table
| Decimal | Binary | Octal | Hexadecimal |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 10 | 1010 | 12 | A |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 255 | 11111111 | 377 | FF |