Final answer:
The Boolean equation can be simplified using the K-Map method, after which the minimal SOP can be realized using NAND & NOR gates through conversions and the application of De Morgan's theorem.
Step-by-step explanation:
To solve the Boolean equation F=∑m(0,2,3,6,7)+d(8,10,11,15) using the K-Map method for simplification, you'll consider 1s for the minterms (0,2,3,6,7) and Xs for the don't-care conditions (8,10,11,15) in a four-variable K-Map. Aiming for the minimal Sum of Products (SOP), you'd group the 1s and Xs maximally to simplify the equation. Once the minimal expression is obtained, you can realize it using only NAND & NOR gates by first converting the SOP to Product of Sums (POS) if necessary and then applying the De Morgan's theorem to construct the circuit with the available logic gates. Without the actual K-Map presented in the question, we cannot visualize the groups or propose the specific minimal SOP expression and the corresponding NAND/NOR realization.