Final answer:
The student asked how to simplify a Boolean equation with K-Map for its minimal SOP and POS forms and then realize the circuits using NAND and NOR gates, respectively.
Step-by-step explanation:
The student is asking about the simplification of a Boolean equation using the K-Map method, specifically asking for minimal Sum of Products (SOP) and Products of Sums (POS) forms. The equation given is F=Σm(0,2,3,6,7)+d(8,10,11,15), where 'm' denotes the min terms (which are the values for which the function is 1) and 'd' denotes the don't-care conditions (values for which the function can be either 0 or 1).
To obtain minimal SOP expressions, K-Maps are used to group adjacent ones and don't-care conditions to simplify the expression as much as possible. Once the simplified SOP form is obtained, it can be realized using only NAND gates, or a combination of NAND and NOR gates, by applying De Morgan's theorem and using NAND gates in place of AND and OR gates.
For minimal POS, the same K-Map process is applied but for the zeros instead of the ones. The simplified POS expression can then be realized using NOR gates, or a combination of NOR and NAND gates, following a similar logic and using De Morgan's theorem to replace OR gates with NOR gates and AND gates with NAND gates.
The answer involves concepts from digital logic design and circuit synthesis, two areas of Electronic Engineering. It is important to understand the use of Karnaugh Maps (K-Maps) for simplification and the realization of logic circuits using specific types of gates.