Solution

The correct answer is (B), (D), (A), (C).

Key Points

• Draw the K-map for the given Boolean function (B): The first step in simplifying a Boolean function using a Karnaugh map (K-map) is to draw the K-map. This involves setting up a grid based on the number of variables in the function.
• Transfer the truth table values to the K-map (D): Next, the truth table values are transferred to the K-map. Each cell in the K-map corresponds to a specific combination of input variables, and the values from the truth table are placed in the appropriate cells.
• Identify and group the largest possible cluster of 1's (A): After transferring the values, the next step is to identify and group the largest possible clusters of 1's in the K-map. These clusters help in simplifying the Boolean expression.
• Write the simplified Boolean expression from the grouped clusters (C): Finally, the simplified Boolean expression is written based on the grouped clusters of 1's. This step involves deriving the simplified terms from the clusters.

Thus the correct answer is ​(B), (D), (A), (C).

Additional Information

• Karnaugh map (K-map): A Karnaugh map is a diagram used in Boolean algebra and digital logic design for the simplification of algebraic expressions. The K-map provides a visual method of grouping expressions with common factors and eliminating unwanted variables.
• Simplification Process: The simplification process using a K-map helps in minimizing the number of logical operations required, which in turn reduces the complexity of digital circuits.
• Grouping Clusters: Grouping the largest possible clusters of 1's is crucial as it ensures that the simplest form of the Boolean expression is achieved. Larger clusters lead to fewer terms in the simplified expression.