Connecting the gates so that the output matches the given truth table or Boolean expression.
Verifying the circuit by constructing its truth table.
Common Logic Gates
Gate
Symbol
Boolean Function
Truth Table
AND
∧
\$A \cdot B\$
\$A\$
\$B\$
\$A \cdot B\$
0
0
0
0
1
0
1
0
0
1
1
1
OR
∨
\$A + B\$
\$A\$
\$B\$
\$A + B\$
0
0
0
0
1
1
1
0
1
1
1
1
NOT
¬
\$\overline{A}\$
\$A\$
\$\overline{A}\$
0
1
1
0
Step‑by‑Step Construction Procedure
Write down the required Boolean expression or the target truth table.
Simplify the expression using Boolean algebra or Karnaugh maps, if possible.
Identify each logical operation in the simplified expression.
Choose a gate for each operation (e.g., AND for multiplication, OR for addition, NOT for inversion).
Draw the circuit diagram, connecting the outputs of earlier gates to the inputs of later gates as dictated by the expression.
Label all inputs, intermediate signals, and the final output.
Verify the circuit by constructing its truth table and confirming that it matches the original specification.
Worked Example
Construct a circuit that implements the Boolean function \$F = (A \cdot B) + (\overline{C})\$ and verify it against the truth table.
1. Identify the sub‑expressions
Term 1: \$A \cdot B\$
Term 2: \$\overline{C}\$
Final OR: \$(A \cdot B) + (\overline{C})\$
2. Choose gates
One AND gate for \$A \cdot B\$.
One NOT gate for \$\overline{C}\$.
One OR gate to combine the two results.
3. Sketch the circuit (suggested diagram)
Suggested diagram: AND gate with inputs A and B, NOT gate with input C, both outputs feeding an OR gate whose output is F.
4. Truth table verification
\$A\$
\$B\$
\$C\$
\$A \cdot B\$
\$\overline{C}\$
\$F\$
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
0
1
The output column \$F\$ matches the expression \$ (A \cdot B) + (\overline{C}) \$, confirming that the constructed circuit is correct.
Practice Questions
Given the Boolean expression \$G = \overline{(A + B)} \cdot C\$, draw the corresponding logic circuit and produce its truth table.
Design a circuit that outputs 1 only when exactly two of the three inputs \$X\$, \$Y\$, \$Z\$ are 1. Provide the Boolean expression, the circuit diagram, and a verification table.
Use a Karnaugh map to simplify \$H = A B \overline{C} + A \overline{B} C + \overline{A} B C + A B C\$ and then construct the minimal circuit.
Attempt each question, then compare your solutions with the answer key provided by your teacher.