Lecture 4: More Boolean Algebra
|
|
- Caren Daniels
- 6 years ago
- Views:
Transcription
1 Lecture 4: More Boolean Algebra Syed M. Mahmud, Ph.D ECE Department Wayne State University Original Source: Prof. Russell Tessier of University of Massachusetts Aby George of Wayne State University ENGIN2 L6: More Boolean Algebra September 5, 23
2 Overview Epressing Boolean functions Relationships between algebraic equations, symbols, and truth tables Simplification of Boolean epressions Minterms and Materms AND-OR representations Product of sums Sum of products ENGIN2 L6: More Boolean Algebra September 5, 23
3 Conversion between Boolean Epression and Truth Table Boolean Epression Truth Table ENGIN2 L6: More Boolean Algebra September 5, 23
4 ENGIN2 L6: More Boolean Algebra September 5, 23 Truth Table to Epression What Boolean function is represented by the following Truth Table? Is it an AND or an OR function? The answer is AND because G= only for one combination of, y and z (=, y= and z=). Therefore, G = yz y z G
5 ENGIN2 L6: More Boolean Algebra September 5, 23 Truth Table to Epression What about G2 and G3? Both G2 and G3 represent AND operations because each one of these two functions is also equal to, only for one combination of, y and z. G2= for =, y= and z=, and G3= for =, y= and z=. Therefore, G2 = yz and G3 = yz y z G2 y z G3
6 ENGIN2 L6: More Boolean Algebra September 5, 23 Truth Table to Epression If G = G+G2+G3, as shown in the following Truth Table, then G = yz + yz + yz y z G G2 G3 G = G+G2+G3
7 Truth Table to Epression Converting a truth table to an epression Each row with output of becomes a product term Sum all the product terms together. y z G Any Boolean Epression can be represented in sum of products form! yz + yz + yz G = yz + yz' +'yz Product Terms Sum of 3 Product Terms ENGIN2 L6: More Boolean Algebra September 5, 23
8 Implementation of the SOP Epression SOP Epression: G = yz + yz' +'yz A SOP epression is implemented using one OR gate and multiple AND gates. This is not a minimum logic. We will minimize later. ENGIN2 L6: More Boolean Algebra September 5, 23
9 Reducing the epression for G using Boolean Algebra G = yz + yz' +'yz Step : Use Theorum (a + a = a) So yz + yz + yz = yz + yz + yz + yz Step 2: Use distributive rule a(b + c) = ab + ac So yz + yz + yz + yz = y(z + z ) + yz( + ) Step 3: Use Postulate 3 (a + a = ) So y(z + z ) + yz( + ) = y. + yz. Step 4: Use Postulate 2 (a. = a) So y. + yz. = y + yz Therefore, G = y + yz ENGIN2 L6: More Boolean Algebra September 5, 23
10 ENGIN2 L6: More Boolean Algebra September 5, 23 Reduced Hardware Implementation Reduced equation requires less hardware! Same function implemented! y z y z G G = yz + yz + yz = y + yz G
11 Product of Sums (POS) Epression Any Boolean Epression can be represented in Product of Sums (POS) form. Let's find a POS epression for G. We have shown how G was written in a SOP epression. Using the same technique we can write a SOP epression for G'. G' = 'y'z'+'y'z+'yz'+y'z'+y'z Using DeMorgan's Theorem we can convert the SOP epression for G' into a POS epression for G ENGIN2 L6: More Boolean Algebra September 5, 23
12 Product of Sums (POS) Epression G' = 'y'z'+'y'z+'yz'+y'z'+y'z G = (G')' = ('y'z'+'y'z+'yz'+y'z'+y'z)' Using DeMorgan G=('y'z')'.('y'z)'.('yz')'.(y'z')'.(y'z)' Using DeMorgan again G=(+y+z).(+y+z').(+y'+z).('+y+z).('+y+z') Sum Terms POS Epression ENGIN2 L6: More Boolean Algebra September 5, 23
13 Summary of SOP and POS Epressions for G SOP Epression: G = yz + yz' +'yz POS Epression: G=(+y+z)(+y+z')(+y'+z)('+y+z)('+y+z') Notice, the SOP epression has 3 Product terms and the POS epression has 5 Sum terms. There are 8 terms in both SOP and POS epressions together. Why? Because G is a function of 3 variable (, y and z), and 3 variables have 8 different combinations. The 's of G are used for SOP and the 's of G are used for POS. ENGIN2 L6: More Boolean Algebra September 5, 23
14 Implementation of the POS Epression POS Epression: G=(+y+z)(+y+z')(+y'+z)('+y+z)('+y+z') A POS epression is implemented using one AND gate and multiple OR gates. ENGIN2 L6: More Boolean Algebra September 5, 23
15 Minterms and Materms The boolean variables and their complements are called Literals. For eample, is a literal, and y' is also a literal. The Product Terms of literals are called Minterms. The Sum Terms of literals are called Materms. ENGIN2 L6: More Boolean Algebra September 5, 23
