©2004 Brooks/Cole FIGURES FOR CHAPTER 2 BOOLEAN ALGEBRA Click the mouse to move to the next page. Use the ESC key to exit this chapter. This chapter in.

Slides:

Advertisements

Similar presentations

Boolean Algebra and Logic Gates

Advertisements

Lecture 5 EGRE 254 1/28/09. 2 Boolean algebra a.k.a. “switching algebra” –deals with Boolean values -- 0, 1 Positive-logic convention –analog voltages.

ECE 238L Computer Logic Design Spring 2010

Chapter 2 Logic Circuits.

ECE 331 – Digital System Design Boolean Algebra (Lecture #3) The slides included herein were taken from the materials accompanying Fundamentals of Logic.

ECE 331 – Digital System Design

ECE 301 – Digital Electronics Boolean Algebra and Standard Forms of Boolean Expressions (Lecture #4) The slides included herein were taken from the materials.

©2004 Brooks/Cole FIGURES FOR CHAPTER 18 CIRCUITS FOR ARITHMETIC OPERATIONS Click the mouse to move to the next page. Use the ESC key to exit this chapter.

Boolean Algebra and Logic Simplification. Boolean Addition & Multiplication Boolean Addition performed by OR gate Sum Term describes Boolean Addition.

Gate Circuits and Boolean Equations BIL- 223 Logic Circuit Design Ege University Department of Computer Engineering.

Boolean Algebra Dr. Bernard Chen Ph.D. University of Central Arkansas Spring 2009.

©2010 Cengage Learning CHAPTER 2 BOOLEAN ALGEBRA 2.1Introduction 2.2Basic Operations 2.3Boolean Expressions and Truth Tables 2.4Basic Theorems 2.5Commutative,

CHAPTER 2 Boolean Algebra

Logic Design CS221 1 st Term Boolean Algebra Cairo University Faculty of Computers and Information.

Binary Logic and Gates Binary variables take on one of two values.

©2004 Brooks/Cole FIGURES FOR CHAPTER 4 APPLICATIONS OF BOOLEAN ALGEBRA MINTERM AND MAXTERM EXPANSIONS Click the mouse to move to the next page. Use the.

Module 4.  Boolean Algebra is used to simplify the design of digital logic circuits.  The design simplification are based on: Postulates of Boolean.

Chapter 2: Boolean Algebra and Logic Gates. F 1 = XY’ + X’Z XYZX’Y’XY’X’ZF1F

Boolean Logic and Circuits ELEC 311 Digital Logic and Circuits Dr. Ron Hayne Images Courtesy of Cengage Learning.

6 - 1 Simplification Theorems Useful for simplification of expressions & therefore simplification of the logic network which results. XY + XY' = ( X +

Binary Logic Section 1.9. Binary Logic Binary logic deals with variables that take on discrete values (e.g. 1, 0) and with operations that assume logical.

©2004 Brooks/Cole FIGURES FOR CHAPTER 3 BOOLEAN ALGEBRA (continued) Click the mouse to move to the next page. Use the ESC key to exit this chapter. This.

1 BOOLEAN ALGEBRA Basic mathematics for the study of logic design is Boolean Algebra Basic laws of Boolean Algebra will be implemented as switching devices.

Boolean Algebra – II. Outline  Basic Theorems of Boolean Algebra  Boolean Functions  Complement of Functions  Standard Forms.

Based on slides by:Charles Kime & Thomas Kaminski © 2004 Pearson Education, Inc. Terms of Use (Hyperlinks are active in View Show mode) Terms of Use ECE/CS.

A. Abhari CPS2131 Chapter 2: Boolean Algebra and Logic Gates Topics in this Chapter: Boolean Algebra Boolean Functions Boolean Function Simplification.

Logic Circuits Lecture 3 By Amr Al-Awamry. Basic Definitions Binary Operators  AND z = x y = x yz=1 if x=1 AND y=1  OR z = x + y z=1 if x=1 OR y=1 

© BYU 03 BA1 Page 1 ECEn 224 Boolean Algebra – Part 1.

