Four-Variable K-Map with Don't Cares: Optimal Use Reduces One Prime Implicant
Logic synthesis tools minimize gate counts by treating undefined states as don't-care conditions, allowing them to selectively expand prime implicants.
The Karnaugh map below defines a four-variable Boolean function F(A, B, C, D). Active minterms are marked with 1, don't-care conditions with X, and all other cells evaluate to 0.
| AB \ CD | 00 | 01 | 11 | 10 | | :--- | :--- | :--- | :--- | :--- | | 00 | 1 | 1 | X | 1 | | 01 | 0 | 0 | 0 | 0 | | 11 | 0 | 0 | 1 | 0 | | 10 | X | X | 0 | 0 |
Determine the minimal sum-of-products (SOP) expression for F. Analyze which don't-care cells contribute to the optimal solution and which ones create unnecessary overlap.
Constraints
- The variables must be ordered
A,B,C,D. - Expressions must be formatted in standard sum-of-products form.
- Use the tick mark (
') for negation, such asA'B.
Topics
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