Question

Simplify the following Boolean expressing using a three-variable K-map.

F (x.y.z) = x' yz+xz

Answer 1

To simplify the Boolean expression F(x,y,z) = x'yz + xz using a three-variable K-map, follow these steps: create the K-map, fill it in with values, identify groups of adjacent 1s, and write the minimized expression.

Step-by-step explanation:

To simplify the Boolean expression F(x,y,z) = x'yz + xz using a three-variable K-map, we can follow these steps:

1. First, we need to create the K-map for the given expression. The K-map for three variables (x, y, z) will have 8 cells.
2. Fill in the K-map with the values of the expression for each combination of variables x, y, and z. For the given expression F(x,y,z) = x'yz + xz, you can use the values of 0 or 1 for each cell based on the Boolean expression.
3. Identify the groups of adjacent 1s in the K-map. Each group should have 2^n cells, where n is a non-negative integer.
4. Write down the minimized Boolean expression by combining these groups of adjacent 1s in the K-map. In this case, the expression will be F(x,y,z) = xz.

So, the simplified Boolean expression using a three-variable K-map is F(x,y,z) = xz.