16 ENGIN2 L6: More Boolean Algebra September 5, 23 Representing Functions with Minterms A SOP epression is a Sum of Minterms. The Minterms of a function correspond to the 's of the function. Shorthand way to represent functions y z G G = yz + yz + yz G = m 3 + m 6 + m 7 = Σm(3, 6, 7)
17 ENGIN2 L6: More Boolean Algebra September 5, 23 Representing Functions with Materms A POS epression is a Product of Materms. The Materms of a function correspond to the 's of the function. Shorthand way to represent functions G = (+y+z)(+y+z )(+y +z)( +y+z)( +y+z ) G = M M M 2 M 4 M 5 = ΠM(,,2,4,5) y z G
18 ENGIN2 L6: More Boolean Algebra September 5, 23 Canonical Forms The Minterm and Materm epressions are also called Canonical Forms y z G G = m 3 + m 6 + m 7 = Σm(3, 6, 7) G = M M M 2 M 4 M 5 = ΠM(,,2,4,5) Canonical Forms
19 Conversion Between Canonical Forms Easy to convert between Minterm and Materm epressions. Since 3 variables can take 8 combinations, if there are N Minterms in the epression for a function, then there will be 8-N Materms in the epression for the function. Similarly, since 4 variables can take 6 combinations, if there are N Minterms in the epression for a function, then there will be 6-N Materms in the epression for the function. Eample: IF F = Σ m(, 3, 6, 7,, 2, 5) THEN F = Π M(, 2, 4, 5, 8, 9,, 3, 4) ENGIN2 L6: More Boolean Algebra September 5, 23
20 Representation in Circuits All logic epressions can be represented in 2-level format Circuits can be reduced to minimal 2-level representation Sum of products representations are most common in industry. ENGIN2 L6: More Boolean Algebra September 5, 23
21 Summary Truth table, circuit, and boolean epression formats are equivalent Easy to translate truth table to SOP and POS representation Boolean algebra rules can be used to reduce circuit size while maintaining function All logic functions can be made from AND, OR, and NOT ENGIN2 L6: More Boolean Algebra September 5, 23
22 Practice Problems Boolean algebra, Basic theorems and Postulates 2., 2.2, 2.3, 2.5, 2.6 Boolean functions 2.8, 2.9, 2., 2.8 Canonical and standard forms and digital logic gates 2.2, 2.22, 2.23, 2.27, 2.28 ENGIN2 L6: More Boolean Algebra September 5, 23
Lecture 6: Gate Level Minimization Syed M. Mahmud, Ph.D ECE Department Wayne State University
Lecture 6: Gate Level Minimization Syed M. Mahmud, Ph.D ECE Department Wayne State University Original Source: Aby K George, ECE Department, Wayne State University Contents The Map method Two variable
More informationThis form sometimes used in logic circuit, example:
Objectives: 1. Deriving of logical expression form truth tables. 2. Logical expression simplification methods: a. Algebraic manipulation. b. Karnaugh map (k-map). 1. Deriving of logical expression from
More informationUniversity of Technology
University of Technology Lecturer: Dr. Sinan Majid Course Title: microprocessors 4 th year معالجات دقيقة المرحلة الرابعة ھندسة الليزر والبصريات االلكترونية Lecture 3 & 4 Boolean Algebra and Logic Gates
More informationLecture 3: Boolean Algebra
Lecture 3: Boolean Algebra Syed M. Mahmud, Ph.D ECE Department Wayne State University Original Source: Prof. Russell Tessier of University of Massachusetts Aby George of Wayne State University Overview
More informationECE 20B, Winter 2003 Introduction to Electrical Engineering, II LECTURE NOTES #2
ECE 20B, Winter 2003 Introduction to Electrical Engineering, II LECTURE NOTES #2 Instructor: Andrew B. Kahng (lecture) Email: abk@ucsd.edu Telephone: 858-822-4884 office, 858-353-0550 cell Office: 3802
More informationECEN 248: INTRODUCTION TO DIGITAL SYSTEMS DESIGN. Week 2 Dr. Srinivas Shakkottai Dept. of Electrical and Computer Engineering
ECEN 248: INTRODUCTION TO DIGITAL SYSTEMS DESIGN Week 2 Dr. Srinivas Shakkottai Dept. of Electrical and Computer Engineering Boolean Algebra Boolean Algebra A Boolean algebra is defined with: A set of
More informationStandard Expression Forms
ThisLecture will cover the following points: Canonical and Standard Forms MinTerms and MaxTerms Digital Logic Families 24 March 2010 Standard Expression Forms Two standard (canonical) expression forms
More informationCS 226: Digital Logic Design
