Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 1 Digital Fundamentals.

Slides:

Advertisements

Similar presentations

Advanced Piloting Cruise Plot.

Advertisements

Feichter_DPG-SYKL03_Bild-01. Feichter_DPG-SYKL03_Bild-02.

© 2008 Pearson Addison Wesley. All rights reserved Chapter Seven Costs.

Copyright © 2003 Pearson Education, Inc. Slide 1 Computer Systems Organization & Architecture Chapters 8-12 John D. Carpinelli.

Chapter 1 The Study of Body Function Image PowerPoint

1 Copyright © 2013 Elsevier Inc. All rights reserved. Chapter 1 Embedded Computing.

Copyright © 2011, Elsevier Inc. All rights reserved. Chapter 6 Author: Julia Richards and R. Scott Hawley.

Author: Julia Richards and R. Scott Hawley

1 Copyright © 2013 Elsevier Inc. All rights reserved. Appendix 01.

1 Copyright © 2013 Elsevier Inc. All rights reserved. Chapter 3 CPUs.

1 Copyright © 2010, Elsevier Inc. All rights Reserved Fig 2.1 Chapter 2.

Properties Use, share, or modify this drill on mathematic properties. There is too much material for a single class, so you’ll have to select for your.

UNITED NATIONS Shipment Details Report – January 2006.

FIGURE 11.1 Circuit for Example 11.1.

FIGURE 12.1 Two variable process-control loops that interact.

FIGURE 9.1 Control of temperature by process control.

FIGURE 3.1 System for illustrating Boolean applications to control.

Curtis Johnson Process Control Instrumentation Technology, 8e]

FIGURE 8.1 Process and controller.

Jeopardy Q 1 Q 6 Q 11 Q 16 Q 21 Q 2 Q 7 Q 12 Q 17 Q 22 Q 3 Q 8 Q 13

Jeopardy Q 1 Q 6 Q 11 Q 16 Q 21 Q 2 Q 7 Q 12 Q 17 Q 22 Q 3 Q 8 Q 13

Properties of Real Numbers CommutativeAssociativeDistributive Identity + × Inverse + ×

FACTORING ax2 + bx + c Think “unfoil” Work down, Show all steps.

Year 6 mental test 5 second questions

Year 6 mental test 10 second questions

Solve Multi-step Equations

REVIEW: Arthropod ID. 1. Name the subphylum. 2. Name the subphylum. 3. Name the order.

Figure 12–1 Basic computer block diagram.

FIGURE 10-1 Crystal structure of a junction diode.

EU market situation for eggs and poultry Management Committee 20 October 2011.

3 Logic The Study of What’s True or False or Somewhere in Between.

Digital Logic Design Gate-Level Minimization

Exclusive-OR and Exclusive-NOR Gates

2 |SharePoint Saturday New York City

FIGURE 17-1 Binary-to-decimal conversion. Dale R. Patrick Electricity and Electronics: A Survey, 5e Copyright ©2002 by Pearson Education, Inc. Upper Saddle.

Copyright © 2013, 2009, 2006 Pearson Education, Inc.

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 Section 5.5 Dividing Polynomials Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1.

Copyright © 2012, Elsevier Inc. All rights Reserved. 1 Chapter 7 Modeling Structure with Blocks.

1 RA III - Regional Training Seminar on CLIMAT&CLIMAT TEMP Reporting Buenos Aires, Argentina, 25 – 27 October 2006 Status of observing programmes in RA.

Factor P 16 8(8-5ab) 4(d² + 4) 3rs(2r – s) 15cd(1 + 2cd) 8(4a² + 3b²)

Basel-ICU-Journal Challenge18/20/ Basel-ICU-Journal Challenge8/20/2014.

© 2012 National Heart Foundation of Australia. Slide 2.

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 Section 5.4 Polynomials in Several Variables Copyright © 2013, 2009, 2006 Pearson Education, Inc.

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 1 Digital Fundamentals.

Understanding Generalist Practice, 5e, Kirst-Ashman/Hull

25 seconds left…...

Januar MDMDFSSMDMDFSSS

Analyzing Genes and Genomes

We will resume in: 25 Minutes.

FIGURE 12-1 PNP transistor symbol and crystal structure.

©Brooks/Cole, 2001 Chapter 12 Derived Types-- Enumerated, Structure and Union.

Essential Cell Biology

Intracellular Compartments and Transport

PSSA Preparation.

Essential Cell Biology

Immunobiology: The Immune System in Health & Disease Sixth Edition

1 Chapter 13 Nuclear Magnetic Resonance Spectroscopy.

FIGURE 13-1 Amplification and reproduction: (a) reproduction; (b) amplification; (c) combined amplification and reproduction. Dale R. Patrick Electricity.

