Hexadecimal Calculator
Convert between decimal, binary, and hexadecimal values. Perform arithmetic operations on hexadecimal numbers.
About the Hexadecimal Calculator
The Hexadecimal Calculator is a versatile tool designed to help with hexadecimal conversions and arithmetic operations. Whether you're a programmer, student, or digital enthusiast, this calculator simplifies working with hex numbers and different number systems.
Understanding Hexadecimal Numbers:
Hexadecimal (base-16) is a number system that uses 16 distinct symbols to represent values:
- Digits 0-9: Represent values 0 to 9
- Letters A-F: Represent values 10 to 15
- Each hex digit represents 4 binary digits (bits)
- Hexadecimal is commonly prefixed with "0x" (e.g., 0x1A)
Hexadecimal-Decimal Conversion Table:
0 = 0
1 = 1
2 = 2
3 = 3
4 = 4
5 = 5
6 = 6
7 = 7
8 = 8
9 = 9
A = 10
B = 11
C = 12
D = 13
E = 14
F = 15
Practical Applications of Hexadecimal:
- Computer Memory Addressing: Memory locations are often represented in hexadecimal
- Color Codes: Web colors use hex codes (e.g., #FF5733)
- Assembly Language: Machine code and assembly often use hex representation
- Debugging: Memory dumps and error codes are commonly displayed in hex
- Network Addresses: MAC addresses use hexadecimal notation
- Digital Systems: Used in digital electronics and microcontroller programming
How to Use This Calculator:
Conversion Mode:
- Enter any number in the input field
- Select the format of your input number (decimal, hex, or binary)
- Choose the desired output format
- Click "Calculate" to see the conversion results
Arithmetic Mode:
- Enter your first hexadecimal number
- Choose the operation you want to perform
- Enter the second hexadecimal number (if required)
- Select your desired result format
- Click "Calculate" to see the result
Bitwise Operations Explained:
| Operation | Symbol | Description | Example |
|---|---|---|---|
| AND | & | Sets each bit to 1 if both bits are 1 | 0xA (1010) & 0x3 (0011) = 0x2 (0010) |
| OR | | | Sets each bit to 1 if at least one bit is 1 | 0xA (1010) | 0x3 (0011) = 0xB (1011) |
| XOR | ^ | Sets each bit to 1 if only one bit is 1 | 0xA (1010) ^ 0x3 (0011) = 0x9 (1001) |
| NOT | ~ | Inverts all bits | ~0xA (1010) = 0xFFFFFFF5 (depends on bit width) |
| Left Shift | << | Shifts all bits left by the specified amount | 0x2 (0010) << 2 = 0x8 (1000) |
| Right Shift | >> | Shifts all bits right by the specified amount | 0x8 (1000) >> 2 = 0x2 (0010) |
Common Hexadecimal Conversions:
| Decimal | Hexadecimal | Binary |
|---|---|---|
| 0 | 0x0 | 0000 |
| 10 | 0xA | 1010 |
| 15 | 0xF | 1111 |
| 16 | 0x10 | 00010000 |
| 255 | 0xFF | 11111111 |
| 256 | 0x100 | 100000000 |
Tips for Working with Hexadecimal
- Remember that each hex digit represents exactly 4 binary digits
- Hex values are case-insensitive (0xAB equals 0xab)
- Powers of 2 have simple hex representations (0x1, 0x2, 0x4, 0x8, 0x10, 0x20, etc.)
- Hex is more compact than binary and easier to read for humans
- When performing bitwise operations, thinking in binary often helps