CS 226: Digital Logic Design 0 1 1 I S 0 1 0 S Department of Computer Science and Engineering, Indian Institute of Technology Bombay. 1 of 29 Objectives In this lecture we will introduce: 1. Logic functions
More informationCombinational Logic Circuits Part II -Theoretical Foundations
Combinational Logic Circuits Part II -Theoretical Foundations Overview Boolean Algebra Basic Logic Operations Basic Identities Basic Principles, Properties, and Theorems Boolean Function and Representations
More informationCPE100: Digital Logic Design I
Chapter 2 Professor Brendan Morris, SEB 3216, brendan.morris@unlv.edu http://www.ee.unlv.edu/~b1morris/cpe100/ CPE100: Digital Logic Design I Section 1004: Dr. Morris Combinational Logic Design Chapter
More informationLecture 5: NAND, NOR and XOR Gates, Simplification of Algebraic Expressions
EE210: Switching Systems Lecture 5: NAND, NOR and XOR Gates, Simplification of Algebraic Expressions Prof. YingLi Tian Feb. 15, 2018 Department of Electrical Engineering The City College of New York The
More informationSlides for Lecture 10
Slides for Lecture 10 ENEL 353: Digital Circuits Fall 2013 Term Steve Norman, PhD, PEng Electrical & Computer Engineering Schulich School of Engineering University of Calgary 30 September, 2013 ENEL 353
More informationMark Redekopp, All rights reserved. Lecture 5 Slides. Canonical Sums and Products (Minterms and Maxterms) 2-3 Variable Theorems DeMorgan s Theorem
Lecture 5 Slides Canonical Sums and Products (Minterms and Materms) 2-3 Variable Theorems DeMorgan s Theorem Using products of materms to implement a function MAXTERMS Question Is there a set of functions
More informationUnit 2 Session - 6 Combinational Logic Circuits
Objectives Unit 2 Session - 6 Combinational Logic Circuits Draw 3- variable and 4- variable Karnaugh maps and use them to simplify Boolean expressions Understand don t Care Conditions Use the Product-of-Sums
More informationWEEK 2.1 BOOLEAN ALGEBRA
WEEK 2.1 BOOLEAN ALGEBRA 1 Boolean Algebra Boolean algebra was introduced in 1854 by George Boole and in 1938 was shown by C. E. Shannon to be useful for manipulating Boolean logic functions. The postulates
More informationLogic and Computer Design Fundamentals. Chapter 2 Combinational Logic Circuits. Part 1 Gate Circuits and Boolean Equations
Logic and Computer Design Fundamentals Chapter 2 Combinational Logic Circuits Part Gate Circuits and Boolean Equations Charles Kime & Thomas Kaminski 28 Pearson Education, Inc. (Hperlinks are active in
More informationChapter 2 : Boolean Algebra and Logic Gates
Chapter 2 : Boolean Algebra and Logic Gates By Electrical Engineering Department College of Engineering King Saud University 1431-1432 2.1. Basic Definitions 2.2. Basic Theorems and Properties of Boolean
More informationDigital Logic Design. Malik Najmus Siraj
Digital Logic Design Malik Najmus Siraj siraj@case.edu.pkedu LECTURE 4 Today s Agenda Recap 2 s complement Binary Logic Boolean algebra Recap Computer Arithmetic Signed numbers Radix and diminished radix
More informationBoolean Algebra and Logic Simplification
S302 Digital Logic Design Boolean Algebra and Logic Simplification Boolean Analysis of Logic ircuits, evaluating of Boolean expressions, representing the operation of Logic circuits and Boolean expressions
More informationChapter 2 Boolean Algebra and Logic Gates
Ch1: Digital Systems and Binary Numbers Ch2: Ch3: Gate-Level Minimization Ch4: Combinational Logic Ch5: Synchronous Sequential Logic Ch6: Registers and Counters Switching Theory & Logic Design Prof. Adnan
More informationCombinatorial Logic Design Principles
Combinatorial Logic Design Principles ECGR2181 Chapter 4 Notes Logic System Design I 4-1 Boolean algebra a.k.a. switching algebra deals with boolean values -- 0, 1 Positive-logic convention analog voltages
More informationFunctions. Computers take inputs and produce outputs, just like functions in math! Mathematical functions can be expressed in two ways:
Boolean Algebra (1) Functions Computers take inputs and produce outputs, just like functions in math! Mathematical functions can be expressed in two ways: An expression is finite but not unique f(x,y)
More informationLearning Objectives 10/7/2010. CE 411 Digital System Design. Fundamental of Logic Design. Review the basic concepts of logic circuits. Dr.
