Four-Variable K-Map: Essential Group of 2 That Cannot Be Replaced by Any Larger Group
Minimization algorithms in logic synthesis prioritize essential prime implicants over simply finding the largest possible groupings.
The Karnaugh map below defines a four-variable Boolean function Y with inputs A, B, C, and D. Some input combinations produce a don't-care condition, marked as X.
| A B \ C D | 00 | 01 | 11 | 10 | |-------------------|----|----|----|----| | 00 | 0 | 1 | 1 | X | | 01 | 0 | 0 | X | X | | 11 | 1 | 1 | 1 | 1 | | 10 | 0 | 0 | X | X |
Determine the minimal Sum of Products expression for Y. Identify which prime implicants are strictly necessary to cover all valid outputs.
Constraints
- Standard SOP minimization rules apply.
- Don't-care conditions (
X) may be included in groups to increase their size, but do not need to be covered.
Topics
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