Question

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

Answer 1

Answer on Question #42971, Math, Abstract Algebra

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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