Hex Addition
Hex A equals 10 and D equals 13 in decimal, so their sum is 23, which is 17 in hexadecimal.
A + D
Result: 17
Hexadecimal Calculator
Use this hexadecimal calculator to solve hex arithmetic and bitwise operations in one place. It accepts hexadecimal inputs, shows decimal equivalents, and explains the result step by step.
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
Enter valid hexadecimal values using digits 0-9 and letters A-F, choose the operation you need, and review the result in both hexadecimal and decimal form.
- Enter your first hexadecimal number (using digits 0-9 and letters A-F).
- Select the operation you want to perform (addition, subtraction, etc.).
- Enter your second hexadecimal number (not needed for NOT operation).
- Click 'Calculate' to see the result and step-by-step explanation.
Tip: the NOT operation uses only the first input and flips each bit represented by that hexadecimal value.
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
Example Hex Calculations
Hex Multiplication
Multiplying 5 by 3 gives 15 in decimal, and 15 is written as F in hexadecimal.
5 × 3
Result: F
Bitwise AND
D is 1101 and B is 1011 in binary, so bitwise AND returns 1001, which is 9 in hex.
D AND B
Result: 9
Bitwise XOR
XOR returns 1 where the bits differ, producing 0110 in binary, which equals 6 in hexadecimal.
D XOR B
Result: 6
Hex Calculator FAQ
What does a hex calculator do?
A hex calculator performs arithmetic and bitwise operations on hexadecimal values and often shows the corresponding decimal result for verification.
Why does hexadecimal use A to F?
Hexadecimal is base 16, so it needs 16 symbols. After 0 through 9, the letters A through F represent decimal values 10 through 15.
What is the difference between hex arithmetic and bitwise operations?
Hex arithmetic treats the input as whole numbers for addition, subtraction, multiplication, and division, while bitwise operations compare or invert the underlying binary bits.
Why is hex useful in computing?
Hex is compact and maps cleanly to binary because each hex digit represents four bits, which makes memory addresses, color codes, and binary data easier to read.