Hexadecimal Calculator
Convert between hexadecimal, decimal, binary, and octal number systems, and perform hex arithmetic operations with our comprehensive hex calculator.
Category: Math
About Hexadecimal Numbers
What is Hexadecimal?
Hexadecimal (or hex) is a base-16 number system that uses 16 distinct symbols: the numbers 0-9 and the letters A-F. The letters A, B, C, D, E, and F represent the decimal values 10, 11, 12, 13, 14, and 15 respectively.
Each hexadecimal digit represents 4 binary digits (bits), making it a compact way to represent binary-coded values. This is why hex is commonly used in computing and digital systems.
Hexadecimal to Decimal Conversion
To convert a hexadecimal number to decimal, multiply each digit by the corresponding power of 16 based on its position, then sum the results.
Example: Hex A7F = (10×16²) + (7×16¹) + (15×16⁰) = 2560 + 112 + 15 = 2687 in decimal
Decimal to Hexadecimal Conversion
To convert from decimal to hexadecimal, repeatedly divide the decimal number by 16. The remainders, read in reverse order (from bottom to top), form the hexadecimal number.
Example: To convert decimal 423 to hex:
- 423 ÷ 16 = 26 with remainder 7
- 26 ÷ 16 = 1 with remainder 10 (A in hex)
- 1 ÷ 16 = 0 with remainder 1
- Reading remainders from bottom to top: 1A7
Common Applications
- Color Codes: RGB colors in HTML/CSS are often specified in hexadecimal (e.g., #FF0000 for red).
- Memory Addresses: Computer memory addresses are typically represented in hex (e.g., 0x7FFF).
- Assembly Language: Many assembly languages use hex for representing machine code and memory locations.
- Error Codes: System error codes and status indicators are often presented in hex.
- MAC Addresses: Network interface hardware addresses use hex notation (e.g., 00:1A:2B:3C:4D:5E).
- Debugging: Memory dumps and debugging information often use hex representation.
Frequently Asked Questions
What is hexadecimal?
Hexadecimal (or hex) is a base-16 number system that uses 16 distinct symbols: the digits 0-9 and the letters A-F (or a-f) to represent values. It's widely used in computing as a more human-friendly way to represent binary values.
Why use hexadecimal instead of binary?
Hexadecimal is more compact than binary (each hex digit represents 4 binary digits), making it easier for humans to read and write. It's commonly used in programming to represent memory addresses, color codes, and other binary data in a more manageable format.
How do I convert between decimal and hexadecimal?
To convert decimal to hex, divide by 16 repeatedly and note the remainders (using A-F for values 10-15) in reverse order. To convert hex to decimal, multiply each digit by the appropriate power of 16 and sum the results. Our calculator handles these conversions automatically.
What are common uses for hexadecimal?
Hexadecimal is commonly used in computer programming to represent memory addresses, binary data in a readable format, RGB color codes (e.g., #FF0000 for red), MAC addresses, and in debugging computer programs.