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If a quad in a K-map appears redundant when grouping is done without wrapping, but becomes useful and necessary after applying wrap-around grouping, should we use the wrapping method and include that quad in the final simplified expression?
If a quad in a K-map appears redundant when grouping is done without wrapping, but becomes useful and necessary after applying wrap-around grouping, should we use the wrapping method and include that quad in the final simplified expression?
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Yes. Wrap-around adjacency is a fundamental K‑map rule, and if a quad only appears when wrapping is used, that quad must be taken as part of the minimal grouping and included in the final simplified expression. K‑map grouping rules Wrapping allowed: In a K‑map, the left and right edges, and the topRead more
Yes. Wrap-around adjacency is a fundamental K‑map rule, and if a quad only appears when wrapping is used, that quad must be taken as part of the minimal grouping and included in the final simplified expression.
K‑map grouping rules
Wrapping allowed: In a K‑map, the left and right edges, and the top and bottom edges, are adjacent; groups may and should wrap around these edges to form larger valid groups.
Largest possible groups: To obtain a minimal expression, always form the largest groups (octets, then quads, then pairs), even if this requires overlapping or wrap‑around groups.
Overlap vs redundancy: Overlapping groups are allowed and often reduce the expression, but a group is redundant only if all its 1s are already covered by other groups and removing it does not leave any 1 uncovered.
Applying this to your situation
See lessIf, after allowing wrap‑around, a quad covers some 1s that would otherwise only be in smaller groups, then that quad is not redundant and should be used; it will generally yield a simpler term.
If a quad becomes completely overlapped by other groups so that every 1 in it is already covered, then it is redundant and should be removed from the final expression; otherwise, include it.