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Codiode/Problems/Combinational Logic

Five-Variable K-Map: Find a Minimal SOP with Both Within-Half and Cross-Fold Groups

HardLogic CircuitAnalyze

Logic synthesis tools optimize hardware routing area by identifying shared implicants across split address spaces.

The function F(A, B, C, D, E) is mapped onto a five-variable Karnaugh map split into two four-variable halves. The left half represents A = 0 and the right half represents A = 1.

The map contains exactly six active minterms where F = 1: m0, m1, and m15 in the A = 0 half, and m16, m20, and m31 in the A = 1 half. All other cells evaluate to 0.

Determine the minimal Sum-of-Products (SOP) expression for F by identifying the optimal combination of within-half and cross-fold prime implicants.

Constraints

  • The five variables are ordered A, B, C, D, E where A is the most significant bit.
  • A cross-fold group must consist of identical cell positions in both the A = 0 and A = 1 halves.
  • Minimal SOP implies the fewest number of product terms, followed by the fewest number of literals.

Topics

Boolean AlgebraLogic MinimizationK-Map5-Variable

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