Perform hexadecimal arithmetic operations (add, subtract, multiply, divide) and convert between hex and decimal values. Essential for programming, web development, and computer science.
The hexadecimal (hex) number system is a base-16 numeral system that uses sixteen distinct symbols: 0-9 and A-F (representing 10-15). Hex is widely used in computing and programming because it provides a more human-friendly representation of binary data, with each hex digit representing exactly four binary digits.
Understanding hexadecimal is essential for web development (color codes), programming (memory addresses), computer graphics, and digital forensics. It's particularly useful for representing large binary numbers in a compact, readable format.
| Hex | Decimal | Binary | Description |
|---|---|---|---|
| 0 | 0 | 0000 | Zero |
| 1 | 1 | 0001 | One |
| 2 | 2 | 0010 | Two |
| 3 | 3 | 0011 | Three |
| 4 | 4 | 0100 | Four |
| 5 | 5 | 0101 | Five |
| 6 | 6 | 0110 | Six |
| 7 | 7 | 0111 | Seven |
| 8 | 8 | 1000 | Eight |
| 9 | 9 | 1001 | Nine |
| A | 10 | 1010 | Ten |
| B | 11 | 1011 | Eleven |
| C | 12 | 1100 | Twelve |
| D | 13 | 1101 | Thirteen |
| E | 14 | 1110 | Fourteen |
| F | 15 | 1111 | Fifteen |
Where n is the position from right (starting at 0)
Web Development: Color codes in CSS use hex format (#FF0000 for red, #00FF00 for green, #0000FF for blue). Each pair represents red, green, and blue intensity from 00 to FF.
Memory Addresses: Computer memory addresses are typically displayed in hexadecimal because it's more compact than binary and easier to read than long decimal numbers.
Programming: Hex literals in code (0xFF, 0x10), bit manipulation, and low-level programming often use hexadecimal for clarity and conciseness.
Digital Forensics: File signatures, data analysis, and debugging tools frequently display data in hexadecimal format for easier pattern recognition.
| Hex Value | Decimal | Common Usage | Description |
|---|---|---|---|
| FF | 255 | Maximum 8-bit value | Highest value in one byte |
| 100 | 256 | 2⁸, start of 9th bit | Common programming boundary |
| 400 | 1024 | 1 KB (1024 bytes) | Memory/storage unit |
| FFFF | 65535 | Maximum 16-bit value | Highest value in two bytes |
| 10000 | 65536 | 2¹⁶, 64K boundary | Classic memory segment size |
| FFFFFF | 16777215 | 24-bit color max | Maximum RGB color value |
RGB Format: Hex colors use the format #RRGGBB where RR is red intensity (00-FF), GG is green (00-FF), and BB is blue (00-FF).
Common Colors: #000000 (black), #FFFFFF (white), #FF0000 (red), #00FF00 (green), #0000FF (blue), #FFFF00 (yellow), #FF00FF (magenta), #00FFFF (cyan).
Short Format: When RGB values are duplicated (#AABBCC), you can use short format (#ABC), where A expands to AA, B to BB, and C to CC.
Hex Literals: Most programming languages support hex literals with 0x prefix (0xFF = 255, 0x10 = 16, 0xDEADBEEF for debugging).
Bit Manipulation: Hex is ideal for bitwise operations because each hex digit corresponds exactly to 4 bits, making bit patterns more visible.
Memory Dumps: Debugging tools display memory contents in hex because it's more compact than binary and shows byte boundaries clearly.
Powers of 16: Memorize key powers: 16¹=16, 16²=256, 16³=4096, 16⁴=65536 for quick mental calculations.
Nibble Grouping: Each hex digit represents 4 bits (a nibble), so two hex digits represent one byte (8 bits).
Case Insensitive: Hex digits A-F can be uppercase or lowercase (A=a, B=b, etc.), but uppercase is more common in technical contexts.