/7/ CE 4 Digital ystem Design Dr. Arshad Aziz Fundamental of ogic Design earning Objectives Review the basic concepts of logic circuits Variables and functions Boolean algebra Minterms and materms ogic
More informationChapter 2: Princess Sumaya Univ. Computer Engineering Dept.
hapter 2: Princess Sumaya Univ. omputer Engineering Dept. Basic Definitions Binary Operators AND z = x y = x y z=1 if x=1 AND y=1 OR z = x + y z=1 if x=1 OR y=1 NOT z = x = x z=1 if x=0 Boolean Algebra
More informationAdministrative Notes. Chapter 2 <9>
Administrative Notes Note: New homework instructions starting with HW03 Homework is due at the beginning of class Homework must be organized, legible (messy is not), and stapled to be graded Chapter 2
More informationEEE130 Digital Electronics I Lecture #4
EEE130 Digital Electronics I Lecture #4 - Boolean Algebra and Logic Simplification - By Dr. Shahrel A. Suandi Topics to be discussed 4-1 Boolean Operations and Expressions 4-2 Laws and Rules of Boolean
More information7.1. Unit 7. Minterm and Canonical Sums 2- and 3-Variable Boolean Algebra Theorems DeMorgan's Theorem Simplification using Boolean Algebra
7.1 Unit 7 Minterm and Canonical Sums 2- and 3-Variable Boolean Algebra Theorems DeMorgan's Theorem Simplification using Boolean Algebra CHECKERS / DECODERS 7.2 7.3 Gates Gates can have more than 2 inputs
More informationMC9211 Computer Organization
MC92 Computer Organization Unit : Digital Fundamentals Lesson2 : Boolean Algebra and Simplification (KSB) (MCA) (29-2/ODD) (29 - / A&B) Coverage Lesson2 Introduces the basic postulates of Boolean Algebra
More informationThe Karnaugh Map COE 202. Digital Logic Design. Dr. Muhamed Mudawar King Fahd University of Petroleum and Minerals
The Karnaugh Map COE 202 Digital Logic Design Dr. Muhamed Mudawar King Fahd University of Petroleum and Minerals Presentation Outline Boolean Function Minimization The Karnaugh Map (K-Map) Two, Three,
More informationChapter 2 Combinational
Computer Engineering 1 (ECE290) Chapter 2 Combinational Logic Circuits Part 1 Gate Circuits and Boolean Equations HOANG Trang Reference: 2008 Pearson Education, Inc. Overview Part 1 Gate Circuits and Boolean
More informationChapter 2 Boolean Algebra and Logic Gates
Chapter 2 Boolean Algebra and Logic Gates Huntington Postulates 1. (a) Closure w.r.t. +. (b) Closure w.r.t.. 2. (a) Identity element 0 w.r.t. +. x + 0 = 0 + x = x. (b) Identity element 1 w.r.t.. x 1 =
More informationDigital Circuit And Logic Design I. Lecture 3
Digital Circuit And Logic Design I Lecture 3 Outline Combinational Logic Design Principles (). Introduction 2. Switching algebra 3. Combinational-circuit analysis 4. Combinational-circuit synthesis Panupong
More informationLogic Design. Chapter 2: Introduction to Logic Circuits
Logic Design Chapter 2: Introduction to Logic Circuits Introduction Logic circuits perform operation on digital signal Digital signal: signal values are restricted to a few discrete values Binary logic
More informationDIGITAL CIRCUIT LOGIC BOOLEAN ALGEBRA
DIGITAL CIRCUIT LOGIC BOOLEAN ALGEBRA 1 Learning Objectives Understand the basic operations and laws of Boolean algebra. Relate these operations and laws to circuits composed of AND gates, OR gates, INVERTERS
More informationChapter 2 Combinational Logic Circuits
Logic and Computer Design Fundamentals Chapter 2 Combinational Logic Circuits Part 1 Gate Circuits and Boolean Equations Charles Kime & Thomas Kaminski 2008 Pearson Education, Inc. (Hyperlinks are active
More informationLecture 6: Manipulation of Algebraic Functions, Boolean Algebra, Karnaugh Maps
EE210: Switching Systems Lecture 6: Manipulation of Algebraic Functions, Boolean Algebra, Karnaugh Maps Prof. YingLi Tian Feb. 21/26, 2019 Department of Electrical Engineering The City College of New York
More informationCHAPTER1: Digital Logic Circuits Combination Circuits
CS224: Computer Organization S.KHABET CHAPTER1: Digital Logic Circuits Combination Circuits 1 PRIMITIVE LOGIC GATES Each of our basic operations can be implemented in hardware using a primitive logic gate.
