Draw a logic diagram of the boolean expression F(X,Y,Z) = ((X’+Y).(X+Y’+Z))’
Understand the Problem
The question asks for the creation of a logic diagram (circuit diagram) that visually represents the given boolean expression F(X,Y,Z) = ((X’+Y).(X+Y’+Z))’. This involves understanding the boolean expression, breaking it down into its constituent logic gates (AND, OR, NOT), and then drawing a circuit diagram showing how these gates are interconnected to implement the overall expression.
Answer
The logic diagram requires NOT gates for X and Y, OR gates, and an AND gate, with a final NOT gate to invert the entire expression.
The logic diagram for the Boolean expression F(X,Y,Z) = ((X’+Y).(X+Y’+Z))’ involves several logic gates. First, implement the expressions inside the parenthesis: (X’+Y) using a NOT gate for X and an OR gate with Y, and (X+Y’+Z) using a NOT gate for Y and an OR gate with X and Z. Then, AND the results of these two expressions. Finally, use a NOT gate to invert the result of the AND operation, which gives the final output F(X,Y,Z).
Answer for screen readers
The logic diagram for the Boolean expression F(X,Y,Z) = ((X’+Y).(X+Y’+Z))’ involves several logic gates. First, implement the expressions inside the parenthesis: (X’+Y) using a NOT gate for X and an OR gate with Y, and (X+Y’+Z) using a NOT gate for Y and an OR gate with X and Z. Then, AND the results of these two expressions. Finally, use a NOT gate to invert the result of the AND operation, which gives the final output F(X,Y,Z).
More Information
Creating logic diagrams from Boolean expressions is a fundamental skill in digital logic design, allowing for the visualization and implementation of complex logical functions using basic logic gates.
Tips
A common mistake is not properly applying DeMorgan's laws when simplifying or implementing complemented expressions, leading to incorrect gate arrangements.
Sources
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