Logic Gates Lecture

Jul 23, 2024

Logic Gates Lecture

Introduction to Logic Gates

  • Definition: A logic gate is a physical device that performs logic operations on one or more logical inputs to produce a single logical output.
  • Logic operations: Inversion, logical multiplication, logical sum, etc.
    • Example: Inversion has one input, logical multiplication can have two or more inputs.

Types of Logic Gates

1. Basic Gates

  • NOT Gate
  • AND Gate
  • OR Gate
  • Reason: Any digital circuit can be implemented using these three gates.

2. Universal Gates

  • NAND Gate
  • NOR Gate
  • Reason: Any digital system can be implemented using only NAND or only NOR gates.

3. Arithmetic Gates

  • XOR Gate
  • XNOR Gate
  • Reason: Used in arithmetic operations.

Focus on NOT Gate

Representation & Operation

  • Symbol:
    • Inputs: A
    • Output: Y = A'
  • Alternative Symbol: Bubble can be placed at the input side.

Truth Table

  • Definition: A table showing all possible combinations of inputs and their respective outputs.
  • NOT Gate Truth Table:
    • Input (A): 0, 1
    • Output (Y = A'): 1, 0

Problem Discussion: IES & GATE Exams

Problem 1

  • Circuit: Two NOT gates with feedback
  • Objective: Determine the type of circuit
  • Options:
    • Buffer
    • Astable Multivibrator
    • Bistable Multivibrator
    • Square Wave Generator
  • Analysis:
    • Buffer: A circuit with the same input and output values (not applicable due to feedback).
    • Bistable Multivibrator: Circuit has two stable states (0 and 1).
    • Astable Multivibrator & Square Wave Generator do not match the circuit behavior.
  • Conclusion: The circuit acts as a Bistable Multivibrator (Option C).

Propagation Delay and Timings

  • Definition: Time taken for the output to stabilize after an input is applied.
  • Example circuit with three NOT gates
    • Initial output Y = 0
    • Output changes according to propagation delays (TPD) of each NOT gate.

Timing Analysis

  • Time period (T): Time after which function repeats
    • T = 6 * TPD (for three NOT gates)
    • General formula: T = 2 * n * TPD (n = number of NOT gates)

Circuit Application

  • Square wave generator
    • Generates square waves with a period based on propagation delays.
    • Also acts as a stable multivibrator, clock generator, and ring oscillator.

Homework Problems

Problem 1

  • Circuit: Five NOT gates
  • Propagation Delay: Each gate has 100 picoseconds
  • Task: Calculate the frequency of generated square wave.

Problem 2

  • Circuit Modification: Feedback from the middle of the circuit
  • Propagation Delay: Each gate has 2 nanoseconds
  • Task: Find the time period of generated square wave.