More informationGate-Level Minimization
Gate-Level Minimization Dr. Bassem A. Abdullah Computer and Systems Department Lectures Prepared by Dr.Mona Safar, Edited and Lectured by Dr.Bassem A. Abdullah Outline 1. The Map Method 2. Four-variable
More informationMark Redekopp, All rights reserved. Lecture 4 Slides. Boolean Algebra Logic Functions Canonical Sums/Products
Lecture 4 Slides Boolean Algebra Logic Functions Canonical Sums/Products LOGIC FUNCTION REPRESENTATION Logic Functions A logic function maps input combinations to an output value ( 1 or ) 3 possible representations
More information211: Computer Architecture Summer 2016
211: Computer Architecture Summer 2016 Liu Liu Topic: Storage Project3 Digital Logic - Storage: Recap - Review: cache hit rate - Project3 - Digital Logic: - truth table => SOP - simplification: Boolean
More informationChapter 4 Optimized Implementation of Logic Functions
Chapter 4 Optimized Implementation of Logic Functions Logic Minimization Karnaugh Maps Systematic Approach for Logic Minimization Minimization of Incompletely Specified Functions Tabular Method for Minimization
More informationTextbook: Digital Design, 3 rd. Edition M. Morris Mano
: 25/5/ P-/70 Tetbook: Digital Design, 3 rd. Edition M. Morris Mano Prentice-Hall, Inc. : INSTRUCTOR : CHING-LUNG SU E-mail: kevinsu@yuntech.edu.tw Chapter 3 25/5/ P-2/70 Chapter 3 Gate-Level Minimization
More informationBoolean Algebra & Logic Gates. By : Ali Mustafa
Boolean Algebra & Logic Gates By : Ali Mustafa Digital Logic Gates There are three fundamental logical operations, from which all other functions, no matter how complex, can be derived. These Basic functions
More informationELCT201: DIGITAL LOGIC DESIGN
ELCT2: DIGITAL LOGIC DESIGN Dr. Eng. Haitham Omran, haitham.omran@guc.edu.eg Dr. Eng. Wassim Alexan, wassim.joseph@guc.edu.eg Lecture 2 Following the slides of Dr. Ahmed H. Madian ذو الحجة 438 ه Winter
More informationChapter 2: Switching Algebra and Logic Circuits
Chapter 2: Switching Algebra and Logic Circuits Formal Foundation of Digital Design In 1854 George Boole published An investigation into the Laws of Thoughts Algebraic system with two values 0 and 1 Used
More information2009 Spring CS211 Digital Systems & Lab CHAPTER 2: INTRODUCTION TO LOGIC CIRCUITS
CHAPTER 2: INTRODUCTION TO LOGIC CIRCUITS What will we learn? 2 Logic functions and circuits Boolean Algebra Logic gates and Synthesis CAD tools and VHDL Read Section 2.9 and 2.0 Terminology 3 Digital
More informationENGR 303 Introduction to Logic Design Lecture 3. Dr. Chuck Brown Engineering and Computer Information Science Folsom Lake College
Introduction to Logic Design Lecture 3 Dr. Chuck rown Engineering and Computer Information Science Folsom Lake College Outline for Todays Lecture Logic Circuits SOP / POS oolean Theorems DeMorgan s Theorem
More informationChapter 2 Combinational Logic Circuits
Logic and Computer Design Fundamentals Chapter 2 Combinational Logic Circuits Part 1 Gate Circuits and Boolean Equations Chapter 2 - Part 1 2 Chapter 2 - Part 1 3 Chapter 2 - Part 1 4 Chapter 2 - Part
More informationStandard & Canonical Forms
1 COE 202- Digital Logic Standard & Canonical Forms Dr. Abdulaziz Y. Barnawi COE Department KFUPM 2 Outline Minterms and Maxterms From truth table to Boolean expression Sum of minterms Product of Maxterms
More informationComputer Organization I. Lecture 13: Design of Combinational Logic Circuits
Computer Organization I Lecture 13: Design of Combinational Logic Circuits Overview The optimization of multiple-level circuits Mapping Technology Verification Objectives To know how to optimize the multiple-level
More informationGoals for Lecture. Binary Logic and Gates (MK 2.1) Binary Variables. Notation Examples. Logical Operations
Introduction to Electrical Engineering, II LETURE NOTES #2 Instructor: Email: Telephone: Office: ndrew. Kahng (lecture) abk@ucsd.edu 858-822-4884 office 3802 P&M lass Website: http://vlsicad.ucsd.edu/courses/ece20b/wi04/
More informationUNIT 5 KARNAUGH MAPS Spring 2011
UNIT 5 KRNUGH MPS Spring 2 Karnaugh Maps 2 Contents Minimum forms of switching functions Two- and three-variable Four-variable Determination of minimum expressions using essential prime implicants Five-variable
More informationChapter-2 BOOLEAN ALGEBRA
Chapter-2 BOOLEAN ALGEBRA Introduction: An algebra that deals with binary number system is called Boolean Algebra. It is very power in designing logic circuits used by the processor of computer system.
