Chapter 5 Karnaugh Maps

# Chapter 5 Karnaugh Maps

## Chapter 5 Karnaugh Maps

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##### Presentation Transcript

1. 1 Chapter 5 Karnaugh Maps Mei Yang

2. 2 Minimum Forms of Switching Functions When a function is realized using AND and OR gates, the cost is directly related the number of gates and gate inputs used. Minimum SOP: A SOP form which (a) has a minimum number of terms and (b) for those expressions which have the same minimum number of terms, has a minimum number of literals. Minimum POS: A POS form which (a) has a minimum number of terms and (b) for those expressions which have the same minimum number of terms, has a minimum number of literals.

3. 3 Minimizing from Minterm form

4. 4 Why Kmap? Problems with the simplification method using Boolean algebra The procedures are difficult to apply in systematic way. It is difficult to tell when you have arrived at a minimum solution. Kmap is a systematic method, which is especially useful for simplifying functions with three or four variables.

5. 5 Plotting Kmaps From truth tables From minterm/maxterm expansions From algebraic expressions Examples on pp. 122-124

6. 6 2-Variable Karnaugh Map

7. 7 3-Variable Karnaugh Map

8. 8 Grouping Principle Groupings can contain only 1s; no 0s. Groups can be formed only at right angles; diagonal groups are not allowed. The number of 1s in a group must be a power of 2 – even if it contains a single 1. The groups must be made as large as possible. Groups can overlap and wrap around the sides of the Kmap. Use the fewest number of groups possible.

9. 9 Grouping of adjacent 1’s

10. 10 3-Variable Karnaugh Map

11. 11

12. 12

13. 13

15. 15 Grouping Example

16. 16 Grouping Example

17. 17 More than One Way of Grouping

18. 18 A Systematic Way for Minimization

19. 19

20. 20

21. 21 Grouping Zeros

22. 22 Minimization Rules

23. 23

24. 24

25. 25 More than one solution

26. 26 Two solutions

27. 27

28. 28

29. 29 5-Variable Karnaugh Map

30. 30 5-Variable Karnaugh Map

31. 31 Example 1: F = ?m(1,2,3,5,6,8,9,10,11,13,24, 25, 26, 27,29)

32. 32 Example 2: F = ?m (0,1,2,4,5,8,9,10,17,18,19,25,26)
The text passage is a transcript or set of slides from a presentation on Karnaugh Maps, which are used in digital logic design to simplify Boolean algebra expressions. It covers the basics of Karnaugh Maps, including how to plot them, the grouping principle, and examples of minimization.
no_question

the passage does not contain any explicit mathematical questions or problems that require solving. it is primarily instructional, explaining concepts and methods related to karnaugh maps.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Chapter 5 Karnaugh Maps

# Chapter 5 Karnaugh Maps

## Chapter 5 Karnaugh Maps

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
##### Presentation Transcript

1. 1 Chapter 5 Karnaugh Maps Mei Yang

2. 2 Minimum Forms of Switching Functions When a function is realized using AND and OR gates, the cost is directly related the number of gates and gate inputs used. Minimum SOP: A SOP form which (a) has a minimum number of terms and (b) for those expressions which have the same minimum number of terms, has a minimum number of literals. Minimum POS: A POS form which (a) has a minimum number of terms and (b) for those expressions which have the same minimum number of terms, has a minimum number of literals.

3. 3 Minimizing from Minterm form

4. 4 Why Kmap? Problems with the simplification method using Boolean algebra The procedures are difficult to apply in systematic way. It is difficult to tell when you have arrived at a minimum solution. Kmap is a systematic method, which is especially useful for simplifying functions with three or four variables.

5. 5 Plotting Kmaps From truth tables From minterm/maxterm expansions From algebraic expressions Examples on pp. 122-124

6. 6 2-Variable Karnaugh Map

7. 7 3-Variable Karnaugh Map

8. 8 Grouping Principle Groupings can contain only 1s; no 0s. Groups can be formed only at right angles; diagonal groups are not allowed. The number of 1s in a group must be a power of 2 – even if it contains a single 1. The groups must be made as large as possible. Groups can overlap and wrap around the sides of the Kmap. Use the fewest number of groups possible.

9. 9 Grouping of adjacent 1’s

10. 10 3-Variable Karnaugh Map

11. 11

12. 12

13. 13

15. 15 Grouping Example

16. 16 Grouping Example

17. 17 More than One Way of Grouping

18. 18 A Systematic Way for Minimization

19. 19

20. 20

21. 21 Grouping Zeros

22. 22 Minimization Rules

23. 23

24. 24

25. 25 More than one solution

26. 26 Two solutions

27. 27

28. 28

29. 29 5-Variable Karnaugh Map

30. 30 5-Variable Karnaugh Map

31. 31 Example 1: F = ?m(1,2,3,5,6,8,9,10,11,13,24, 25, 26, 27,29)

32. 32 Example 2: F = ?m (0,1,2,4,5,8,9,10,17,18,19,25,26)
user
The text passage is a transcript or set of slides from a presentation on Karnaugh Maps, which are used in digital logic design to simplify Boolean algebra expressions. It covers the basics of Karnaugh Maps, including how to plot them, the grouping principle, and examples of minimization.

TYPE: NO_QUESTION

The passage does not contain any explicit mathematical questions or problems that require solving. It is primarily instructional, explaining concepts and methods related to Karnaugh Maps.