Find the Boolean expression corresponding to the digital circuit given below.
Understand the Problem
The question is asking to determine the Boolean expression that represents the digital circuit shown in the image. This involves analyzing the logic gates in the circuit and translating their configuration into a Boolean algebra expression.
Answer
The Boolean expression is $(A + B)C'$.
Answer for screen readers
The Boolean expression corresponding to the digital circuit is $F = (A + B)C'$.
Steps to Solve
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Identify the first logic gate The first two variables, $A$ and $B$, go into an OR gate. The output of this gate can be represented as: $$ Y = A + B $$
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Identify the second logic gate The variable $C$ goes into a NOT gate. The output of this gate can be represented as: $$ Z = C' $$
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Identify the third logic gate The outputs from the first OR gate ($Y$) and the NOT gate ($Z$) then feed into an AND gate. The final expression for the output of this AND gate is: $$ F = Y \cdot Z = (A + B) \cdot C' $$
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Simplify the expression The final Boolean expression representing the entire circuit can be written as: $$ F = (A + B)C' $$
The Boolean expression corresponding to the digital circuit is $F = (A + B)C'$.
More Information
In digital logic design, understanding how to translate circuit diagrams into Boolean expressions is fundamental. The combination of various logic gates (AND, OR, NOT) produces specific logical functions that can be simplified using Boolean algebra.
Tips
- Misidentifying the type of gates (e.g., confusing AND with OR).
- Forgetting to apply the NOT gate correctly to the inputs, resulting in incorrect expressions.
- Neglecting the correct order of operations when combining outputs from different gates.
