Introduction. 1854: Logical algebra was published by George Boole known today as Boolean Algebra
|
|
|
- Paul Reeves
- 6 years ago
- Views:
Transcription
1 oolean lgebra
2 Introduction 1854: Logical algebra was published by George oole known today as oolean lgebra It s a convenient way and systematic way of expressing and analyzing the operation of logic circuits. 1938: Claude Shannon was the first to apply oole s work to the analysis and design of logic circuits.
3 oolean Operations & Expressions Variable a symbol used to represent a logical quantity. Complement the inverse of a variable and is indicated by a bar over the variable. Literal a variable or the complement of a variable.
4 oolean ddition oolean addition is equivalent to the OR operation sum term is produced by an OR operation with no ND ops involved. i.e.,, C, C D sum term is equal to 1 when one or more of the literals in the term are 1. sum term is equal to 0 only if each of the literals is 0.
5 oolean Multiplication oolean multiplication is equivalent to the ND operation product term is produced by an ND operation with no OR ops involved. i.e.,, C, CD product term is equal to 1 only if each of the literals in the term is 1. product term is equal to 0 when one or more of the literals are 0.
6 Laws & Rules of oolean lgebra The basic laws of oolean algebra: The commutative laws (กฏการสล บท )บท ) กฏการสล บท )บท )) The associative laws (กฏการจ ดกล มดกล บท )ม กฏการจ ดกล มดกล บท )ม) The distributive laws (กฏการกระจ ดกล มายกล มาย)
7 Commutative Laws The commutative law of addition for two variables is written as: The commutative law of multiplication for two variables is written as:
8 ssociative Laws The associative law of addition for 3 variables is written as: (C) ()C C C (C) The associative law of multiplication for 3 variables is written as: (C) ()C C ()C C C (C) C ()C
9 Distributive Laws The distributive law is written for 3 variables as follows: (C) C C C X C C X X(C) XC
10 Rules of oolean lgebra ( )( C) C,, and C can represent a single variable or a combination of variables.
11 DeMorgan s Theorems DeMorgan s theorems provide mathematical verification of: the equivalency of the NND and negative-or gates the equivalency of the NOR and negative-nd gates.
12 DeMorgan s Theorems The complement of two or more NDed variables is equivalent to the OR of the complements of the individual variables. NND Negative-OR X Y X Y The complement of two or more ORed variables is equivalent to the ND of the complements of the individual variables. NOR X Y Negative-ND X Y
13 DeMorgan s Theorems (Exercises) pply DeMorgan s theorems to the expressions: X Y Z X Y Z X Y Z W X Y Z
14 DeMorgan s Theorems (Exercises) pply DeMorgan s theorems to the expressions: ( C) D C DEF CD EF C D( E F )
15 oolean nalysis of Logic Circuits oolean algebra provides a concise way to express the operation of a logic circuit formed by a combination of logic gates so that the output can be determined for various combinations of input values.
16 oolean Expression for a Logic Circuit To derive the oolean expression for a given logic circuit, begin at the left-most inputs and work toward the final output, writing the expression for each gate. C D CD CD (CD)
17 Constructing a Truth Table for a Logic Circuit Once the oolean expression for a given logic circuit has been determined, a truth table that shows the output for all possible values of the input variables can be developed. Let s take the previous circuit as the example: (CD) There are four variables, hence 16 (2 4 ) combinations of values are possible.
18 Constructing a Truth Table for a Logic Circuit Evaluating the expression To evaluate the expression (CD),, first find the values of the variables that make the expression equal to 1 (using the rules for oolean add & mult). In this case, the expression equals 1 only if 1 and CD1 because (CD)
19 Constructing a Truth Table for a Logic Circuit Evaluating the expression (cont ) Now, determine when CD term equals 1. The term CD1 if either 1 or CD1 or if both and CD equal 1 because CD 10 1 CD 01 1 CD 11 1 The term CD1 only if C1 and D1
20 Constructing a Truth Table for a Logic Circuit Evaluating the expression (cont ) Summary: (CD)1 When 1 and 1 regardless of the values of C and D When 1 and C1 and D1 regardless of the value of The expression (CD)0 for all other value combinations of the variables.
