Five-Variable K-Map: Find a Minimal SOP with Both Within-Half and Cross-Fold Groups
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, EwhereAis the most significant bit. - A cross-fold group must consist of identical cell positions in both the
A = 0andA = 1halves. - Minimal SOP implies the fewest number of product terms, followed by the fewest number of literals.
Topics
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