Overview
This lecture covers the XOR and XNOR logic gates, their truth tables, Boolean expressions, symbols, and key properties.
XOR Gate (Exclusive OR)
- XOR (Exclusive OR) gate has two inputs and one output.
- Its truth table outputs 1 when inputs are different; 0 when inputs are the same.
- Boolean expression: ( f = A'B + AB' ) or ( f = A \oplus B ).
- Symbol: Similar to OR gate but with an extra curved line before the input.
- Used in applications such as parity checkers.
XNOR Gate (Exclusive NOR)
- XNOR gate is the inverse of XOR; also called the equivalence gate.
- Its truth table outputs 1 when inputs are the same; 0 when inputs are different.
- Boolean expression: ( f = A'B' + AB ).
- Symbol: Similar to XOR symbol with a negation bubble on the output.
XOR Gate Properties and Examples
- ( A \oplus 0 = A ) (XOR with 0 returns the original value).
- ( A \oplus 1 = A' ) (XOR with 1 inverts the value).
- XOR is commutative: ( A \oplus B = B \oplus A ).
- XOR is associative: ( (A \oplus B) \oplus C = A \oplus (B \oplus C) ).
Key Terms & Definitions
- XOR (Exclusive OR) gate — Outputs 1 if inputs are different, 0 if inputs are the same.
- XNOR (Exclusive NOR) gate — Outputs 1 if inputs are the same, 0 if different.
- Boolean expression — Logical equation representing gate output.
- Parity Checker — Circuit that checks if the number of 1s is even or odd.
Action Items / Next Steps
- Review the truth tables, Boolean expressions, and symbols for XOR and XNOR gates.
- Practice simplifying Boolean expressions involving XOR and XNOR.
- Prepare for questions on properties and applications of XOR/XNOR gates.