21 Constructing a Truth Table for a Logic Circuit Putting the results in truth table format (CD)1 When 1 and 1 regardless of the values of C and D When 1 and C1 and D1 regardless of the value of INPUTS OUTPUT C D (CD)
EEE130 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
CMSC 313 Lecture 16 Postulates & Theorems of Boolean Algebra Semiconductors CMOS Logic Gates
CMSC 33 Lecture 6 Postulates & Theorems of oolean lgebra Semiconductors CMOS Logic Gates UMC, CMSC33, Richard Chang Last Time Overview of second half of this course Logic gates & symbols
12/31/2010. Overview. 05-Boolean Algebra Part 3 Text: Unit 3, 7. DeMorgan s Law. Example. Example. DeMorgan s Law
Overview 05-oolean lgebra Part 3 Text: Unit 3, 7 EEGR/ISS 201 Digital Operations and omputations Winter 2011 DeMorgan s Laws lgebraic Simplifications Exclusive-OR and Equivalence Functionally omplete NND-NOR
CHAPTER 3 LOGIC GATES & BOOLEAN ALGEBRA
CHPTER 3 LOGIC GTES & OOLEN LGER C H P T E R O U T C O M E S Upon completion of this chapter, student should be able to: 1. Describe the basic logic gates operation 2. Construct the truth table for basic
Why digital? Overview. Number Systems. Binary to Decimal conversion
Why digital? Overview It has the following advantages over analog. It can be processed and transmitted efficiently and reliably. It can be stored and retrieved with greater accuracy. Noise level does not
Lecture 3. Title goes here 1. level Networks. Boolean Algebra and Multi-level. level. level. level. level
Lecture 3 Dr Richard Reilly Dept. of Electronic & Electrical Engineering Room 53, Engineering uilding oolean lgebra and Multi- oolean algebra George oole, little formal education yet was a brilliant scholar.
ENGR 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
BOOLEAN ALGEBRA. Introduction. 1854: Logical algebra was published by George Boole known today as Boolean Algebra
BOOLEAN ALGEBRA Introduction 1854: Logical algebra was published by George Boole known today as Boolean Algebra It s a convenient way and systematic way of expressing and analyzing the operation of logic
Logic Gates and Boolean Algebra
Logic Gates and oolean lgebra The ridge etween Symbolic Logic nd Electronic Digital Computing Compiled y: Muzammil hmad Khan mukhan@ssuet.edu.pk asic Logic Functions and or nand nor xor xnor not 2 Logic
Combinational logic. Possible logic functions of two variables. Minimal set of functions. Cost of different logic functions.
Combinational logic Possible logic functions of two variables Logic functions, truth tables, and switches NOT, ND, OR, NND, NOR, OR,... Minimal set xioms and theorems of oolean algebra Proofs by re-writing
Digital Design 2. Logic Gates and Boolean Algebra
Digital Design 2. Logic Gates and oolean lgebra József Sütő ssistant Lecturer References: [1] D.M. Harris, S.L. Harris, Digital Design and Computer rchitecture, 2nd ed., Elsevier, 213. [2] T.L. Floyd,
Unit 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
Theorem/Law/Axioms Over (.) Over (+)
material prepared by: MUKESH OHR Follow me on F : http://www.facebook.com/mukesh.sirji4u OOLEN LGER oolean lgebra is a set of rules, laws and theorems by which logical operations can be mathematically
COSC3330 Computer Architecture Lecture 2. Combinational Logic
COSC333 Computer rchitecture Lecture 2. Combinational Logic Instructor: Weidong Shi (Larry), PhD Computer Science Department University of Houston Today Combinational Logic oolean lgebra Mux, DeMux, Decoder
Part 5: Digital Circuits
Characteristics of any number system are: Part 5: Digital Circuits 5.: Number Systems & Code Conversions. ase or radix is equal to the number of possible symbols in the system 2. The largest value of digit
Learning Objectives. Boolean Algebra. In this chapter you will learn about:
Ref. Page Slide /78 Learning Objectives In this chapter you will learn about: oolean algebra Fundamental concepts and basic laws of oolean algebra oolean function and minimization Logic gates Logic circuits
Goals 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/
Appendix A: Digital Logic. Principles of Computer Architecture. Principles of Computer Architecture by M. Murdocca and V. Heuring
- Principles of Computer rchitecture Miles Murdocca and Vincent Heuring 999 M. Murdocca and V. Heuring -2 Chapter Contents. Introduction.2 Combinational Logic.3 Truth Tables.4 Logic Gates.5 Properties
Lecture 1. Notes. Notes. Notes. Introduction. Introduction digital logic February Bern University of Applied Sciences
Output voltage Input voltage 3.3V Digital operation (Switch) Lecture digital logic February 26 ern University of pplied Sciences Digital vs nalog Logic =? lgebra Logic = lgebra oolean lgebra Exercise Rev.
