Overview
This lecture explains universal gates, focusing on NAND and NOR gates, and demonstrates how they can be used to create basic logic gates (AND, OR, NOT).
Logic Gates Recap
- Logic gates process binary inputs to produce a specific output.
- Basic gates: AND, OR, and NOT.
- Derived gates: NAND, NOR, EXOR, EXNOR, formed from basic gates.
Universal Gates
- Universal gates can construct any basic gate (AND, OR, NOT).
- NAND and NOR are the two universal gates.
- Called "universal" because all other logic gates can be built from them.
NAND Gate as Universal Gate
- NAND gate symbol includes a circle, indicating inversion (complement).
- NAND as NOT: Connecting both inputs to the same value gives NOT output.
- NAND as AND: Cascading two NAND gates produces an AND function.
- NAND as OR: Using De Morgan’s Law and the duality principle, combining NAND outputs can form an OR gate.
NOR Gate as Universal Gate
- NOR as NOT: Both inputs connected to the same value outputs NOT.
- NOR as OR: Passing an OR output through a NOR twice gives the original OR function.
- NOR as AND: By applying the duality principle, appropriate wiring of NOR gates results in an AND operation.
Key Terms & Definitions
- Logic Gate — Electronic device that performs a logic operation on one or more binary inputs.
- Basic Gates — Fundamental gates: AND, OR, NOT.
- Derived Gates — Gates made from basic gates, e.g., NAND, NOR, EXOR, EXNOR.
- Universal Gate — A gate (NAND or NOR) that can be used to build any basic gate.
- NAND Gate — Outputs false only when all inputs are true; acts as universal gate.
- NOR Gate — Outputs true only when all inputs are false; also a universal gate.
- Duality Principle — Interchanging AND/OR and 1/0 yields valid logic statements.
Action Items / Next Steps
- Review the construction of AND, OR, and NOT gates using only NAND or only NOR gates.
- Prepare any questions regarding universal gates for the next session.