•commutative law of additionepsem.upc.edu/~jesusv/cap_4_algebra_boole_a_2p.pdftitle: microsoft...

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Digital Fundamentals, 9/eDigital Fundamentals, 9/e

Copyright ©2006 by Pearson Education, Inc.Copyright ©2006 by Pearson Education, Inc.

Upper Saddle River, New Jersey 07458Upper Saddle River, New Jersey 07458

All rights reserved.All rights reserved.

Slide 1

Boolean Operations and ExpressionsBoolean Operations and Expressions

•• AdditionAddition

0 + 0 = 00 + 0 = 0

0 + 1 = 10 + 1 = 1

1 + 0 = 11 + 0 = 1

1 + 1 = 11 + 1 = 1

•• MultiplicationMultiplication

0 * 0 = 00 * 0 = 0

0 * 1 = 00 * 1 = 0

1 * 0 = 01 * 0 = 0

1 * 1 = 11 * 1 = 1

CHAPTER 4 CHAPTER 4

Boolean Algebra and Logic SimplificationBoolean Algebra and Logic Simplification

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Slide 2

Laws of Boolean AlgebraLaws of Boolean Algebra

•• Commutative Law of Addition:Commutative Law of Addition:

A + B = B + AA + B = B + A

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Slide 3


•• Commutative Law of Multiplication:Commutative Law of Multiplication:

A * B = B * AA * B = B * A

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Slide 4


•• Associative Law of Addition:Associative Law of Addition:

A + (B + C) = (A + B) + CA + (B + C) = (A + B) + C

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Slide 5


•• Associative Law of Multiplication:Associative Law of Multiplication:

A * (B * C) = (A * B) * CA * (B * C) = (A * B) * C

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Slide 6


•• Distributive Law:Distributive Law:

A(B + C) = AB + ACA(B + C) = AB + AC

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Slide 7

Rules of Boolean AlgebraRules of Boolean Algebra

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Slide 8


•• Rule 1Rule 1

OR Truth Table

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Slide 9


•• Rule 2Rule 2

OR Truth Table

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Slide 10


•• Rule 3Rule 3

AND Truth Table

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Slide 11


•• Rule 4Rule 4

AND Truth Table

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Slide 12


•• Rule 5Rule 5

OR Truth Table

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Slide 13

Rules of Boolean Algebra Rules of Boolean Algebra

•• Rule 6Rule 6

OR Truth Table

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Slide 14


•• Rule 7Rule 7

AND Truth Table

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Slide 15


•• Rule 8Rule 8

AND Truth Table

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Slide 16


•• Rule 9Rule 9

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Slide 17


•• Rule 10: A + AB = ARule 10: A + AB = A

AND Truth Table OR Truth Table

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Slide 18


•• Rule 11:Rule 11: BABAA ++++====++++


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Slide 19


•• Rule 12: (A + B)(A + C) = A + BCRule 12: (A + B)(A + C) = A + BC


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Slide 20

DeMorgan’sDeMorgan’s TheoremsTheorems

•• Theorem 1Theorem 1

•• Theorem 2Theorem 2

YXXY ++++====

YXYX ====++++

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Slide 21

Standard Forms of Boolean ExpressionsStandard Forms of Boolean Expressions

•• The sumThe sum--ofof--product (SOP) formproduct (SOP) formExample: X = AB + CD + EFExample: X = AB + CD + EF

•• The product of sum (POS) formThe product of sum (POS) formExample: X = (A + B)(C + D)(E + F)Example: X = (A + B)(C + D)(E + F)

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Slide 22

The The KarnaughKarnaugh MapMap

3-Variable Karnaugh Map3-Variable Example

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Slide 23


4-Variable Karnaugh Map

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Slide 24


4-Variable Example

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Slide 25


5-Variable Karnaugh Mapping

•commutative law of additionepsem.upc.edu/~jesusv/cap_4_algebra_boole_a_2p.pdftitle: microsoft...

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