Hexadecimal Calculator
What is Hexadecimal?
Hexadecimal (or hex) is a base-16 number system that uses sixteen distinct symbols: the numbers 0-9 and the letters A-F (or a-f) to represent values. It provides a more human-friendly way to represent binary-coded values in computing systems.
Hexadecimal Number System
In the hexadecimal system, each position represents a power of 16:
| Decimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| Hexadecimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Decimal | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|---|---|---|
| Hexadecimal | 8 | 9 | A | B | C | D | E | F |
For example, the hexadecimal number 1A3 equals (1×16²) + (10×16¹) + (3×16⁰) = 256 + 160 + 3 = 419 in decimal.
Hexadecimal Operations
Hex Addition
Hex addition follows the same principles as decimal addition, but with 16 possible digits:
- When the sum exceeds F (15), carry 1 to the next position
- Example: 9 + 8 = 11 (in hex, not 17)
Hex Subtraction
Hex subtraction follows similar rules to decimal subtraction:
- When borrowing is needed, borrow 16 (not 10)
- Example: 5 - 7 requires borrowing, so it becomes 15 - 7 = 8
Hex Multiplication
Hex multiplication is similar to decimal multiplication:
- Multiply each digit of the second number with each digit of the first
- Use the hex multiplication table for single-digit products
- Add the partial products in the appropriate positions
Hex Division
Hex division follows the same long division process as decimal:
- Divide the dividend by the divisor using hex arithmetic
- Calculate the quotient and remainder
- The process is the same as decimal division but using base-16
Applications of Hexadecimal
Hexadecimal is widely used in computing and digital systems:
- Memory addresses and memory dumps
- Assembly language programming
- Color representation in HTML and CSS (e.g., #FF5733)
- IPv6 addresses
- Machine code representation
- Debugging and error codes
How to Use the Hexadecimal Calculator
Our hexadecimal calculator offers several functions:
- Convert between hexadecimal, decimal, and binary number systems
- Perform hexadecimal arithmetic operations (addition, subtraction, multiplication, division)
- View step-by-step solutions for hexadecimal operations
- Perform bitwise operations on hexadecimal numbers
Simply enter your values, select the operation you want to perform, and click "Calculate" to see the results.