Out the following steps in the proper sequence for simplifying a Boolean…

2024

Out the following steps in the proper sequence for simplifying a Boolean function using a Karnaugh map (K-map). (A) Identify and group the largest possible cluster of 1's (B) Draw the K-map for the given Boolean function (C) Write the simplified Boolean expression from the grouped clusters (D) Transfer the truth table values to the K-map
Choose the correct answer from the options given below:

  1. A.

    (B), (D), (A), (C)

  2. B.

    (D), (B), (A), (C)

  3. C.

    (B), (A), (D), (C)

  4. D.

    (A), (B), (C), (D)

Attempted by 386 students.

Show answer & explanation

Correct answer: A

Correct sequence:

  1. Draw the Karnaugh map for the given Boolean function (set up the correct number of variables, cell order, and labels).

  2. Transfer the truth table values to the K-map (fill each cell with the function value from the truth table).

  3. Identify and group the largest possible clusters of 1s (groups must be powers of two: 1, 2, 4, 8, ...; groups may overlap and wrap around map edges).

  4. Write the simplified Boolean expression from the grouped clusters (derive a product or sum term for each group, then combine).

Why this order?

You need the map layout before placing values so each truth-table entry maps to the correct cell. Grouping depends on the placed values, and simplification follows directly from those groups.

Quick tips:

  • Always form the largest possible groups (they yield the simplest terms).

  • Groups can overlap if that helps make them larger and reduce terms.

  • Remember wrap-around adjacency: opposite edges are adjacent in a K-map.

  • Check for redundant groups and remove them when they do not change the simplified expression.

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