Four-Variable K-Map: Minimal SOP Has More Terms Than Minimal POS
Logic synthesis tools evaluate both sum-of-products and product-of-sums forms to minimize standard cell area. Defaulting to one form without analyzing the truth table often leads to redundant hardware.
The Boolean function F(A, B, C, D) is specified by the minterms m(4, 5, 7, 8, 9, 11, 12, 13, 15). The corresponding maxterms are M(0, 1, 2, 3, 6, 10, 14).
Map the function to determine the minimal SOP and POS expressions for F. Evaluate the gate count required for a two-level implementation of each form to identify the most efficient hardware mapping.
Constraints
- Assume all inputs
A,B,C, andDare available in both true and complement forms. - Gate count calculations should include all necessary AND, OR, or NOR gates in a standard two-level implementation.
- Do not count inverters used for input signals.
Topics
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