Is the K-map shown below a faithful representation of the Truth Table?

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BlackTom AI · Accepted Answer

To assess whether a Karnaugh map (K-map) faithfully represents a truth table, we need to compare the map’s cell layout and labeling with the exact minterms of the Boolean function as listed in the truth table.

First, confirm the variable ordering and the Gray-code labeling used on the K-map axes. A faithful K-map must label the rows and columns with adjacent bit patterns that differ by only one variable between neighboring cells. If the labeling deviates from Gray code, or if the order of variables on axes does not match the truth table’s variable order, some minterms will be mapped to incorrect cells, making the K-map unfaithful.

Second, check how each cell corresponds to a truth-table entry. Each cell should represent a specific combination of input variables, and the cell’s value (0, 1, or don't-care) should match the truth table’s output for that input combination. A mismatch in any cell indicates the K-map is not a faithful representation.

Third, consider the wrap-around (edge) adjacencies. K-maps rely on the fact that opposite edges wrap around, so cells on the edges that are logically adjacent in the Boolean space should be grouped together correctly. If wrap-around adjacencies are ignored or misapplied, the map may still look plausible but fail to reflect the actual function, especially when minimizing.

Fourth, account for don’t-care terms if present. If the truth table includes don't-care entries, a faithful K-map should incorporate them accordingly during grouping to achieve a correct minimal expression. Misuse of don't-cares can lead to an incorrect or non-minimal solution, even if the map’s cell values otherwise align.

Fifth, verify consistency with the number of variables. A K-map for n variables has 2^n cells. If the map shown has a different cell count, or if the cell arrangement is inconsistent with the number of input variables in the truth table, the representation cannot be faithful.

Without seeing the actual K-map image and the corresponding truth table entries, these are the key criteria you would use to judge faithfulness. Look for correct Gray-code labeling, proper cell-to-minterm mapping, proper edge wrap-around, appropriate handling of don't-cares, and the correct overall grid size for the number of variables involved.

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

Is the K-map shown below a faithful representation of the Truth Table?

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