Combinational Logic Circuits

Introduction to Combinational Logic

• Combinational logic consists of combinations of logic gates to create specialized truth tables.
• Logic gates discussed:
  • AND Gate: Outputs 1 only when all inputs are 1.
  • OR Gate: Outputs 1 if any input is 1.
  • Exclusive OR Gate: Outputs 1 if there is an odd number of 1s at the input.

Example Scenario

Classroom Alarm System

• Components:
  • Door open sensor (contact switch)
  • Motion detectors
  • Glass break detectors
• Functionality:
  • Alarm is connected to sensors to determine when to set off.

Initial Logic

• Condition to set off the alarm:
  • Alarm should go off if:
    • Motion is detected
    • Door is open
    • Glass is broken
• This corresponds to an OR gate with inputs from the three sensors.

Improved Logic with Armed Signal

• Armed Signal:
  • Represents if the alarm system is armed (1) or disarmed (0).
• New Condition:
  • Alarm goes off when:
    • System is armed AND (door is open OR motion is detected OR glass is broken).
• Boolean Expression:
  • Alarm = A AND (D OR M OR G)
    • Where:
      • A = Armed signal
      • D = Door open
      • M = Motion detected
      • G = Glass broken

Logic Circuit Construction

• Important to note the order of operations in logic circuits:
  • 1st: Parentheses
  • 2nd: AND operations
  • 3rd: OR operations
• Steps to form the circuit and expression:
  1. Combine D and M using an OR gate.
  2. Combine A with (D OR M) using an AND gate.
  3. Finally, combine the output with G using an OR gate.

Summary of Boolean Expression Steps

1. Combine D and M to get (D OR M).
2. Combine A with (D OR M): A AND (D OR M).
3. Combine with G: (A AND (D OR M)) OR G.

Next Steps

• In the next lesson, convert this Boolean expression into a truth table.
• Discuss the symbol for the inverter.