Question

Create the Kmaps and then simplify for the following function: F(x, y, z) = x'y'z' + x'yz' + xy'z' + xyz'

Answer 1

To simplify the function F(x, y, z) = x'y'z' + x'yz' + xy'z' + xyz', we can create K-maps for each term and then combine the resulting simplified expressions.

Step-by-step explanation:

To simplify the given function F(x, y, z) = x'y'z' + x'yz' + xy'z' + xyz', we can create a Karnaugh map (K-map) for each term and then combine the resulting simplified expressions.

Here are the K-maps for each term:

x'y'z':

1. On the K-map for x'y'z', mark the cell where x=0, y=0, and z=0 with a 1.
2. Combine the marked cells to obtain the simplified expression: x'y'z' = z'

x'yz':

1. On the K-map for x'yz', mark the cell where x=0, y=1, and z=0 with a 1.
2. Combine the marked cells to obtain the simplified expression: x'yz' = y'z'

xy'z':

1. On the K-map for xy'z', mark the cell where x=1, y=0, and z=0 with a 1.
2. Combine the marked cells to obtain the simplified expression: xy'z' = x'z'

xyz':

1. On the K-map for xyz', mark the cell where x=1, y=1, and z=0 with a 1.
2. Combine the marked cells to obtain the simplified expression: xyz' = x'z'

Now, we can combine the simplified expressions: z' + y'z' + x'z' + x'z' = z' + y'z' + x'z'