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## Chapter 5 Karnaugh Maps

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**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

**14. **14 Boolean Adjacency

**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)