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Chapter 4

Chapter 4. Boolean Algebra and Logic Simplification. Boolean Operations and Expressions. Boolean Addition (OR). Boolean Multiplication (AND). Laws and Rules of Boolean Algebra. Laws: Commutative Associative Distributive Rules. Figure 4--1 Application of commutative law of addition.

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Chapter 4

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  1. Chapter 4 Boolean Algebra and Logic Simplification

  2. Boolean Operations and Expressions • Boolean Addition (OR)

  3. Boolean Multiplication (AND)

  4. Laws and Rules of Boolean Algebra • Laws: • Commutative • Associative • Distributive • Rules

  5. Figure 4--1 Application of commutative law of addition.

  6. Figure 4--2 Application of commutative law of multiplication.

  7. Figure 4--3 Application of associative law of addition

  8. Figure 4--4 Application of associative law of multiplication

  9. Figure 4--5 Application of distributive law

  10. Rules of Boolean Algebra

  11. Figure 4--6 RULE 1

  12. Figure 4--7 RULE 2

  13. Figure 4--8 RULE 3

  14. Figure 4--9 RULE 4

  15. Figure 4--10 RULE 5

  16. Figure 4--11 RULE 6

  17. Figure 4--7 RULE 7

  18. Figure 4--13 RULE 8

  19. Figure 4--14 RULE 9

  20. DeMorgan’s Theorem Figure 4--15 Gate equivalencies and the corresponding truth tables that illustrate DeMorgan’s theorems. Notice the equality of the two output columns in each table. This shows that the equivalent gates perform the same logic function.

  21. Boolean Expression for a Logic Circuit Figure 4--16 A logic circuit showing the development of the Boolean expression for the output.

  22. Constructing a Truth Table for a Logic Circuit • Evaluating the expression and putting results in truth table format

  23. Simplification Using Boolean Algebra

  24. Figure 4--17 Gate circuits for Example 4-8

  25. Standard Forms of Boolean Expressions • Sum-of-Products (SOP) Form • Product-of-Sum (POS) Form

  26. SOP Form Figure 4--18 Implementation of the SOP expression AB + BCD + AC.

  27. Standard SOP Form

  28. Binary Representation of Product Term

  29. POS Form Figure 4--19 Implementation of the POS expression (A + B)(B + C + D) (A + C).

  30. Standard POS Form

  31. Binary Representation of Sum Term

  32. Converting Standard SOP to Standard POS

  33. Converting SOP to Truth Table

  34. Converting POS to Truth Table

  35. Determining Standard Expressions from Truth Table

  36. Karnaugh Map Figure 4--20 A 3-variable Karnaugh map showing product terms.

  37. Figure 4--21 A 4-variable Karnaugh map.

  38. Figure 4--22 Adjacent cells on a Karnaugh map are those that differ by only one variable. Arrows point between adjacent cells.

  39. Karnaugh Map SOP Minimization Figure 4--23 Example of mapping a standard SOP expression.

  40. Figure 4--24

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