Karnaugh map optimization with don't-care entries In a BCD-to-decimal (or similar) logic design, some input combinations never occur. These are treated as special 'don't-care' terms on the K-map and may be assigned as 0 or 1 to simplify the final minimized expression. Which completion correctly describes this practice?

Introduction / Context:In digital logic design, especially with encoders/decoders such as BCD-to-decimal converters, certain input combinations never occur in normal operation. On a Karnaugh map (K-map), these unused states are labeled as don't-care entries and can be flexibly treated to reduce logic complexity.

Given Data / Assumptions:

• The circuit has input codes that will not appear in practice (e.g., BCD values 1010–1111).
• K-map minimization is being used to simplify the Boolean function.
• Don't-care cells may be set to either 0 or 1 exclusively for simplification.

Concept / Approach:Don't-care terms (often marked X) allow grouping with adjacent 1-cells to form larger K-map groups (1, 2, 4, 8, …). Larger groups yield fewer literals and simpler sums-of-products (SOP) or products-of-sums (POS) expressions. If including a don't-care would complicate a grouping, it can be left as 0. The designer chooses the assignment that leads to the simplest result.

Step-by-Step Solution:Identify all valid 1-cells (where the function must be 1).Mark invalid/unused input combinations as don't-care (X) on the K-map.Create the largest possible power-of-two groups, using X cells as 1s when helpful.Write the minimized expression from the resulting groups.

Verification / Alternative check:After minimization, verify the expression produces correct outputs for all valid inputs and is unconstrained for the don't-care inputs. Simulation or a truth table check confirms functional correctness with fewer gates.

Why Other Options Are Wrong:

• “spurious, ANDs, ORs, eliminate” mislabels don't-cares and confuses the mechanism.
• “duplicate, 1s, 0s, verify” mischaracterizes their role; they are not duplicates.
• “spurious, 1s, 0s, simplify” again misnames them; the standard term is don't-care.

Common Pitfalls:

• Treating don't-cares as fixed values rather than flexible assignments.
• Forgetting that don't-cares must not affect correctness for valid input codes.

Final Answer:don't care, 1s, 0s, simplify