Karnaugh map adjacency rule: In a K-map, the cell in the top row is considered adjacent to the corresponding cell directly below it in the bottom row due to wraparound. Assess this statement.

Electronics Combinational Logic Circuits Difficulty: Easy
Choose an option
  • A
    Correct
  • B
    Incorrect
  • C
    Only true for 2-variable maps
  • D
    Only true for don’t-care cells

Answer

Correct Answer: Correct

Explanation

Introduction / Context: Karnaugh maps (K-maps) visualize adjacency in Boolean spaces, enabling grouping of 1-cells to simplify expressions. The map wraps around at the edges so that cells differing in only one variable are considered neighbors even across boundaries.Given Data / Assumptions:

  • K-map uses Gray-coded ordering along rows and columns.
  • Edge adjacency follows toroidal wraparound (left-right and top-bottom).
  • Adjacency implies one-bit Hamming distance between cells.

Concept / Approach: Because the variable ordering is Gray coded, the first and last rows (and columns) differ by only one variable for corresponding columns (or rows). Therefore, the top-row cell and the bottom-row cell directly beneath/above it are adjacent, allowing valid grouping across the border.Step-by-Step Solution:

Consider a 4-variable K-map with rows AB and columns CD in Gray code.Row AB = 00 (top) and AB = 01, 11, 10 (middle), and AB = 00 wraps to AB = 10 (bottom) with one-bit difference.Thus, top/bottom cells align as neighbors for grouping 2, 4, 8, etc. cells.This enables larger implicants and greater simplification.

Verification / Alternative check:

Draw a 3- or 4-variable K-map and confirm that opposite edges correspond to single-bit changes; edges are conceptually “touching.”

Why Other Options Are Wrong:

Incorrect: Ignores the Gray code and toroidal adjacency.Only true for 2-variable / don’t-care cells: Adjacency rules are general; don’t-cares can be used, but they are not required for edge adjacency.

Common Pitfalls:

Treating the K-map as a flat grid without wraparound, which prevents optimal grouping.Misaligning Gray code order, breaking single-bit adjacency.

Final Answer:

Correct
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