際際滷

際際滷Share a Scribd company logo

Karnaugh Map Simplification Rules.pptx

Download as PPTX, PDF
P
Pooja Dixit

The document discusses rules for minimizing Boolean functions using K-maps. It explains that K-maps are used to graphically represent Boolean functions according to the number of variables. Values are filled in the K-map and grouped based on several rules: groups must contain only 0s or 1s but not both; groups can overlap; groups must contain a power of 2 cells and be horizontal or vertical only; groups should be as large as possible with fewest groups overall. Examples are provided to illustrate opposite and corner grouping.

1 of 6
Download to read offline
Prof. Neeraj Bhargava Mrs. Pooja Dixit Department of Computer Science, School of Engineering & System Sciences MDS University Ajmer, Rajasthan
To minimize the given Boolean function, We draw a K Map according to the number of variables it contains. We fill the K Map with 0s and 1s according to its function. Then, we minimize the function in accordance with the following rules. Rule-01: We can either group 0s with 0s or 1s with 1s but we can not group 0s and 1s together. X representing dont care can be grouped with 0s as well as 1s. NOTE There is no need of separately grouping Xs i.e. they can be ignored if all 0s and 1s are already grouped.
Rule-02: Groups may overlap each other. Rule-03: We can only create a group whose number of cells can be represented in the power of 2. In other words, a group can only contain 2n i.e. 1, 2, 4, 8, 16 and so on number of cells. Example-
Rule-04: Groups can be only either horizontal or vertical. We can not create groups of diagonal or any other shape.
Rule-05: Each group should be as large as possible. Example-
Rule-06: Opposite grouping and corner grouping are allowed. The example of opposite grouping is shown illustrated in Rule- 05. The example of corner grouping is shown below. Example- Rule-07: There should be as few groups as possible.

More Related Content

Karnaugh Map Simplification Rules.pptx

  • 1. Prof. Neeraj Bhargava Mrs. Pooja Dixit Department of Computer Science, School of Engineering & System Sciences MDS University Ajmer, Rajasthan
  • 2. To minimize the given Boolean function, We draw a K Map according to the number of variables it contains. We fill the K Map with 0s and 1s according to its function. Then, we minimize the function in accordance with the following rules. Rule-01: We can either group 0s with 0s or 1s with 1s but we can not group 0s and 1s together. X representing dont care can be grouped with 0s as well as 1s. NOTE There is no need of separately grouping Xs i.e. they can be ignored if all 0s and 1s are already grouped.
  • 3. Rule-02: Groups may overlap each other. Rule-03: We can only create a group whose number of cells can be represented in the power of 2. In other words, a group can only contain 2n i.e. 1, 2, 4, 8, 16 and so on number of cells. Example-
  • 4. Rule-04: Groups can be only either horizontal or vertical. We can not create groups of diagonal or any other shape.
  • 5. Rule-05: Each group should be as large as possible. Example-
  • 6. Rule-06: Opposite grouping and corner grouping are allowed. The example of opposite grouping is shown illustrated in Rule- 05. The example of corner grouping is shown below. Example- Rule-07: There should be as few groups as possible.