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Codiode/Problems/Combinational Logic

Three-Variable K-Map with Don't-Cares

MediumLogic CircuitAnalyze

Logic synthesis tools exploit undefined states in state machines to aggressively reduce gate counts. The truth table below defines a 3-variable function with inputs A, B, and C, and output Y. The output contains three active minterms and two don't-care conditions represented by X.

| A | B | C | Y | |---|---|---|---| | 0 | 0 | 0 | 1 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | X | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | X | | 1 | 1 | 1 | 0 |

Evaluate the function and determine the minimal Sum of Products expression. Identify which don't-care cells minimize the logic and which bloat the final circuit.

Constraints

  • Standard Karnaugh map grouping rules apply.
  • Groups must be rectangular and contain a power-of-two number of cells.
  • The final expression must be in minimal Sum of Products (SOP) form.

Topics

Boolean AlgebraMinimizationK-MapDont Cares

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