Ee2 chapter5 de_morgan'stheorem

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Ee2 chapter5 de_morgan'stheorem

  1. 1. IT2001PAEngineering Essentials (2/2)Chapter 5 - DeMorgans Theorem Lecturer Namelecturer_email@ite.edu.sg Nov 20, 2012Contact Number
  2. 2. Chapter 5 - DeMorgans TheoremLesson ObjectivesUpon completion of this topic, you should be able to: State DeMorgans Theorem. IT2001PA Engineering Essentials (2/2) 2
  3. 3. Chapter 5 - DeMorgans TheoremSpecific Objectives Students should be able to :  State the purposes of DeMorgan’s Theorem.  State the two basic theorems in Boolean algebra (DeMorgan’s Theorem). A*B=A+B A+B=A*B IT2001PA Engineering Essentials (2/2)
  4. 4. Chapter 5 - DeMorgans TheoremIntroduction DeMorgans theorems are extremely useful in simplifying expressions in which a product or sum of variables is inverted. IT2001PA Engineering Essentials (2/2) 4
  5. 5. Chapter 5 - DeMorgans TheoremDeMorgan’s Theorem DeMorgan’s Theorem (1) states that when the OR sum of two variables is inverted, it is the same as inverting each variable individually and then ANDing these inverted variables. DeMorgan’s Theorem (2) states that when the AND product of two variables is inverted, it is the same as inverting each variable individually and then ORing them. IT2001PA Engineering Essentials (2/2) 5
  6. 6. Chapter 5 - DeMorgans TheoremSteps to Apply DeMorgan’s Theorem DeMorgan’s Theorem A*B=A+B A+B=A*B DeMorgans theorem can be applied in 3 steps :  Complement the entire expression.  Change all OR signs to AND and all AND signs to ORs.  Complement each of the individual variables. IT2001PA Engineering Essentials (2/2) 6
  7. 7. Chapter 5 - DeMorgans TheoremStep 1: Complement the entire expression. Complement entire expression IT2001PA Engineering Essentials (2/2) 7
  8. 8. Chapter 5 - DeMorgans TheoremStep 2: Change all OR signs to ANDs and allANDs signs to ORs Complement entire expression Change OR sign to AND sign IT2001PA Engineering Essentials (2/2) 8
  9. 9. Chapter 5 - DeMorgans TheoremStep 3: Complement each of the individualvariables. Complement entire expression Change OR sign to AND sign Complement each variable IT2001PA Engineering Essentials (2/2) 9
  10. 10. Chapter 5 - DeMorgans TheoremResult IT2001PA Engineering Essentials (2/2) 10
  11. 11. Chapter 5 - DeMorgans TheoremImplications of DeMorgan’s Theorem x+y=x.y A A B A+B = B A.B The above two representations are equivalent. A NOR gate is equivalent to an AND gate with inverters on each of its inputs. IT2001PA Engineering Essentials (2/2) 11
  12. 12. Chapter 5 - DeMorgans TheoremImplications of DeMorgan’s Theorem A NAND gate is equivalent to an OR gate with inverters on each of its inputs. IT2001PA Engineering Essentials (2/2) 12
  13. 13. Chapter 5 - DeMorgans TheoremNext Lesson IT2001PA Engineering Essentials (2/2) 13

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