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# Ee2 chapter6 applicationof_demorgan'stheorem

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• 1. IT2001PAEngineering Essentials (2/2)Chapter 6 - Application of DeMorgansTheorem Lecturer Namelecturer_email@ite.edu.sg Nov 20, 2012Contact Number
• 2. Chapter 6 - Application of DeMorgans TheoremLesson ObjectivesUpon completion of this topic, you should be able to: Use DeMorgans theorems to derive equivalent logic gate symbols. IT2001PA Engineering Essentials (2/2) 2
• 3. Chapter 6 - Application of DeMorgans TheoremSpecific Objectives Students should be able to :  Simplify Boolean expressions using DeMorgan’s theorems.  Draw the equivalent logic gate circuits after simplifying the Boolean expressions. IT2001PA Engineering Essentials (2/2)
• 4. Chapter 6 - Application of DeMorgans TheoremRevision A practical operational way to look at DeMorgans Theorem :  inversion bar of an expression may be broken at any point.  the operation at that point replaced by its opposite (i.e., AND replaced by OR or vice versa). IT2001PA Engineering Essentials (2/2) 4
• 5. Chapter 6 - Application of DeMorgans TheoremExample 1 Simplify the circuit below using DeMorgan’s Theorem IT2001PA Engineering Essentials (2/2) 5
• 6. Chapter 6 - Application of DeMorgans TheoremExample 1 First step in the process is by writing the outputs for the And gate and the inverter. IT2001PA Engineering Essentials (2/2) 6
• 7. Chapter 6 - Application of DeMorgans TheoremExample 1 Next, label the outputs of the first NOR gate and the NAND gate IT2001PA Engineering Essentials (2/2) 7
• 8. Chapter 6 - Application of DeMorgans TheoremExample 1 Finally, we write an expression (or pair of expressions) for the last NOR gate. IT2001PA Engineering Essentials (2/2) 8
• 9. Chapter 6 - Application of DeMorgans TheoremExample 1 Now, we reduce this expression, using the identities, properties, rules, and theorems (DeMorgans) of Boolean algebra. IT2001PA Engineering Essentials (2/2) 9
• 10. Chapter 6 - Application of DeMorgans TheoremWorking IT2001PA Engineering Essentials (2/2) 10
• 11. Chapter 6 - Application of DeMorgans TheoremExample 1 The equivalent gate circuit for this much-simplified expression is as follows IT2001PA Engineering Essentials (2/2) 11
• 12. Chapter 6 - Application of DeMorgans Theorem Example 2 Write the Boolean equation for the circuit shown  simplify the equation  draw the logic circuit of the  simplified equation. B B B(A+C) A (A+C) C X Warning buzzer C FIG 1 IT2001PA Engineering Essentials (2/2) 12
• 13. Chapter 6 - Application of DeMorgans Theorem Solution A B Warning C buzzer X=A*B + C IT2001PA Engineering Essentials (2/2) 13
• 14. Chapter 6 - Application of DeMorgans Theorem Example Write the Boolean equation for the circuit shown  Use DeMorgan’s theorem and then Boolean algebra rule to  simplify the equation  draw the logic circuit of the simplified equation. A B X C FIG 2 IT2001PA Engineering Essentials (2/2) 14
• 15. Chapter 6 - Application of DeMorgans Theorem Solution A Not used B X=B* C C Simplified logic circuit for Fig 2. IT2001PA Engineering Essentials (2/2) 15
• 16. Chapter 6 - Application of DeMorgans TheoremDeMorgan’s Application DeMorgan’s Theorem is useful in the implementation of the basic gate operations with alternative gates, particularly with NAND and NOR gates which are readily available in IC form. IT2001PA Engineering Essentials (2/2) 16
• 17. Chapter 6 - Application of DeMorgans TheoremNext Lesson IT2001PA Engineering Essentials (2/2) 17