Electronics Engineering (ELEX) Board Practice Exam

Which combination cannot be grouped in Karnaugh maps?

1. Adjacent corners

2. Horizontal pairs

3. Vertical pairs

4. Diagonal corners

The correct answer is: Diagonal corners

In Karnaugh maps, groupings of adjacent cells are used to simplify Boolean expressions. The ability to combine cells is crucial to attain the simplest form of a logic function. When considering the combinations mentioned, adjacent corners cannot be groups in a standard Karnaugh map. This is primarily because adjacency in a Karnaugh map refers to shared sides or edges, while diagonal corners do not share edges. In essence, for a grouping to be valid, the cells must be directly next to each other either horizontally or vertically. Horizontal pairs and vertical pairs are valid groupings as they involve cells that are side-by-side or stacked directly on top of each other, allowing for effective simplification of the Boolean expression. Adjacent corners and pairs positioned horizontally or vertically adhere to the rules of forming groups, but diagonal corners break this guideline since they do not meet the adjacency criteria defined by the map structure. Thus, diagonal corners cannot be grouped because they break the fundamental principle of adjacency required for effective grouping in Karnaugh maps, making them non-compliant with the rules of simplification.