Having read this workbook you should be able to: design a logic circuit from its Boolean equation or truth table.
Objectives Having read this workbook you should be able to: analyse a given logic circuit by deriving its oolean equation and completing its truth table. design a logic circuit from its oolean equation
Electronics. 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
Boolean Algebra. Boolean Variables, Functions. NOT operation. AND operation. AND operation (cont). OR operation
oolean lgebra asic mathematics for the study of logic design is oolean lgebra asic laws of oolean lgebra will be implemented as switching devices called logic gates. Networks of Logic gates allow us to
EECS150 - 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
LOGIC GATES A Y=A+B. Logic symbol of OR gate B The Boolean expression of OR gate is Y = A + B, read as Y equals A 'OR' B.
LOGIC GTS J-Physics INTRODUCTION : logic gate is a digital circuit which is based on certain logical relationship between the input and the output voltages of the circuit. The logic gates are built using
Outline. EECS150 - Digital Design Lecture 4 - Boolean Algebra I (Representations of Combinational Logic Circuits) Combinational Logic (CL) Defined
EECS150 - Digital Design Lecture 4 - Boolean Algebra I (Representations of Combinational Logic Circuits) January 30, 2003 John Wawrzynek Outline Review of three representations for combinational logic:
BOOLEAN ALGEBRA INVESTIGATIONS
OOLEN LGER INVESTIGTIONS NMES: dapted from http://educ.queensu.ca/~compsci/resources/oollogic/assocdistrib.html 1 1. If one of the inputs is always 1 (true), what is the output? 1 Therefore, + 1 = 1 0
Digital 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
CS 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
Chapter 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
New Students Day Activity
Course: S ELECTRONICS New Students Day ctivity Introduction: In S Level Electronics you need to gain an understanding of the electronic circuits so that you can then start to design your own circuits like
Chapter 7 Combinational Logic Networks
Overview Design Example Design Example 2 Universal Gates NND-NND Networks NND Chips Chapter 7 Combinational Logic Networks SKEE223 Digital Electronics Mun im/rif/izam KE, Universiti Teknologi Malaysia
Unit 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
Digital Fundamentals
Digital Fundamentals Tenth Edition Floyd hapter 5 Modified by Yuttapong Jiraraksopakun Floyd, Digital Fundamentals, 10 th 2008 Pearson Education ENE, KMUTT ed 2009 2009 Pearson Education, Upper Saddle
Prove that if not fat and not triangle necessarily means not green then green must be fat or triangle (or both).
