Karnaugh Map (K-Map) Fundamentals
📌 The primary goal of using a K-Map is simplifying Boolean functions to achieve an equivalent function with fewer literals or operations, leading to simpler circuits.
🗺️ The K-Map, invented by Maurice Karnaugh in 1953, is a graphical method using square cells representing minterms, where adjacent cells differ by only one literal.
🔢 For two variables (X and Y), the cell ordering (e.g., 00, 01, 11, 10) is crucial, ensuring only a single variable changes between neighboring cells.

K-Map Structure for Different Variables
📐 K-Maps for two variables use four squares; for three variables, they use eight squares, with a specific ordering for the columns/rows (e.g., for three variables X, Y, Z, the columns might be 00, 01, 11, 10 for YZ).
🔗 The adjacency rule—where neighboring cells differ by only one literal—applies universally across all dimensions (rows and columns) of the K-Map.
🔢 K-Maps for four variables follow the same adjacency principle, maintaining the sequential change of only one literal between adjacent cells.

Filling and Utilizing the K-Map
✅ To fill the K-Map, cells corresponding to '1' (true) in the function are marked with '1', and the rest are typically filled with '0' (or left blank if only grouping the '1's).
🔲 Minterms are mapped based on their binary representation; for example, $x'yz'$ (010) corresponds to the cell where X is 0, Y is 1, and Z is 0.
📝 K-Maps can be populated directly from the function's expression or derived from a Truth Table by transferring each '1' output to its corresponding cell.

Key Points & Insights
➡️ Simplification means fewer logic gates, resulting in simpler and often more cost-effective circuit implementation.
➡️ Always verify the Gray code ordering (00, 01, 11, 10) in rows and columns, as incorrect sequencing violates the adjacency rule.
➡️ K-Maps provide a visual shortcut for applying Boolean algebra laws to reduce complex expressions efficiently.

📸 Video summarized with SummaryTube.com on Oct 13, 2025, 02:26 UTC