Four-Variable K-Map: Group That Wraps Across the Top-Bottom Border
Karnaugh maps exploit Gray code adjacency to visually reveal boolean minimizations that are easily missed in algebraic manipulation. The logical structure of a K-map is a torus. The edges connect continuously across the boundaries.
The four-variable K-map below represents a logic function Y with inputs A, B, C, and D.
| A B \ C D | 00 | 01 | 11 | 10 | | :--- | :--- | :--- | :--- | :--- | | 00 | 0 | 1 | 1 | 0 | | 01 | 0 | 0 | 1 | 1 | | 11 | 0 | 0 | 0 | 0 | | 10 | 0 | 1 | 1 | 0 |
Identify all valid prime implicants and determine the minimal sum-of-products expression for Y.
Constraints
- Assume standard sum-of-products (SOP) format.
- Variables in product terms must be ordered alphabetically.
- Use the apostrophe character (') to denote negation.
Topics
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