Karnaugh map minimization rule: When simplifying a Boolean function with a Karnaugh map, you must use the ________ number of loops (groups), while making each loop as large as possible.

Introduction / Context:
Karnaugh maps (K-maps) are a visual method for minimizing Boolean expressions. A key rule is to cover all 1-cells (or 0-cells for POS) using the fewest number of groups, and to make each group as large as allowed by adjacency and the power-of-two constraint. This question checks your understanding of the “fewest groups, largest size” principle.

Given Data / Assumptions:

• K-maps arrange truth table outputs in Gray-code order to expose adjacencies.
• Groups (loops) must contain 1, 2, 4, 8, … cells (powers of two).
• Groups may wrap around edges and may overlap when it reduces literal count.

Concept / Approach:
Minimization is achieved by maximizing group size (reduces literals per term) and minimizing group count (reduces number of terms). Thus, the correct strategy is to use the minimum number of groups, each being as large as possible within constraints.

Step-by-Step Solution:

Verification / Alternative check:
Compare the resulting expression's literal count with one formed from smaller or more numerous groups; the minimal grouping yields fewer literals and fewer terms, verifying optimality for two-level logic.

Why Other Options Are Wrong:

• maximum: Maximizing the number of loops increases terms and is non-minimal.
• median: There is no “median” strategy in K-maps.
• Karnaugh: Not a valid quantitative choice.
• power-of-two only (count unspecified): True about size, but the rule asked for the count; it must be minimized.

Common Pitfalls:
Forgetting wrap-around adjacencies; avoiding overlap even when it reduces terms; making many small groups instead of fewer large ones.

Final Answer:
minimum