More informationEx: Boolean expression for majority function F = A'BC + AB'C + ABC ' + ABC.
Boolean Expression Forms: Sum-of-products (SOP) Write an AND term for each input combination that produces a 1 output. Write the input variable if its value is 1; write its complement otherwise. OR the
More informationDigital Logic Design. Combinational Logic
Digital Logic Design Combinational Logic Minterms A product term is a term where literals are ANDed. Example: x y, xz, xyz, A minterm is a product term in which all variables appear exactly once, in normal
More informationUnit 2 Boolean Algebra
Unit 2 Boolean Algebra 1. Developed by George Boole in 1847 2. Applied to the Design of Switching Circuit by Claude Shannon in 1939 Department of Communication Engineering, NCTU 1 2.1 Basic Operations
More informationChapter 2. Boolean Algebra and Logic Gates
Chapter 2 Boolean Algebra and Logic Gates Basic Definitions A binary operator defined on a set S of elements is a rule that assigns, to each pair of elements from S, a unique element from S. The most common
More informationII. COMBINATIONAL LOGIC DESIGN. - algebra defined on a set of 2 elements, {0, 1}, with binary operators multiply (AND), add (OR), and invert (NOT):
ENGI 386 Digital Logic II. COMBINATIONAL LOGIC DESIGN Combinational Logic output of digital system is only dependent on current inputs (i.e., no memory) (a) Boolean Algebra - developed by George Boole
More informationSlide Set 3. for ENEL 353 Fall Steve Norman, PhD, PEng. Electrical & Computer Engineering Schulich School of Engineering University of Calgary
Slide Set 3 for ENEL 353 Fall 2016 Steve Norman, PhD, PEng Electrical & Computer Engineering Schulich School of Engineering University of Calgary Fall Term, 2016 SN s ENEL 353 Fall 2016 Slide Set 3 slide
More informationBoolean Algebra and Logic Gates
Boolean Algebra and Logic Gates ( 范倫達 ), Ph. D. Department of Computer Science National Chiao Tung University Taiwan, R.O.C. Fall, 2017 ldvan@cs.nctu.edu.tw http://www.cs.nctu.edu.tw/~ldvan/ Outlines Basic
More informationCS 121 Digital Logic Design. Chapter 2. Teacher Assistant. Hanin Abdulrahman
CS 121 Digital Logic Design Chapter 2 Teacher Assistant Hanin Abdulrahman 1 2 Outline 2.2 Basic Definitions 2.3 Axiomatic Definition of Boolean Algebra. 2.4 Basic Theorems and Properties 2.5 Boolean Functions
More informationSimplification of Boolean Functions. Dept. of CSE, IEM, Kolkata
Simplification of Boolean Functions Dept. of CSE, IEM, Kolkata 1 Simplification of Boolean Functions: An implementation of a Boolean Function requires the use of logic gates. A smaller number of gates,
More informationDIGITAL CIRCUIT LOGIC BOOLEAN ALGEBRA
DIGITAL CIRCUIT LOGIC BOOLEAN ALGEBRA 1 Learning Objectives Understand the basic operations and laws of Boolean algebra. Relate these operations and laws to circuits composed of AND gates, OR gates, INVERTERS
More informationIntroduction to Digital Logic Missouri S&T University CPE 2210 Boolean Representations
Introduction to Digital Logic Missouri S&T University CPE 2210 Egemen K. Çetinkaya Egemen K. Çetinkaya Department of Electrical & Computer Engineering Missouri University of Science and Technology cetinkayae@mst.edu
More informationElectronics. Overview. Introducction to Synthetic Biology
Electronics Introducction to Synthetic iology E Navarro Montagud P Fernandez de Cordoba JF Urchueguía Overview Introduction oolean algebras Logical gates Representation of boolean functions Karnaugh maps
More informationLecture 5. Karnaugh-Map
Lecture 5 - Lecture 5 Karnaugh-Map Lecture 5-2 Karnaugh-Map Set Logic Venn Diagram K-map Lecture 5-3 K-Map for 2 Variables Lecture 5-4 K-Map for 3 Variables C C C Lecture 5-5 Logic Expression, Truth Table,
More informationCHAPTER 2 BOOLEAN ALGEBRA
CHAPTER 2 BOOLEAN ALGEBRA This chapter in the book includes: Objectives Study Guide 2.1 Introduction 2.2 Basic Operations 2.3 Boolean Expressions and Truth Tables 2.4 Basic Theorems 2.5 Commutative, Associative,
More informationComputer Organization I
Computer Organization I Lecture 6: Boolean Algebra /2/29 Wei Lu CS283 Overview Two Principles in Boolean Algebra () Duality Principle (2) Complement Principle Standard Form of Logic Expression () Sum of
More informationEECS150 - Digital Design Lecture 19 - Combinational Logic Circuits : A Deep Dive
EECS150 - Digital Design Lecture 19 - Combinational Logic Circuits : A Deep Dive March 30, 2010 John Wawrzynek Spring 2010 EECS150 - Lec19-cl1 Page 1 Boolean Algebra I (Representations of Combinational
More informationEXPERIMENT #4: SIMPLIFICATION OF BOOLEAN FUNCTIONS