CONSENSUS THEOREM Choopan Rattanapoka.

CEC 220 Digital Circuit Design Boolean Algebra Friday, January 17 CEC 220 Digital Circuit Design Slide 1 of 22.

CMPUT Computer Organization and Architecture II1 CMPUT329 - Fall 2002 Topic2: DeMorgan Laws José Nelson Amaral.

Conversion from one number base to another Binary arithmetic Equation simplification DeMorgan’s Laws Conversion to/from SOP/POS Reading equations from.

BOOLEAN ALGEBRA – Digital Circuit 1 Choopan Rattanapoka.

Boolean Algebra and Logic Gates

Module –I Boolean Algebra Digital Design Amit Kumar Assistant Professor SCSE, Galgotias University, Greater Noida.

ECEN 248: INTRODUCTION TO DIGITAL SYSTEMS DESIGN Lecture 4 Dr. Shi Dept. of Electrical and Computer Engineering.

ECE DIGITAL LOGIC LECTURE 8: BOOLEAN FUNCTIONS Assistant Prof. Fareena Saqib Florida Institute of Technology Spring 2016, 02/11/2016.

CEC 220 Digital Circuit Design Boolean Algebra II Fri, Sept 4 CEC 220 Digital Circuit Design Slide 1 of 13.

Boolean Algebra. BOOLEAN ALGEBRA Formal logic: In formal logic, a statement (proposition) is a declarative sentence that is either true(1) or false (0).

Boolean Algebra ELEC 311 Digital Logic and Circuits Dr. Ron Hayne Images Courtesy of Cengage Learning.

Lecture 5 More Boolean Algebra A B. Overview °Expressing Boolean functions °Relationships between algebraic equations, symbols, and truth tables °Simplification.

©2010 Cengage Learning SLIDES FOR CHAPTER 3 BOOLEAN ALGEBRA (continued) Click the mouse to move to the next page. Use the ESC key to exit this chapter.

Objectives The student will be able to:

Speaker: Fuw-Yi Yang 楊伏夷伏夷非征番, 道德經察政章(Chapter 58) 伏者潛藏也

ECE 301 – Digital Electronics

Chapter 3 Notes – Part II Review Questions

Boolean Algebra.

Unit 2 Boolean Algebra.

CS 105 Digital Logic Design

Gate Circuits and Boolean Equations

CHAPTER 3 BOOLEAN ALGEBRA (continued)

CHAPTER 2 Boolean Algebra

CHAPTER 1 : INTRODUCTION

CHAPTER 2 Boolean Algebra This chapter in the book includes:

Lecture 3 Algebraic Simplification

Princess Sumaya University

Boolean Algebra – Part 1 ECEn 224.

Lecture 2-1 Boolean Algebra

SLIDES FOR CHAPTER 2 BOOLEAN ALGEBRA

Topic1: Boolean Algebra José Nelson Amaral

FIGURES FOR CHAPTER 2 BOOLEAN ALGEBRA

Lecture 3: Boolean Algebra

Boolean Algebra.

Boolean Algebra.

Boolean Algebra & Logic Circuits

Basic Logic Gates 1.

Boolean Algebra.

BOOLEAN ALGEBRA AND LOGIC SIMPLIFICATION Part (a)

CHAPTER 3 BOOLEAN ALGEBRA (continued)

BOOLEAN ALGEBRA.

