1. What is Binary XOR Operation?

The XOR (exclusive OR) operation is a binary operation that compares two binary digits and returns 1 if the digits are different and 0 if they are the same. It's a fundamental operation in computer science and digital electronics.

2. How Does the Calculator Work?

The calculator performs the XOR operation on each corresponding pair of bits:

Where:

• \( \text{bin1} \) — First binary number
• \( \text{bin2} \) — Second binary number
• \( \oplus \) — XOR operator

Truth Table:

bin1	bin2	Result
0	0	0
0	1	1
1	0	1
1	1	0

3. Importance of XOR Operation

Details: XOR is widely used in cryptography, error detection and correction, digital logic circuits, and various algorithms. It's a fundamental operation in computer science with many practical applications.

4. Using the Calculator

Tips: Enter two binary numbers (containing only 0s and 1s). The calculator will automatically pad the shorter number with leading zeros to match lengths before performing the XOR operation.

5. Frequently Asked Questions (FAQ)

Q1: What happens if inputs have different lengths?
A: The calculator automatically pads the shorter binary number with leading zeros to match the length of the longer number.

Q2: Can I input non-binary numbers?
A: No, the calculator only accepts binary inputs (0s and 1s). Any other characters will result in an error message.

Q3: What are some applications of XOR?
A: XOR is used in cryptography (e.g., one-time pads), error detection (parity checks), digital logic circuits, and various algorithms like swapping values without temporary storage.

Q4: How is XOR different from OR?
A: OR returns 1 if either or both inputs are 1. XOR returns 1 only if exactly one input is 1 (exclusive OR).

Q5: Can XOR be used for encryption?
A: Yes, XOR is a fundamental operation in many encryption algorithms. When combined with a random key, it can provide strong encryption.