XOR Gate (Exclusive OR)

The XOR gate (Exclusive OR) outputs HIGH when its inputs are different. If both inputs are the same (both 0 or both 1), the output is LOW. XOR is fundamental to arithmetic, parity checking, and encryption.

Objectives

• Understand XOR vs regular OR
• Use XOR for parity generation and checking
• Apply XOR in binary addition (half adder)
• Understand XOR's self-inverse property
• Use XOR for controlled inversion and encryption

Key Takeaways

• XOR outputs HIGH when inputs are DIFFERENT
• XOR outputs LOW when inputs are the SAME
• Notation: A ⊕ B, A ^ B, A XOR B
• Self-inverse: A ⊕ A = 0, A ⊕ B ⊕ B = A
• Multi-input XOR = 1 when ODD number of 1s
• Common IC: 74HC86 (four 2-input XOR gates)
• Essential for parity, addition, comparators, and encryption

Applications

• Parity Generation: XOR all bits to get parity bit for error detection
• Binary Addition: XOR produces the sum bit in a half adder
• Comparator: XOR outputs 1 when inputs differ (inequality detection)
• Controlled Inverter: XOR with 0 passes signal, XOR with 1 inverts it
• Encryption: XOR with key encrypts; XOR again decrypts (stream ciphers)

Practice Problems

Problem 1: What is 1 XOR 1?

Problem 2: What is 0 XOR 1 XOR 1 XOR 0?

Problem 3: Simplify A XOR A XOR A

Problem 4: Find parity of 11010111