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Codiode/Problems/Combinational Logic

Three-Variable K-Map: Minimal SOP vs Minimal POS

MediumLogic CircuitAnalyze

Logic synthesis tools evaluate multiple boolean representations because Sum-of-Products is not always the most efficient silicon implementation. Functions with a high density of 1-cells often yield smaller circuits when synthesized as Product-of-Sums.

A combinational logic block implements a three-variable function f(A, B, C). The function outputs 1 for minterms 0, 2, 3, 4, 5, and 7. All other minterms output 0.

Map the function to a Karnaugh map. Determine the minimal Sum-of-Products (SOP) by grouping the 1-cells and the minimal Product-of-Sums (POS) by grouping the 0-cells. Evaluate the gate count for both implementations assuming standard AND/OR logic where inputs are already available in both true and complemented forms.

Constraints

  • Standard SOP and POS forms must be fully minimized.
  • Gate count assumes multi-input AND/OR gates are available as single gates.
  • Inverters are not included in the gate count.

Topics

boolean-algebrasopposk-mapgate-optimization

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