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Understanding Combinational Logic Circuits

May 10, 2025

Combinational Logic Circuits

Introduction to Combinational Logic

  • Combinational logic involves combinations of logic gates to create specialized truth tables.
  • Important gates discussed:
    • AND Gate: Outputs 1 only when all inputs equal 1.
    • OR Gate: Outputs 1 if any input equals 1.
    • Exclusive OR (XOR) Gate: Outputs 1 if there is an odd number of 1s at its input.

Example of a Combinational Logic Circuit

Scenario: Classroom Alarm System

  1. Components of the System:

    • Door Open Sensor: Contact switch that is closed when the door is closed and open when the door is open.
    • Motion Detectors: Detect motion in the room.
    • Glass Break Detectors: Detect if glass is broken.
    • Alarm System: Monitors sensors to set off the alarm.

  2. Alarm Trigger Logic:

    • The alarm should go off if:
      • Motion is detected OR
      • The door is open OR
      • The glass is broken.
    • This can be represented as an OR gate with three inputs: Door (D), Motion (M), Glass (G).

Armed Signal

  • An armed signal indicates whether the alarm system is armed (1) or disarmed (0).
  • New requirement: The alarm should only go off if the system is armed AND one of the sensors is triggered.

Logical Representation

  • Boolean expression:
    • Alarm = A AND (D OR M OR G)
    • Where A = armed signal, D = door, M = motion, G = glass.

Order of Operations in Logic

  • Order of Precedence:
    1. Parentheses
    2. AND operations
    3. OR operations
  • This is similar to mathematical operations (multiplication before addition).

Steps to Create the Circuit

  1. Combine D (door) and M (motion) using an OR gate: (D OR M).
  2. Combine the armed signal (A) with the output of (D OR M) using an AND gate: A AND (D OR M).
  3. Finally, combine the output with G (glass) using an OR gate:
    • Result: (A AND (D OR M)) OR G.

Summary

  • The alarm goes off if:
    • The system is armed AND (the door is open OR motion is detected) OR (the glass is broken).
  • The next lesson will cover converting this circuit expression into a truth table and discuss the inverter symbol.

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