Presentation transcript:

©2004 Brooks/Cole FIGURES FOR CHAPTER 2 BOOLEAN ALGEBRA Click the mouse to move to the next page. Use the ESC key to exit this chapter. This chapter in the book includes: Objectives Study Guide 2.1Introduction 2.2Basic Operations 2.3Boolean Expressions and Truth Tables 2.4Basic Theorems 2.5Commutative, Associative, and Distributive Laws 2.6Simplification Theorems 2.7Multiplying Out and Factoring 2.8DeMorgan’s Laws Problems Laws and Theorems of Boolean Algebra

©2004 Brooks/Cole Section 2.2, p. 34 X' = 1 if X = 0 X' = 0 if X = 1

©2004 Brooks/Cole Section 2.2, p. 34

©2004 Brooks/Cole Section 2.2, p. 35

©2004 Brooks/Cole Section 2.2, p. 35

©2004 Brooks/Cole Section 2.2, p. 35 T = AB

©2004 Brooks/Cole Section 2.2, p. 35 T = A+B

©2004 Brooks/Cole Figure 2-1: Circuits for Expressions (2-1) and (2-2)

©2004 Brooks/Cole Figure 2-2: 2-Input Circuit

©2004 Brooks/Cole Table 2-1: Truth Table for 3 variables

©2004 Brooks/Cole Section 2.4, p. 38

©2004 Brooks/Cole Section 2.4, p. 38

©2004 Brooks/Cole Section 2.4, p. 39

©2004 Brooks/Cole Section 2.4, p. 39

©2004 Brooks/Cole Section 2.4, p. 39

©2004 Brooks/Cole Section 2.4, p. 39

©2004 Brooks/Cole Table 2-2: Proof of Associative Law for AND

©2004 Brooks/Cole Figure 2-3: Associative Law for AND and OR

©2004 Brooks/Cole Section 2.6, p. 42

©2004 Brooks/Cole Figure 2-4: Equivalent Gate Circuits

©2004 Brooks/Cole EXAMPLE 1 Simplify Z = A'BC + A' This expression has the same form as (2-13) if we let X = A' and Y = BC Therefore, the expression simplifies to Z = X + X Y = X = A'. Simplify (p )

©2004 Brooks/Cole EXAMPLE 1: Factor A + B'CD. This is of the form X + YZ where X = A, Y = B', and Z = CD, so A + B'CD = (X + Y)(X + Z) = (A + B')(A + CD) A + CD can be factored again using the second distributive law, so A + B'CD = (A + B')(A + C)(A + D) EXAMPLE 2: Factor AB' + C'D EXAMPLE 3: Factor C'D + C'E' + G'H Factor (p )

©2004 Brooks/Cole Figure 2-5: Circuits for Equations (2-15) and (2-17)

©2004 Brooks/Cole Figure 2-6: Circuits for Equations (2-18) and (2-20)

©2004 Brooks/Cole Operations with 0 and 1: 1. X + 0 = X1D. X 1 = X 2. X +1 = 12D. X 0 = 0 Idempotent laws: 3. X + X = X3D. X X = X Involution law: 4. (X')' = X Laws of complementarity: 5. X + X' = 15D. X X' = 0 LAWS AND THEOREMS (a)

©2004 Brooks/Cole Commutative laws: 6. X + Y = Y + X6D. XY = YX Associative laws: 7. (X + Y) + Z = X + (Y + Z)7D. (XY)Z = X(YZ) = XYZ = X + Y + Z Distributive laws: 8. X(Y + Z) = XY + XZ8D. X + YZ = (X + Y)(X + Z) Simplification theorems: 9. XY + XY' = X9D. (X + Y)(X + Y') = X 10. X + XY = X10D. X(X + Y) = X 11. (X + Y')Y = XY11D. XY' + Y = X + Y LAWS AND THEOREMS (b)

©2004 Brooks/Cole DeMorgan's laws: 12. (X + Y + Z +...)' = X'Y'Z'...12D. (XYZ...)' = X' + Y' + Z' +... Duality: 13. (X + Y + Z +...) D = XYZ...13D. (XYZ...) D = X + Y + Z +... Theorem for multiplying out and factoring: 14. (X + Y)(X' + Z) = XZ + X'Y14D. XY + X'Z = (X + Z)(X' + Y) Consensus theorem: 15. XY + YZ + X'Z = XY + X'Z15D. (X + Y)(Y + Z)(X' + Z) = (X + Y)(X' + Z) LAWS AND THEOREMS (c)