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

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BlackTom AI · Accepted Answer

To decide whether the K-map is a faithful representation of the Truth Table, we need to compare the mapping of each input combination to the corresponding cell in the K-map with the actual output from the Truth Table.

First, check the labeling and ordering: in a standard 4-variable K-map, the rows are labeled by AB in Gray code order (00, 01, 11, 10) and the columns by CD in Gray code order (00, 01, 11, 10). If the image uses a non-standard or inconsistent ordering, the cells will not correspond to the same input combinations as in the Truth Table, making the map unfaithful even if the visual placement of 1s looks similar.

Second, examine the cell values: each 1 in the Truth Table should appear in the K-map at the cell corresponding to its AB and CD values. If any row/column pairing in the K-map shows a 1 (or a 0) that contradicts the Truth Table entry for that input combination, the representation is not faithful. Also, don’t confuse don’t-care (X) entries with fixed 0/1 outputs; X entries should be placed in cells marked as dont-care so they can be freely grouped during minimization, but they should not force a 1 where the Truth Table specifies 0 unless you intend to use that flexibility.

Third, consider the handling of unspecified/N/A lines: if the Truth Table includes entries that are not applicable or are labeled differently (e.g., N/A rows), ensure the K-map does not accidentally assign a concrete 0 or 1 to those input combinations. An accurate K-map only covers the defined input combinations; don’t use others to infer incorrect values.

Fourth, look for wrap-around adjacency: K-maps rely on adjacency between edge cells (the leftmost and rightmost columns, as well as top and bottom rows) for grouping. If the map visually places 1s in cells that should be adjacent but the map doesn’t reflect the proper Gray-code adjacency, the map might mislead about possible reductions, even if it initially appears to match the TT.

Fifth, inspect the diagram for any transcription or labeling errors: a mismatch between the depicted variables (e.g., labeling the axes differently, or misplacing a bit in a cell) immediately breaks faithfulness, regardless of how the rest of the map looks.

In summary, without a precise one-to-one check of every input combination against the Truth Table and without confirming Gray-code ordering and proper handling of X/don’t-care entries, you cannot conclusively deem the K-map faithful from the image alone. Common pitfalls to watch for include incorrect AB/CD ordering, wrong cell mapping for specific minterms, misrepresented don’t-care entries, and improper treatment of N/A entries. If any of these are present in the shown diagram, the map is not a faithful representation. If all these aspects align exactly with the Truth Table, then it would be faithful; otherwise, it would not.

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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