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Codiode/Problems/Combinational Logic

Four-Variable K-Map: Two Valid Minimal Covers Exist

HardLogic CircuitAnalyze

Logic synthesis tools frequently encounter multiple equivalent optimal circuits when minimizing Boolean functions, requiring arbitrary choices to proceed.

The four-variable Karnaugh map below defines the function F(A, B, C, D) using standard minterm notation. The ones are placed at minterms m(0, 1, 4, 5, 6, 7, 10, 11, 14, 15). All other positions evaluate to zero.

Identify the essential prime implicants required for any valid solution. Determine the remaining uncovered minterms and evaluate the available prime implicants that can cover them. Extract all valid minimal Sum of Products (SOP) expressions for F and establish why they are mathematically equivalent.

Constraints

  • Assume standard K-map variable ordering where AB defines the rows and CD defines the columns.
  • A minimal SOP expression must contain the absolute minimum number of product terms, and the minimum total number of literals across those terms.

Topics

Boolean AlgebraMinimizationKarnaugh MapPrime Implicants

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