1. What is 3-Input XOR?

The 3-input XOR (exclusive OR) is a logical operation that outputs true (1) when an odd number of its inputs are true (1), and false (0) otherwise. It's an extension of the standard 2-input XOR gate.

2. How Does the Calculator Work?

The calculator uses the XOR operation:

Where:

• \( a \) — First input bit (0 or 1)
• \( b \) — Second input bit (0 or 1)
• \( c \) — Third input bit (0 or 1)
• \( \oplus \) — XOR operation

Explanation: The operation returns 1 when an odd number of inputs are 1, and 0 when an even number of inputs are 1 (including when all inputs are 0).

3. Truth Table

A	B	C	Output
0	0	0	0
0	0	1	1
0	1	0	1
0	1	1	0
1	0	0	1
1	0	1	0
1	1	0	0
1	1	1	1

4. Using the Calculator

Tips: Select either 0 or 1 for each of the three inputs (A, B, and C). The calculator will compute and display the XOR result.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between XOR and OR?
A: OR returns 1 when any input is 1. XOR returns 1 only when an odd number of inputs are 1 (for 3-input XOR).

Q2: Can XOR have more than 2 inputs?
A: Yes, multi-input XOR gates exist and follow the "odd parity" rule where output is 1 for an odd number of 1 inputs.

Q3: What are practical applications of 3-input XOR?
A: Used in parity generation/checking, error detection, cryptography, and arithmetic circuits.

Q4: How does 3-input XOR differ from 2-input XOR?
A: 2-input XOR is true when inputs differ. 3-input XOR is true when an odd number of inputs are true.

Q5: Is XOR associative?
A: Yes, (A XOR B) XOR C = A XOR (B XOR C), which is why we can chain XOR operations.