1. IT2001PA
Engineering Essentials (2/2)
Chapter 5 - DeMorgan's Theorem
Lecturer Name
lecturer_email@ite.edu.sg
Nov 20, 2012
Contact Number

2. Chapter 5 - DeMorgan's Theorem
Lesson Objectives
Upon completion of this topic, you should be able to:
 State DeMorgan's Theorem.
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3. Chapter 5 - DeMorgan's Theorem
Specific 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 - DeMorgan's Theorem
Introduction
 DeMorgan's theorems are extremely useful in
simplifying expressions in which a product or sum of
variables is inverted.
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5. Chapter 5 - DeMorgan's Theorem
DeMorgan’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.
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6. Chapter 5 - DeMorgan's Theorem
Steps to Apply DeMorgan’s Theorem
 DeMorgan’s Theorem
A*B=A+B
A+B=A*B
 DeMorgan's 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.
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7. Chapter 5 - DeMorgan's Theorem
Step 1: Complement the entire expression.
Complement entire
expression
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8. Chapter 5 - DeMorgan's Theorem
Step 2: Change all OR signs to ANDs and all
ANDs signs to ORs
Complement entire
expression
Change OR sign to AND
sign
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9. Chapter 5 - DeMorgan's Theorem
Step 3: Complement each of the individual
variables.
Complement entire
expression
Change OR sign to AND
sign
Complement each
variable
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10. Chapter 5 - DeMorgan's Theorem
Result
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11. Chapter 5 - DeMorgan's Theorem
Implications 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.
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12. Chapter 5 - DeMorgan's Theorem
Implications of DeMorgan’s Theorem
 A NAND gate is equivalent to an OR gate with
inverters on each of its inputs.
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13. Chapter 5 - DeMorgan's Theorem
Next Lesson
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