Determine the simplified Boolean expression for segment c from using the K-map:

Question

BlackTom AI · Accepted Answer

We are given a multiple-choice question: Determine the simplified Boolean expression for segment c from using the K-map.
Option A: A'B' + A'C. This expression combines terms that may cover certain minterms, but it does not obviously align with the simplified form derived from the K-map for segment c. It mixes A' with B' and A' with C, which is not directly the minimal cover seen in typical K-map groupings for this segment.
Option B: C' + B + D. This form suggests a sum of literals where C is negated, or B is asserted, or D is asserted. In many K-map simplifications for a 4-variable function, a term like C' + B + D indicates that whenever C is 0, or B is 1, or D is 1, the function is 1. This pattern often arises from either a large group that covers all cells except a few, or from combining adjacent groups to yield a minimal cover. If the K-map grouping for segment c indeed results in a coverage that collapses to C' + B + D, this would be the succinct expression.
Option C: A'C' + A'D + A'C. Here we have a sum of products all containing A'. This would imply the function is determined by A' in combination with various C and D terms. However, in many K-map simplifications, such a structure would be redundant if B or C terms alone already cover the necessary minterms. The presence of A' in all terms doesn't typically yield the minimal form for a segment labeled c.
Option D: A'C' + A'D + A'B. This option also uses A' across all product terms, with C', D, and B varying. Similar to Option C, this can indicate a restricted region of the map dependent on A' but may not produce the smallest sum-of-products unless those three terms are all required to cover disjoint regions. If the K-map grouping for segment c includes a more economical cover that avoids the A'B or A'C redundancy, this option would be overly complex.
At this point, we should compare how the K-map grouping typically collapses for segment c. If the map shows a large grouping that eliminates dependence on A entirely and leaves a simple sum involving C', B, and D, then Option B would be the minimal expression. The other options either overcount terms or rely on A' in all products, which is often not necessary when B, C, and D can cover the required minterms more efficiently.
Therefore, the reasoning leads to Option B as the most plausible minimal expression for segment c, given the common K-map reduction patterns where a dominant C' term or a B or D term can cover remaining ones, simplifying the expression to C' + B + D.

EE-110 - SEC001 - INTRODUCTION TO DIGITAL LOGIC ❓Quiz 5

Determine the simplified Boolean expression for segment c from using the K-map:

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