Answer :
From the K-map, we can see that there are two groups of adjacent 1's. Grouping these 1's, we get the following simplified Boolean function:[tex]\[F(a, b, c, d, e, f, g) = \overline{a}e + \overline{b}ef + c\overline{d}g\].[/tex]
To obtain the simplified Boolean function of F(a, b, c, d, e, f, g) from the given minterms, we need to use the Karnaugh map (K-map) method.
Here are the minterms provided: m(78, 82, 100, 101, 104, 108).
Let's construct a Karnaugh map with inputs abcdefg and group the minterms based on the binary representation of their indices.
Now, let's fill in the K-map with the corresponding minterms.
From the K-map, we can see that there are two groups of adjacent 1's. Grouping these 1's, we get the following simplified Boolean function:
[tex]\[F(a, b, c, d, e, f, g) = \overline{a}e + \overline{b}ef + c\overline{d}g\][/tex]
This is the simplified Boolean function for the given minterms m(78, 82, 100, 101, 104, 108).
To know more about simplified Boolean function:
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