Question

Simplify the following Boolean function:
F = A’C + A’B + AB’C + BC, using K-map?

Answer 1

Answer on Question # 43500, Engineering, Other

Task: Simplify the following Boolean function:

$$F = A'C + A'B + AB'C + BC$$

, using K-map?

Solution:

So, we must do for simplifying the following Boolean function:

1. Construct a K-map.

2. Find all groups of horizontal or vertical adjacent squares that contain 1.

a. Each group must be either rectangular or square with 2° squares.

b. Each group should be as large as possible.

c. Each 1 on the K-map must be covered at least once. The same 1 can be included in several groups if necessary.

d. Nonessential groups are omitted. (A nonessential group does not contain a 1 that is not covered by any other group)

e. Adjacency applies to both vertical and horizontal borders.

3. Translate each group into a product term by eliminating any variable whose value changes from cell to cell.

4. Sum all the product terms.

$$F = A'C + A'B + AB'C + BC$$$$F = C + A'B$$

Answer:

$$F = C + A'B$$

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