Karnaugh map grouping rules When combining adjacent 1-cells in a K-map during simplification, groups must contain how many cells?

Introduction / Context:Karnaugh maps (K-maps) visually minimize Boolean expressions by grouping adjacent cells. Proper grouping directly reduces literal count and gate usage in the final logic circuit.

Given Data / Assumptions:

• We group adjacent 1s (for SOP) on a map arranged in Gray-code order.
• Wrap-around adjacency (edges touch) is allowed.
• Goal: largest possible groups to maximize simplification.

Concept / Approach:Legal K-map groups must contain a number of cells equal to a power of two. This ensures that one or more variables drop out (become don’t-cares) when forming the simplified product term. Valid group sizes are 1, 2, 4, 8, 16, and so on, depending on map size.

Step-by-Step Solution:Identify adjacent 1-cells.Combine them into the largest possible groups of size 1, 2, 4, 8, etc.Translate each group into a product term where changing variables are eliminated.OR all product terms to obtain the minimized SOP expression.

Verification / Alternative check:Examine an example: a 4-variable K-map allows groups of 1, 2, 4, 8, or 16 cells. Each doubling removes another variable from the corresponding product term.

Why Other Options Are Wrong:“2s” or “4s” only: too restrictive; valid groups are not limited to a single size.“3s”: invalid—groups must be powers of two to eliminate variables cleanly.

Common Pitfalls:Overlooking wrap-around adjacency and forming smaller groups than necessary, which leads to suboptimal simplification.

Final Answer:1, 2, 4, 8, etc.