Overview
This lecture covers the four main derived logic gates—NAND, NOR, XOR, and XNOR—including their definitions, symbols, and truth tables.
Derived Gates Overview
- Derived gates are created by combining or complementing basic gates (AND, OR, NOT).
- The four main derived gates are NAND, NOR, XOR, and XNOR.
NAND Gate
- The NAND gate is the complement of the AND gate.
- Its symbol is an AND gate with a small circle (representing NOT) at the output.
- Boolean expression: (A â‹… B)'
- Truth table: Output is false only if both inputs are true; otherwise, output is true.
NOR Gate
- The NOR gate is the complement of the OR gate.
- Its symbol is an OR gate with a small circle at the output.
- Boolean expression: (A + B)'
- Truth table: Output is true only if both inputs are false; otherwise, output is false.
XOR Gate
- The XOR (exclusive OR) gate outputs true only when exactly one input is true.
- Symbol: OR gate with an added curve; algebraic symbol is a plus inside a circle.
- Boolean expression: A ⊕ B
- Truth table: Output is true if inputs are different; false if both are the same.
XNOR Gate
- The XNOR (exclusive NOR) gate is the complement of the XOR gate.
- Symbol: XOR gate symbol with a small circle at the output.
- Boolean expression: (A ⊕ B)'
- Truth table: Output is true if both inputs are the same; false if inputs are different.
Key Terms & Definitions
- Derived Gate — A logic gate formed by combining or complementing basic gates.
- NAND Gate — Outputs false only when all inputs are true; otherwise, true.
- NOR Gate — Outputs true only when all inputs are false; otherwise, false.
- XOR Gate — Outputs true only when exactly one input is true.
- XNOR Gate — Outputs true when all inputs are equal; otherwise, false.
Action Items / Next Steps
- Review the symbols, Boolean expressions, and truth tables for all four derived gates.
- Prepare for upcoming sessions by revising basic logic gates (AND, OR, NOT).