Thomas L. Floyd Digital Fundamentals, 9e

Energy Generation in Mitochondria and Chlorplasts

FIGURE 3-1 Basic parts of a computer. Dale R. Patrick Electricity and Electronics: A Survey, 5e Copyright ©2002 by Pearson Education, Inc. Upper Saddle.

CHAPTER 4 Boolean Algebra and Logic Simplification

Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle.

Figure A--1 Thomas L. Floyd Digital Fundamentals, 8e Copyright ©2003 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

© 2009 Pearson Education, Upper Saddle River, NJ All Rights ReservedFloyd, Digital Fundamentals, 10 th ed Digital Fundamentals Tenth Edition Floyd.

Presentation transcript:

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 1 Digital Fundamentals CHAPTER 4 Boolean Algebra and Logic Simplification

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 2 Boolean Operations and Expressions

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 3 Boolean Operations and Expressions AdditionAddition = = = = 1 MultiplicationMultiplication 0 * 0 = 0 0 * 1 = 0 1 * 0 = 0 1 * 1 = 1

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 4 Laws and Rules of Boolean Algebra Laws and Rules of Boolean Algebra

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 5 Laws Boolean Algebra Laws Boolean Algebra Commutative LawsCommutative Laws Associative LawsAssociative Laws Distributive LawDistributive Law

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 6 Laws of Boolean Algebra Commutative Law of Addition:Commutative Law of Addition: A + B = B + A

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 7 Laws of Boolean Algebra Commutative Law of Multiplication:Commutative Law of Multiplication: A * B = B * A

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 8 Laws of Boolean Algebra Laws of Boolean Algebra Associative Law of Addition:Associative Law of Addition: A + (B + C) = (A + B) + C

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 9 Laws of Boolean Algebra Laws of Boolean Algebra Associative Law of Multiplication:Associative Law of Multiplication: A * (B * C) = (A * B) * C

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 10 Laws of Boolean Algebra Laws of Boolean Algebra Distributive Law:Distributive Law: A(B + C) = AB + AC

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 11 Rules of Boolean Algebra

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 12 Rules of Boolean Algebra Rule 1Rule 1 OR Truth Table

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 13 Rules of Boolean Algebra Rule 2Rule 2 OR Truth Table

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 14 Rules of Boolean Algebra Rule 3Rule 3 AND Truth Table

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 15 Rules of Boolean Algebra Rule 4Rule 4 AND Truth Table

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 16 Rules of Boolean Algebra Rule 5Rule 5 OR Truth Table

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 17 Rules of Boolean Algebra Rule 6Rule 6 OR Truth Table

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 18 Rules of Boolean Algebra Rule 7Rule 7 AND Truth Table

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 19 Rules of Boolean Algebra Rule 8Rule 8 AND Truth Table

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 20 Rules of Boolean Algebra Rule 9Rule 9

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 21 Rules of Boolean Algebra Rule 10: A + AB = ARule 10: A + AB = A AND Truth TableOR Truth Table

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 22 Rules of Boolean Algebra Rule 11:Rule 11: AND Truth TableOR Truth Table

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 23 Rules of Boolean Algebra Rule 12: (A + B)(A + C) = A + BCRule 12: (A + B)(A + C) = A + BC AND Truth TableOR Truth Table

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 24 DeMorgans Theorem

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 25 DeMorgans Theorems Theorem 1Theorem 1 Theorem 2Theorem 2 Remember: Break the bar, change the sign

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 26 Standard Forms of Boolean Expressions

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 27 Standard Forms of Boolean Expressions The sum-of-product (SOP) formThe sum-of-product (SOP) form Example: X = AB + CD + EF The product of sum (POS) formThe product of sum (POS) form Example: X = (A + B)(C + D)(E + F)

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 28 The Karnaugh Map

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 29 The Karnaugh Map 3-Variable Karnaugh Map3-Variable Example

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 30 The Karnaugh Map 4-Variable Karnaugh Map 4-Variable Example

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 31 The Karnaugh Map 5-Variable Karnaugh Mapping

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 32 VHDL

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 33 VHDL VHDL OperatorsVHDL Operatorsandornotnandnorxorxnor VHDL ElementsVHDL Elementsentityarchitecture

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 34 VHDL VHDL Entity StructureEntity StructureExample: entity AND_Gate1 is port(A,B:in bit:X:out bit); end entity AND_Gate1

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 35 VHDL VHDL ArchitectureArchitectureExample: architecture LogicFunction of AND_Gate1 is begin X<=A and B; end architecture LogicFunction

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Slide 36 Hardware Description Languages (HDL) Hardware Description Languages (HDL) Boolean Expressions in VHDLBoolean Expressions in VHDL ANDX <= A and B; ORX <= A or B; NOTX <= A not B; NANDX <= A nand B; NORX <= A nor B; XORX <= A xor B; XNORX <= A xnor B;