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Karnaugh maps vs. truth tables: A Karnaugh map (K-map) is essentially a rearranged visualization of a truth table that aids grouping and minimization.

Difficulty: Easy

Correct
Incorrect
Only true for 3 variables
Ambiguous because of Gray coding
Insufficient information

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:

The function is defined over n variables (commonly 2–6 in practice for K-maps).
Truth table rows correspond to K-map cells.

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.

Karnaugh maps vs. truth tables: A Karnaugh map (K-map) is essentially a rearranged visualization of a truth table that aids grouping and minimization.

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