Difficulty: Easy
Correct Answer: Correct
Explanation:
Introduction / Context:A K-map is a structured arrangement of truth table entries using Gray code ordering to place adjacent minterms next to each other, making common implicants visually obvious for simplification.
Given Data / Assumptions:
Concept / Approach:The K-map preserves truth table information but rearranges it on a grid so that adjacency corresponds to single-literal differences. This enables grouping of 1s (or 0s in POS) into powers-of-two blocks to eliminate literals.
Step-by-Step Solution:
Step 1: Map each minterm from the truth table to a K-map cell using Gray code order.Step 2: Identify adjacent 1s to form groups of size 1, 2, 4, 8, etc.Step 3: Derive a simplified SOP (or POS) by eliminating changing literals within each group.Verification / Alternative check:Back-translate K-map groupings to an equivalent truth table; the outputs match by construction.
Why Other Options Are Wrong:
Incorrect: Disagrees with the definition of K-maps.Only true for 3 variables: Works for 2–6 variables typically; maps scale by dimensions.Ambiguous/Insufficient: Gray coding clarifies adjacency, not the fundamental equivalence of information.Common Pitfalls:Forgetting wrap-around adjacency on K-map edges, which can miss larger groups.
Final Answer:Correct
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