EXPERIMENT #4: SIMPLIFICATION OF BOOLEAN FUNCTIONS OBJECTIVES: Simplify Boolean functions using K-map method Obtain Boolean expressions from timing diagrams Design and implement logic circuits Equipment
More informationCombinational Logic Design Principles
Combinational Logic Design Principles Switching algebra Doru Todinca Department of Computers Politehnica University of Timisoara Outline Introduction Switching algebra Axioms of switching algebra Theorems
More informationUNIT 4 MINTERM AND MAXTERM EXPANSIONS
UNIT 4 MINTERM AND MAXTERM EXPANSIONS Spring 2 Minterm and Maxterm Expansions 2 Contents Conversion of English sentences to Boolean equations Combinational logic design using a truth table Minterm and
More informationSignals and Systems Digital Logic System
Signals and Systems Digital Logic System Prof. Wonhee Kim Chapter 2 Design Process for Combinational Systems Step 1: Represent each of the inputs and outputs in binary Step 1.5: If necessary, break the
More informationMinimization techniques
Pune Vidyarthi Griha s COLLEGE OF ENGINEERING, NSIK - 4 Minimization techniques By Prof. nand N. Gharu ssistant Professor Computer Department Combinational Logic Circuits Introduction Standard representation
More informationChapter 2: Boolean Algebra and Logic Gates
Chapter 2: Boolean Algebra and Logic Gates Mathematical methods that simplify binary logics or circuits rely primarily on Boolean algebra. Boolean algebra: a set of elements, a set of operators, and a
More informationDIGITAL ELECTRONICS & it0203 Semester 3
DIGITAL ELECTRONICS & it0203 Semester 3 P.Rajasekar & C.M.T.Karthigeyan Asst.Professor SRM University, Kattankulathur School of Computing, Department of IT 8/22/2011 1 Disclaimer The contents of the slides
More informationINTRO TO I & CT. (Boolean Algebra and Logic Simplification.) Lecture # By: Department of CS & IT.
INTRO TO I & CT. (Boolean Algebra and Logic Simplification.) Lecture # 13-14 By: M.Nadeem Akhtar. Department of CS & IT. URL: https://sites.google.com/site/nadeemcsuoliict/home/lectures 1 Boolean Algebra
More informationChapter 2 (Lect 2) Canonical and Standard Forms. Standard Form. Other Logic Operators Logic Gates. Sum of Minterms Product of Maxterms
Chapter 2 (Lect 2) Canonical and Standard Forms Sum of Minterms Product of Maxterms Standard Form Sum of products Product of sums Other Logic Operators Logic Gates Basic and Multiple Inputs Positive and
More informationLogic Gate Level. Part 2
Logic Gate Level Part 2 Constructing Boolean expression from First method: write nonparenthesized OR of ANDs Each AND is a 1 in the result column of the truth table Works best for table with relatively
More informationCombinational Logic Fundamentals
Topic 3: Combinational Logic Fundamentals In this note we will study combinational logic, which is the part of digital logic that uses Boolean algebra. All the concepts presented in combinational logic
More informationDigital Design. Digital Design
Principles Of Digital Design Chapter 3 Boolean Algebra and Logic Design Boolean Algebra Logic Gates Digital Design Implementation Technology ASICs Gate Arrays Basic Algebraic Properties A set is a collection
More informationCprE 281: Digital Logic
CprE 281: Digital Logic Instructor: Alexander Stoytchev http://www.ece.iastate.edu/~alexs/classes/ Boolean Algebra CprE 281: Digital Logic Iowa State University, Ames, IA Copyright Alexander Stoytchev
More informationSimplifying Logic Circuits with Karnaugh Maps
Simplifying Logic Circuits with Karnaugh Maps The circuit at the top right is the logic equivalent of the Boolean expression: f = abc + abc + abc Now, as we have seen, this expression can be simplified
More informationWEEK 3.1 MORE ON KARNAUGH MAPS
WEEK 3. MORE ON KARNAUGH MAPS Don t Cares Sometimes, we might have inputs and it doesn t matter what the output is; i.e., we don t care what the output is. These situations are called don t cares. Rather
More informationEECS150 - Digital Design Lecture 4 - Boolean Algebra I (Representations of Combinational Logic Circuits)
EECS150 - Digital Design Lecture 4 - Boolean Algebra I (Representations of Combinational Logic Circuits) September 5, 2002 John Wawrzynek Fall 2002 EECS150 Lec4-bool1 Page 1, 9/5 9am Outline Review of
More informationLecture 2 Review on Digital Logic (Part 1)
Lecture 2 Review on Digital Logic (Part 1) Xuan Silvia Zhang Washington University in St. Louis http://classes.engineering.wustl.edu/ese461/ Grading Engagement 5% Review Quiz 10% Homework 10% Labs 40%
More informationLOGIC GATES. Basic Experiment and Design of Electronics. Ho Kyung Kim, Ph.D.
