Overview
This lecture discusses logic gates with multiple inputs, focusing on how AND and OR gates operate with three or more inputs, and demonstrates how to derive Boolean expressions for such circuits.
Multi-Input Logic Gates
- AND and OR gates can have more than two inputs (e.g., three, four, or more).
- A multi-input AND gate outputs 1 only when all its inputs are 1.
- A multi-input OR gate outputs 1 if at least one of its inputs is 1.
- The working principle of multi-input gates is the same as for two-input gates.
Truth Table for Three Inputs
- Three inputs (A, B, C) produce 8 possible input combinations.
- For a three-input AND gate (output F = A AND B AND C), only one combination (A=1, B=1, C=1) gives F=1; all others give F=0.
- For a three-input OR gate (output G = A OR B OR C), all combinations except A=0, B=0, C=0 give G=1.
Boolean Expression Example
- Given three inputs (A, B, C) to a three-input AND gate.
- A fourth input (D) is passed through a NOT gate (inverter); NOT gates can have only one input.
- Outputs of AND gate (A AND B AND C) and NOT gate (D') are inputs to an OR gate.
- Boolean output for the circuit is: F = (A AND B AND C) OR (D')
Key Terms & Definitions
- AND gate — Outputs 1 only when all inputs are 1.
- OR gate — Outputs 1 if at least one input is 1.
- NOT gate (Inverter) — Outputs the opposite value of its input (1 becomes 0, 0 becomes 1).
- Boolean Expression — A mathematical way to describe the logic of a circuit using AND, OR, and NOT operators.
Action Items / Next Steps
- Practice drawing truth tables for gates with more than two inputs.
- Write Boolean expressions for given logic circuits with multiple-input gates.