Ee2 chapter6 applicationof_demorgan'stheorem

Apr 13, 2023

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IT2001PAEngineering Essentials (2/2)

Chapter 6 - Application of DeMorgan's Theorem

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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.

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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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