Basic Eperiment and Design of Electronics LOGIC GATES Ho Kyung Kim, Ph.D. hokyung@pusan.ac.kr School of Mechanical Engineering Pusan National University Outline Boolean algebra Logic gates Karnaugh maps
More informationChapter 2 Combinational Logic Circuits
Logic and Computer Design Fundamentals Chapter 2 Combinational Logic Circuits Part 2 Circuit Optimization Charles Kime & Thomas Kaminski 2004 Pearson Education, Inc. Terms of Use (Hyperlinks are active
More informationEC-121 Digital Logic Design
EC-121 Digital Logic Design Lecture 2 [Updated on 02-04-18] Boolean Algebra and Logic Gates Dr Hashim Ali Spring 2018 Department of Computer Science and Engineering HITEC University Taxila!1 Overview What
More informationL4: Karnaugh diagrams, two-, and multi-level minimization. Elena Dubrova KTH / ICT / ES
L4: Karnaugh diagrams, two-, and multi-level minimization Elena Dubrova KTH / ICT / ES dubrova@kth.se Combinatorial system a(t) not(a(t)) A combinatorial system has no memory - its output depends therefore
More information14:332:231 DIGITAL LOGIC DESIGN. Combinational Circuit Synthesis
:: DIGITAL LOGIC DESIGN Ivan Marsic, Rutgers University Electrical & Computer Engineering all Lecture #: Combinational Circuit Synthesis I Combinational Circuit Synthesis Recall: Combinational circuit
More informationCombinational Logic. Review of Combinational Logic 1
Combinational Logic! Switches -> Boolean algebra! Representation of Boolean functions! Logic circuit elements - logic gates! Regular logic structures! Timing behavior of combinational logic! HDLs and combinational
More informationCHAPTER III BOOLEAN ALGEBRA
CHAPTER III- CHAPTER III CHAPTER III R.M. Dansereau; v.. CHAPTER III-2 BOOLEAN VALUES INTRODUCTION BOOLEAN VALUES Boolean algebra is a form of algebra that deals with single digit binary values and variables.
More informationBoolean Algebra. The Building Blocks of Digital Logic Design. Section. Section Overview. Binary Operations and Their Representation.
Section 3 Boolean Algebra The Building Blocks of Digital Logic Design Section Overview Binary Operations (AND, OR, NOT), Basic laws, Proof by Perfect Induction, De Morgan s Theorem, Canonical and Standard
More informationBOOLEAN ALGEBRA CLASS XII. Presented By : Dinesh Patel PGT CS KV IIT Powai
BOOLEAN ALGEBRA CLASS II Presented By : Dinesh Patel PGT CS KV IIT Powai Introduction Boolean Algebra is a set of rules and regulation which is suitable for Digital Circuits, whose answer is either True
More informationCover Sheet for Lab Experiment #3
The University of Toledo EECS:1100 R2 Digital Logic Design Dr. Anthony D. Johnson Cover Sheet for Lab Experiment #3 Student Names Course Section Anthony Phillips 003 Alexander Beck 003 Report turned in
More informationEEA051 - Digital Logic 數位邏輯 吳俊興高雄大學資訊工程學系. September 2004
EEA051 - Digital Logic 數位邏輯 吳俊興高雄大學資訊工程學系 September 2004 Boolean Algebra (formulated by E.V. Huntington, 1904) A set of elements B={0,1} and two binary operators + and Huntington postulates 1. Closure
More informationZ = F(X) Combinational circuit. A combinational circuit can be specified either by a truth table. Truth Table
Lesson Objectives In this lesson, you will learn about What are combinational circuits Design procedure of combinational circuits Examples of combinational circuit design Combinational Circuits Logic circuit
More informationUnit 2 Boolean Algebra
Unit 2 Boolean Algebra 2.1 Introduction We will use variables like x or y to represent inputs and outputs (I/O) of a switching circuit. Since most switching circuits are 2 state devices (having only 2
More informationCircuits & Boolean algebra.
Circuits & Boolean algebra http://xkcd.com/730/ CSCI 255: Introduction to Embedded Systems Keith Vertanen Copyright 2011 Digital circuits Overview How a switch works Building basic gates from switches
More information