K-map grouping rules — which cell combinations are NOT valid to group? In Karnaugh map minimization, identify the combination below that cannot be grouped into valid power-of-two implicants.

Introduction / Context:
Karnaugh maps (K-maps) simplify Boolean expressions by grouping adjacent 1-cells (or 0-cells for POS) into power-of-two blocks. Understanding what counts as adjacency is crucial to form correct groups and achieve minimal logic.

Given Data / Assumptions:

• Adjacency is defined between cells that differ by exactly one variable (Gray code ordering).
• Wrapping is allowed—edges and corners can be adjacent across the map boundaries.
• Groups must be 1, 2, 4, 8, … cells in rectangular shapes.

Concept / Approach:
Valid groupings include horizontally or vertically adjacent cells, with edge wrap making opposite edges (and therefore corners) adjacent. Overlapping groups are permitted when they enable larger implicants. Diagonal cells are not adjacent (they differ in two variables) and therefore cannot be grouped together as a pair by themselves.

Step-by-Step Solution:
Check “corners in the same row/column”: with wrap-around, corner cells can join to form a 2-cell or 4-cell group.Check “overlapping combinations”: allowed if each group size is a power of two and improves simplification.Check “diagonal”: diagonally opposite cells differ in two variables; not adjacent; cannot form a valid 2-cell group.

Verification / Alternative check:
Label a 4-variable K-map in Gray code. Compare coordinates of diagonal cells; Hamming distance is 2, confirming non-adjacency. Contrast with edge-adjacent cells where Hamming distance is 1, validating permitted groupings.

Why Other Options Are Wrong:

• Corners in same row/column: valid due to wrap-around adjacency.
• Overlapping: permitted and often necessary to achieve larger implicants.

Common Pitfalls:

• Forgetting edge wrap makes opposite edges adjacent.
• Forming L-shaped or diagonal-only groups, which violate the rectangular, power-of-two rule.

Final Answer:
diagonal