Construct a logic circuit

3.2 Logic Gates and Logic Circuits

What is a Logic Gate?

Think of a logic gate as a tiny decision maker that takes one or more binary inputs (0 or 1) and produces a single binary output. It’s like a traffic light that decides whether cars can go or must stop based on the signals it receives.

Common Logic Gates

Gate Symbol Boolean Expression
AND ∧ $A \land B$
OR ∨ $A \lor B$
NOT ¬ $¬A$
NAND ⊼ $¬(A \land B)$
NOR ⊽ $¬(A \lor B)$
XOR ⊕ $A \oplus B$
XNOR ⊙ $¬(A \oplus B)$
Exam Tip: Remember that NAND and NOR are universal gates; you can build any other gate using only NAND or only NOR. This is useful for simplifying circuit designs.

Truth Tables

A B AND OR XOR
0 0 0 0 0
0 1 0 1 1
1 0 0 1 1
1 1 1 1 0
Analogy: Imagine each input as a switch that can be either ON (1) or OFF (0). The gate decides the state of the output switch based on the rules above.

Constructing a Logic Circuit: XOR Example

Goal: Build a circuit that outputs 1 only when exactly one of the two inputs is 1 (XOR). This is useful for error detection or simple arithmetic.

  1. Start with two inputs, A and B.
  2. Use two AND gates:
    • AND1 takes A and ¬B → output A ∧ ¬B.
    • AND2 takes ¬A and B → output ¬A ∧ B.
  3. Use an OR gate to combine the outputs of AND1 and AND2:
    • Output = (A ∧ ¬B) ∨ (¬A ∧ B) = A ⊕ B.
  4. Optional: If you only have NAND gates, replace each AND with a NAND followed by a NOT (another NAND with both inputs tied together).
Exam Tip: When asked to design a circuit, always start by writing the Boolean expression, then decompose it into basic gates. Show the step‑by‑step decomposition in your answer.

Practical Tips for Building Circuits

  • Use breadboard or simulation software (e.g., Logisim) to test your design before building.
  • Label all wires clearly to avoid confusion.
  • Check power supply levels: logic gates usually operate at 5 V or 3.3 V.
  • Remember that noise can cause false triggers; use proper decoupling capacitors if needed.
Final Exam Reminder: Be ready to sketch a circuit diagram, write the Boolean expression, and explain the truth table. Practice drawing both the diagram and the table from memory!

Revision

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