1. What is XOR Operation?

The XOR (exclusive OR) is a bitwise operation that outputs true only when inputs differ. For numbers, it performs bit-by-bit comparison and returns 1 where bits differ and 0 where they are the same.

2. How Does the Calculator Work?

The calculator performs XOR operation on all input numbers:

Where:

• \( a_1, a_2, \dots, a_n \) — Input integers
• \( \oplus \) — XOR operator

Explanation: The operation is performed sequentially on all numbers. For example: 5 ^ 3 = 6 (since 101 ^ 011 = 110 in binary).

3. Properties of XOR

Details: XOR has several important properties:

• Commutative: A ^ B = B ^ A
• Associative: (A ^ B) ^ C = A ^ (B ^ C)
• Identity element: A ^ 0 = A
• Self-inverse: A ^ A = 0

4. Using the Calculator

Tips: Enter comma-separated integers (e.g., "5, 3, 9"). The calculator will ignore non-numeric values and empty entries.

5. Frequently Asked Questions (FAQ)

Q1: What happens if I enter non-integer numbers?
A: The calculator will use the integer part of each number (e.g., 5.9 becomes 5).

Q2: What's the XOR of a single number?
A: The XOR of a single number is the number itself (A ^ 0 = A).

Q3: What's the XOR of an empty list?
A: The XOR of no numbers is 0 (the identity element for XOR).

Q4: What are practical uses of XOR?
A: XOR is used in cryptography, error detection, and various bit manipulation algorithms.

Q5: How does XOR differ from OR?
A: OR returns 1 if either bit is 1, while XOR returns 1 only if exactly one bit is 1.