Hexadecimal Calculator

Use this hexadecimal calculator for adding, subtracting, multiplying and dividing hex numbers. You can also perform bitwise operations like AND, OR, XOR, and NOT.

Hex Calculator

Enter hexadecimal numbers (using 0-9 and A-F), select an operation, and click Calculate to see the result with step-by-step solution.

Result

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 to represent values. It's commonly used in computing as a more human-friendly way to represent binary-coded values.

Each hex digit represents 4 binary digits (bits), making it easier to read and write binary numbers. For example, the hex number 1A3F is equivalent to the decimal number 6719.

Hexadecimal Operations

  • Addition: Adding hex numbers works similar to decimal addition, but carries occur when a sum equals or exceeds 16.
  • Subtraction: Subtracting hex numbers follows similar rules to decimal subtraction, but borrows are in base 16.
  • Multiplication: Hex multiplication can be done directly or by converting to decimal, multiplying, then converting back to hex.
  • Division: Hex division is typically done by converting to decimal, dividing, then converting the result back to hex.

Bitwise Operations in Hex

  • AND (&): Performs a bitwise AND operation on each pair of corresponding bits. If both bits are 1, the result is 1; otherwise, it's 0.
  • OR (|): Performs a bitwise OR operation. If either bit is 1, the result is 1; otherwise, it's 0.
  • XOR (^): Performs a bitwise XOR (exclusive OR). If the bits are different, the result is 1; if they're the same, it's 0.
  • NOT (~): Performs a bitwise NOT operation, which inverts all the bits (0 becomes 1, and 1 becomes 0).

How to Use This Calculator

  1. Enter your first hexadecimal number (using digits 0-9 and letters A-F).
  2. Select the operation you want to perform (addition, subtraction, etc.).
  3. Enter your second hexadecimal number (not needed for NOT operation).
  4. Click 'Calculate' to see the result and step-by-step explanation.

Applications of Hexadecimal

  • Memory addresses and debugging in computer programming
  • Color representation in web design (e.g., #FF5733 for a shade of orange)
  • Assembly language and machine code representation
  • Network addressing and MAC addresses