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Apr 13, 2023
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IT2001PAEngineering Essentials (2/2)
Chapter 6 - Application of DeMorgan's Theorem
2
Chapter 6 - Application of DeMorgan's Theorem
IT2001PA Engineering Essentials (2/2)
Lesson Objectives
Upon completion of this topic, you should be able to: Use DeMorgan's theorems to derive equivalent logic
gate symbols.
Chapter 6 - Application of DeMorgan's Theorem
IT2001PA Engineering Essentials (2/2)
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.
4
Chapter 6 - Application of DeMorgan's Theorem
IT2001PA Engineering Essentials (2/2)
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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Chapter 6 - Application of DeMorgan's Theorem
IT2001PA Engineering Essentials (2/2)
Example 1
Simplify the circuit below using DeMorgan’s Theorem
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Chapter 6 - Application of DeMorgan's Theorem
IT2001PA Engineering Essentials (2/2)
Example 1
First step in the process is by writing the outputs for the And gate and the inverter.
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Chapter 6 - Application of DeMorgan's Theorem
IT2001PA Engineering Essentials (2/2)
Example 1 Next, label the outputs of the first NOR gate and the
NAND gate
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Chapter 6 - Application of DeMorgan's Theorem
IT2001PA Engineering Essentials (2/2)
Example 1
Finally, we write an expression (or pair of expressions) for the last NOR gate.
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Chapter 6 - Application of DeMorgan's Theorem
IT2001PA Engineering Essentials (2/2)
Example 1
Now, we reduce this expression,
using the identities, properties, rules, and theorems (DeMorgan's) of Boolean algebra.
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Chapter 6 - Application of DeMorgan's Theorem
IT2001PA Engineering Essentials (2/2)
Working
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Chapter 6 - Application of DeMorgan's Theorem
IT2001PA Engineering Essentials (2/2)
Example 1
The equivalent gate circuit for this much-simplified expression is as follows
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Chapter 6 - Application of DeMorgan's Theorem
IT2001PA Engineering Essentials (2/2)
Example 2
Write the Boolean equation for the circuit shown
simplify the equation
draw the logic circuit of the
simplified equation.
Warning buzzer
X
C
B(A+C)BB
AC
(A+C)
FIG 1
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Chapter 6 - Application of DeMorgan's Theorem
IT2001PA Engineering Essentials (2/2)
Solution
Warning buzzer
X=A*B + C
C
BA
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Chapter 6 - Application of DeMorgan's Theorem
IT2001PA Engineering Essentials (2/2)
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.
XB
FIG 2
A
C
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Chapter 6 - Application of DeMorgan's Theorem
IT2001PA Engineering Essentials (2/2)
Solution
A
X = B * C
Simplified logic circuit for Fig 2.
B
C
Not used
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Chapter 6 - Application of DeMorgan's Theorem
IT2001PA Engineering Essentials (2/2)
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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Chapter 6 - Application of DeMorgan's Theorem
IT2001PA Engineering Essentials (2/2)
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