Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

No Downloads

Total views

285

On SlideShare

0

From Embeds

0

Number of Embeds

0

Shares

0

Downloads

26

Comments

0

Likes

1

No embeds

No notes for slide

- 1. IT2001PAEngineering Essentials (2/2)Chapter 5 - DeMorgans Theorem Lecturer Namelecturer_email@ite.edu.sg Nov 20, 2012Contact Number
- 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. 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. 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. 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. 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. Chapter 5 - DeMorgans TheoremStep 1: Complement the entire expression. Complement entire expression IT2001PA Engineering Essentials (2/2) 7
- 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. 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. Chapter 5 - DeMorgans TheoremResult IT2001PA Engineering Essentials (2/2) 10
- 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. 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. Chapter 5 - DeMorgans TheoremNext Lesson IT2001PA Engineering Essentials (2/2) 13

No public clipboards found for this slide

×
### Save the most important slides with Clipping

Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.

Be the first to comment