Find the Boolean expression corresponding to the digital circuit given below.
Understand the Problem
The question is asking for the Boolean expression that corresponds to a given digital circuit. To solve this, we need to analyze the circuit components and their connections to derive the correct Boolean expression.
Answer
The Boolean expression is $(A + B)C'$.
Answer for screen readers
The Boolean expression corresponding to the digital circuit is $(A + B)C'$.
Steps to Solve
- Identify the Circuit Components
In the circuit, we have two inputs, A and B, going into an OR gate. The output of the OR gate will be $A + B$. The input C goes into a NOT gate.
- Determine Input to the AND Gate
The output from the OR gate ($A + B$) is combined with the output from the NOT gate (which is $C'$ since the NOT gate inverts C). So the input to the AND gate is $(A + B)$ and $C'$.
- Write the Output from the AND Gate
The output of the AND gate will be given by the expression:
$$ (A + B)C' $$
- Final Output of the Circuit
Since there are no further operations on the output after the AND gate, the final Boolean expression corresponding to the digital circuit is:
$$ (A + B)C' $$
The Boolean expression corresponding to the digital circuit is $(A + B)C'$.
More Information
This expression indicates that the output is true if either A or B is true, and C is false. It can be useful in various applications, particularly in digital logic design and simplifying Boolean expressions.
Tips
- Misreading the logic gates can lead to incorrect Boolean expressions.
- Forgetting to include the output of NOT gates when combining with other gates.
