1. What is XOR Operation?

The XOR (exclusive OR) operation is a logical operation that outputs true only when inputs differ (one is true, the other is false). For numbers, it performs bitwise comparison of their binary representations.

2. How Does the Calculator Work?

The calculator performs sequential XOR operations on all input numbers:

Where:

• \( \oplus \) — XOR operator
• \( \text{Number}_1, \text{Number}_2, \ldots \) — Input integers

Explanation: The calculator converts all numbers to integers, then performs XOR operation sequentially on all of them.

3. Properties of XOR

Details: XOR has several important properties:

• Commutative: A ⊕ B = B ⊕ A
• Associative: A ⊕ (B ⊕ C) = (A ⊕ B) ⊕ C
• A ⊕ A = 0
• A ⊕ 0 = A

4. Using the Calculator

Tips: Enter numbers separated by commas (e.g., "5, 3, 9"). The calculator will ignore non-numeric values and perform XOR on all valid integers.

5. Frequently Asked Questions (FAQ)

Q1: What happens if I enter non-integer numbers?
A: The calculator will convert them to integers before performing XOR operation.

Q2: What's the maximum number of inputs?
A: There's no strict limit, but very large lists may cause performance issues.

Q3: Can I use hexadecimal or binary numbers?
A: Currently only decimal numbers are supported. You can convert them to decimal first.

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

Q5: Why does XORing a number with itself give 0?
A: Because all bits are identical, so each bit comparison results in 0.