Final answer:
The function G(w, x, y, z) is simplified using a Karnaugh map by grouping adjacent minterms to find the simplest sum of products form. The final simplified expression is G = xz + wžyž + wyž, indicating a combination of three product terms representing the original function.
Step-by-step explanation:
The question asks how to simplify the given function G(w, x, y, z) = ∑m(5,7,8,10,13,14,15) using a Karnaugh map (K-map). To simplify the function, we need to plot the given minterms on a K-map and group the adjacent ones to find the simplest sum of products form of the function.
We start by creating a 4-variable K-map since we have four variables (w, x, y, z). Each cell of the K-map corresponds to a minterm. The 1's are placed in the cells of the K-map correspondent to the given minterms: 5, 7, 8, 10, 13, 14, and 15. After placing the 1's, we look for groups of 1's that can be powers of two (1, 2, 4, 8, etc.). These groups can be made horizontally or vertically but not diagonally, and each group should be as large as possible.
Once the groups are formed, we can determine the simplified expression for each group by looking at which variables are constant within the group. The final expression for the function G is the sum of these simplified expressions. According to the question, the simplification should result in G = xz + wžyž + wyž.