Hex Calculator - Hexadecimal Arithmetic Operations & Conversions

What is a Hexadecimal Calculator?

A hexadecimal calculator is a specialized tool designed to perform arithmetic operations and conversions involving hexadecimal (base-16) numbers. Hexadecimal is a number system that uses 16 distinct symbols: 0-9 and A-F, where A represents 10, B represents 11, and so on up to F representing 15.

Our comprehensive hex calculator provides two main functionalities:

Hexadecimal Arithmetic Operations: Perform addition, subtraction, multiplication, division, and bitwise operations on hex numbers
Number Base Conversions: Convert between hexadecimal, decimal, and binary number systems

Key Features of Our Hex Calculator

Arithmetic Operations

Addition (+): Add two hexadecimal numbers
Subtraction (-): Subtract one hex number from another
Multiplication (×): Multiply two hexadecimal numbers
Division (÷): Divide one hex number by another
Bitwise AND (&): Perform bitwise AND operation
Bitwise OR (|): Perform bitwise OR operation
Bitwise XOR (^): Perform bitwise XOR operation

Number Base Conversions

Hex to Decimal: Convert hexadecimal numbers to decimal
Decimal to Hex: Convert decimal numbers to hexadecimal
Hex to Binary: Convert hexadecimal numbers to binary
Binary to Hex: Convert binary numbers to hexadecimal

Understanding Hexadecimal Numbers

Hexadecimal is a positional number system with base 16. Each position represents a power of 16, and the value of each digit is multiplied by 16 raised to the power of its position.

Hexadecimal Digits

Hex Digit	Decimal Value	Binary Value
0	0	0000
1	1	0001
2	2	0010
3	3	0011
4	4	0100
5	5	0101
6	6	0110
7	7	0111
8	8	1000
9	9	1001
A	10	1010
B	11	1011
C	12	1100
D	13	1101
E	14	1110
F	15	1111

Common Use Cases

Computer Programming

Hexadecimal is widely used in computer programming for:

Memory addresses and pointers
Color codes in web development (e.g., #FF0000 for red)
Character encoding (ASCII/Unicode)
Debugging and low-level programming

Digital Electronics

In digital electronics, hexadecimal is used for:

Representing binary data in a more compact form
Configuring hardware registers
Memory dumps and debugging
Network protocols and data transmission

How to Use Our Hex Calculator

For Arithmetic Operations:

Select the desired operation from the dropdown menu
Enter the first hexadecimal value in the "First Hex Value" field
Enter the second hexadecimal value in the "Second Hex Value" field
The result will be calculated automatically and displayed in the result area

For Number Conversions:

Select the conversion type from the dropdown menu
Enter the value to convert in the "Input Value" field
The converted result will appear automatically in the result area

Examples

Arithmetic Examples

Addition: A1B2 + C3D4 = 16F86
Subtraction: FF - 10 = EF
Multiplication: 5 × 3 = F
Division: 1E ÷ 3 = A

Conversion Examples

Hex to Decimal: FF = 255
Decimal to Hex: 4096 = 1000
Hex to Binary: A1 = 10100001
Binary to Hex: 11010110 = D6

Frequently Asked Questions

What is the difference between hexadecimal and decimal numbers?

Decimal uses base 10 with digits 0-9, while hexadecimal uses base 16 with digits 0-9 and A-F. Hexadecimal is more compact for representing binary data and is commonly used in computer programming and digital electronics.

Why is hexadecimal used in computer programming?

Hexadecimal is used because it's a convenient way to represent binary data. Each hexadecimal digit represents exactly 4 binary digits, making it easy to convert between hex and binary. It's also more compact than binary notation and easier to read than decimal for memory addresses and data values.

How do I convert a large decimal number to hexadecimal?

To convert a large decimal number to hexadecimal, repeatedly divide the number by 16 and collect the remainders. The remainders (0-15) correspond to hex digits (0-F). Read the remainders from bottom to top to get the hexadecimal representation.

What are bitwise operations in hexadecimal?

Bitwise operations (AND, OR, XOR) work on the individual bits of numbers. In hexadecimal, these operations are performed on the binary representation of the hex numbers. For example, A (1010) AND 3 (0011) = 2 (0010).

Can I use lowercase letters in hexadecimal input?

Yes, our calculator accepts both uppercase and lowercase letters for hexadecimal input. The letters A-F and a-f are treated as equivalent. The output will always be displayed in uppercase for consistency.

What happens if I try to divide by zero in hexadecimal?

Division by zero is not allowed in any number system, including hexadecimal. Our calculator will display an error message if you attempt to divide by zero, preventing invalid calculations.