Содержание
- 2. Boolean Algebra Invented by George Boole in 1854 An algebraic structure defined by a set B
- 3. Binary Logic and Gates Binary variables take on one of two values. Logical operators operate on
- 4. Logic Gates In the earliest computers, switches were opened and closed by magnetic fields produced by
- 5. Logical Operations The three basic logical operations are: AND OR NOT AND is denoted by a
- 6. Truth Tables
- 7. Operator Definitions
- 8. Produce a truth table l In the BooleanAlgebra, verify using truth table that (X + Y)’
- 9. 1. Write the boolean expression for the below circuit
- 10. 2. Write the boolean expression for the below circuit
- 11. Problem 1 A system used 3 switches A,B and C; a combination of switches determines whether
- 12. A nuclear power station has a safety system based on three inputs to a logic circuit(network).
- 13. Logic Diagrams and Expressions
- 14. Boolean Algebra
- 15. Some Properties of Boolean Algebra Boolean Algebra is defined in general by a set B that
- 16. Dual of a Boolean Expression Example: F = (A + C) · B + 0 dual
- 17. Boolean Algebraic Proof – Example 1 A + A · B = A (Absorption Theorem) Proof
- 18. Boolean Algebraic Proof – Example 2
- 19. Proof
- 20. Minimization of Boolean Expression
- 21. Simplification of Boolean Algebra (A + B)(A + C) = A + BC This rule can
- 22. Logic Diagram
- 23. Useful Theorems
- 24. De morgan’s Law
- 25. Gate equivalencies and the corresponding truth tables that illustrate De Morgan's theorems.
- 26. Truth Table to Verify De Morgan’s
- 27. Simplification-Example Using Boolean algebra techniques, simplify this expression: AB + A(B + C) + B(B +
- 29. Truth Tables – Cont’d
- 30. Logic Diagram 1 0 0
- 31. Logic Diagram
- 32. Logic Diagram 1 1 0
- 33. Logic Diagram
- 34. Expression Simplification
- 35. Canonical Forms….. Minterms and Maxterms Sum-of-products (SOP) Canonical Form Product-of-sum (POS) Canonical Form Representation of Complements
- 36. Minterms
- 37. Maxterms
- 38. Minterms & Maxterms for 2 variables
- 39. Minterms & Maxterms for 3 variables
- 40. The Standard SOP Form A standard SOP expression is one in which all the variables in
- 41. Converting Product Terms to Standard SOP (example) Convert the following Boolean expression into standard SOP form:
- 42. Sum-Of- Product (SOP)
- 43. Sum-Of-Minterm Examples
- 44. Implementation of an SOP AND/OR implementation NAND/NAND implementation X=AB+BCD+AC A B B C D A C
- 45. The Standard POS Form A standard POS expression is one in which all the variables in
- 46. Converting a Sum Term to Standard POS (example) Convert the following Boolean expression into standard POS
- 47. Product-Of-Maxterm (POM)
- 48. Product-Of-Maxterm Examples
- 49. Converting to Sum-of-Minterms Form
- 50. Converting to Product-of-Maxterms Form
- 51. Conversions Between Canonical Forms
- 52. Standard Sum-of-Products (SOP)
- 53. Three-way light control
- 54. Three-way light control
- 55. Car safety alarm
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