Question

Using Karnaugh maps, determine a minimal SOP and POS expression for each of the following Boolean functions

a) f(x, y, z) = Σm(1, 3, 4, 5, 6, 7)

Answer 1

To determine the minimal SOP and POS expressions for the given Boolean function f(x, y, z) = Σm(1, 3, 4, 5, 6, 7), we can use Karnaugh maps. The minimal SOP expression is x'z + y'z, and the minimal POS expression is (x+y')(x+z')(y+z).

Step-by-step explanation:

To determine the minimal SOP and POS expressions for the given Boolean function, we can use Karnaugh maps. The expression f(x, y, z) = ∑m(1, 3, 4, 5, 6, 7) represents a sum of minterms.

We start by constructing a Karnaugh map for three variables (x, y, z). Then we fill in the corresponding minterms with 1s in the map. We group adjacent 1s to form a minimal SOP expression. In this case, the groups are (1, 3), (4, 5, 6, 7).

Converting these groups to SOP expression, we get f(x, y, z) = x'z + y'z.

For the POS expression, we group adjacent 0s in the Karnaugh map instead. The groups are (0, 2), (0, 1, 3).

Converting these groups to POS expression, we get f(x, y, z) = (x+y')(x+z')(y+z).