1. IT2001PA
Engineering Essentials (2/2)
Chapter 6 - Application of DeMorgan's
Theorem
Lecturer Name
lecturer_email@ite.edu.sg
Nov 20, 2012
Contact Number

2. Chapter 6 - Application of DeMorgan's Theorem
Lesson Objectives
Upon completion of this topic, you should be able to:
 Use DeMorgan's theorems to derive equivalent logic
gate symbols.
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3. Chapter 6 - Application of DeMorgan's Theorem
Specific 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 DeMorgan's Theorem
Revision
 A practical operational way to look at DeMorgan's
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).
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5. Chapter 6 - Application of DeMorgan's Theorem
Example 1
 Simplify the circuit below using DeMorgan’s Theorem
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6. Chapter 6 - Application of DeMorgan's Theorem
Example 1
 First step in the process is by writing the outputs for the
And gate and the inverter.
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7. Chapter 6 - Application of DeMorgan's Theorem
Example 1
 Next, label the outputs of the first NOR gate and the
NAND gate
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8. Chapter 6 - Application of DeMorgan's Theorem
Example 1
 Finally, we write an expression (or pair of expressions)
for the last NOR gate.
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9. Chapter 6 - Application of DeMorgan's Theorem
Example 1
 Now, we reduce this expression,
 using the identities, properties, rules, and theorems
(DeMorgan's) of Boolean algebra.
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10. Chapter 6 - Application of DeMorgan's Theorem
Working
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11. Chapter 6 - Application of DeMorgan's Theorem
Example 1
 The equivalent gate circuit for this much-simplified
expression is as follows
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12. Chapter 6 - Application of DeMorgan's 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
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13. Chapter 6 - Application of DeMorgan's Theorem
Solution
A
B
Warning
C buzzer
X=A*B + C
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14. Chapter 6 - Application of DeMorgan's 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
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15. Chapter 6 - Application of DeMorgan's Theorem
Solution
A Not used
B
X=B* C
C
Simplified logic circuit for Fig 2.
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16. Chapter 6 - Application of DeMorgan's Theorem
DeMorgan’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.
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17. Chapter 6 - Application of DeMorgan's Theorem
Next Lesson
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