Difficulty: Easy
Correct Answer: produce the simplest sum-of-products expression
Explanation:
Introduction / Context:
Karnaugh maps (K-maps) are a visual method for simplifying Boolean functions, especially up to 4 or 5 variables. They help designers move from raw truth tables to minimal gate-level forms quickly. This question asks what a K-map most directly achieves in practice.
Given Data / Assumptions:
Concept / Approach:
K-maps identify adjacent 1-cells (or 0-cells for POS) to form implicants, then essential prime implicants, yielding a minimal expression. The canonical result most directly associated with K-maps is a minimal sum-of-products (SOP); alternatively, by mapping 0s, one may obtain minimal product-of-sums (POS).
Step-by-Step Solution:
Place truth-table 1s (and X don’t-cares) on the K-map.Group adjacent cells in powers of two to cover all 1s with as few groups as possible.Translate each group into a product term (for SOP).Sum all product terms to form the minimal SOP expression.
Verification / Alternative check:
Compare with algebraic minimization (Quine–McCluskey or computer-aided tools). The K-map solution’s gate count should be minimal or tie for minimal with other methods.
Why Other Options Are Wrong:
Eliminating the need for simplification is misleading; K-maps are a simplification tool. “Any circuit with just AND/OR” is not a unique K-map promise. “Signal flow picture” describes block diagrams, not K-maps’ tabular adjacency logic.
Common Pitfalls:
Incorrect wrapping adjacency and overlooking don’t-cares often lead to nonminimal results. Mixing SOP and POS rules mid-process causes errors.
Final Answer:
produce the simplest sum-of-products expression
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