In Karnaugh-map (K-map) simplification, certain input combinations are irrelevant to the final function (for example, invalid BCD codes in a BCD-to-decimal converter). What are these entries called, and how may they be treated during grouping to achieve a simpler expression?

Introduction / Context:
Karnaugh maps (K-maps) are a visual method to minimize Boolean expressions by grouping adjacent 1s into powers-of-two rectangles. In many real systems, some input combinations never occur or have outputs that do not matter. Recognizing and using these conditions properly can lead to significantly simpler hardware implementations with fewer gates and less propagation delay.

Given Data / Assumptions:

• Some input patterns are irrelevant (e.g., BCD codes 1010 to 1111 are invalid).
• These map cells can be assigned flexibly to help simplification.
• Goal: reduce logic by forming larger groups in the K-map.

Concept / Approach:
Such irrelevant combinations are called don’t-care conditions (often marked X or d). When minimizing, you are free to treat a don’t-care cell as either 1 or 0 in whichever way allows you to form larger groups (1, 2, 4, 8, … cells), thereby producing a simpler sum-of-products (SOP) or product-of-sums (POS) expression. After minimization, the implemented circuit need not produce a defined value for those unused combinations, which is acceptable by specification.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

Common Pitfalls:

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