hapter : oolean lgebra.) Definition of oolean lgebra The oolean algebra is named after George ool who developed this algebra (854) in order to analyze logical problems. n example to such problem is: Prove
Lecture 2. Notes. Notes. Notes. Boolean algebra and optimizing logic functions. BTF Electronics Fundamentals August 2014
Lecture 2 Electronics ndreas Electronics oolean algebra and optimizing logic functions TF322 - Electronics Fundamentals ugust 24 Exercise ndreas ern University of pplied Sciences Rev. 946f32 2. of oolean
2. Associative Law: A binary operator * on a set S is said to be associated whenever (A*B)*C = A*(B*C) for all A,B,C S.
BOOLEAN ALGEBRA 2.1 Introduction Binary logic deals with variables that have two discrete values: 1 for TRUE and 0 for FALSE. A simple switching circuit containing active elements such as a diode and transistor
UNIT 8A Computer Circuitry: Layers of Abstraction. Boolean Logic & Truth Tables
UNIT 8 Computer Circuitry: Layers of bstraction 1 oolean Logic & Truth Tables Computer circuitry works based on oolean logic: operations on true (1) and false (0) values. ( ND ) (Ruby: && ) 0 0 0 0 0 1
Boole Algebra and Logic Series
S1 Teknik Telekomunikasi Fakultas Teknik Elektro oole lgebra and Logic Series 2016/2017 CLO1-Week2-asic Logic Operation and Logic Gate Outline Understand the basic theory of oolean Understand the basic
INTRO 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
2009 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
LOGIC GATES (PRACTICE PROBLEMS)
LOGIC GTES (PRCTICE PROLEMS) Key points and summary First set of problems from Q. Nos. 1 to 9 are based on the logic gates like ND, OR, NOT, NND & NOR etc. First four problems are basic in nature. Problems
Gates. Quiz 1 will cover up to and including this lecture. The book says something about NAND... maybe an in-law. Is he talking about BILL??? 6.
Gates Is he talking about ILL??? The book says something about NND... maybe an in-law. WRD & HLSTED 6.4 NERD KIT Quiz will cover up to and including this lecture 6.4 - Fall 22 9/7/2 L4 - Gates Quick Review
EECS Variable Logic Functions
EECS150 Section 1 Introduction to Combinational Logic Fall 2001 2-Variable Logic Functions There are 16 possible functions of 2 input variables: in general, there are 2**(2**n) functions of n inputs X
Department of Electrical and Computer Engineering University of Wisconsin - Madison. ECE/CS 352 Digital System Fundamentals.
Last (family) name: First (given) name: Student I.D. #: Circle section: Lipasti Kim Department of Electrical and Computer Engineering University of Wisconsin - Madison ECE/CS 352 Digital System Fundamentals
Lecture 10: 09//25/03 A.R. Neureuther Version Date 09/14/03 EECS 42 Introduction to Digital Electronics Andrew R. Neureuther
EECS 42 Intro. Digital Electronics Fall 23 Lecture : 9//25/3.R. Neureuther Version Date 9/4/3 EECS 42 Introduction to Digital Electronics ndrew R. Neureuther Lecture # Prof. King: asic Digital locks 2
WEEK 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
Ch 2. Combinational Logic. II - Combinational Logic Contemporary Logic Design 1
Ch 2. Combinational Logic II - Combinational Logic Contemporary Logic Design 1 Combinational logic Define The kind of digital system whose output behavior depends only on the current inputs memoryless:
Boolean 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
CHAPTER 7 MULTI-LEVEL GATE CIRCUITS NAND AND NOR GATES
CHAPTER 7 MULTI-LEVEL GATE CIRCUITS NAND AND NOR GATES This chapter in the book includes: Objectives Study Guide 7.1 Multi-Level Gate Circuits 7.2 NAND and NOR Gates 7.3 Design of Two-Level Circuits Using
Switches: basic element of physical implementations
Combinational logic Switches Basic logic and truth tables Logic functions Boolean algebra Proofs by re-writing and by perfect induction Winter 200 CSE370 - II - Boolean Algebra Switches: basic element
3.4 Set Operations Given a set A, the complement (in the Universal set U) A c is the set of all elements of U that are not in A. So A c = {x x / A}.
3.4 Set Operations Given a set, the complement (in the niversal set ) c is the set of all elements of that are not in. So c = {x x /. (This type of picture is called a Venn diagram.) Example 39 Let = {1,
Logic Design Combinational Circuits. Digital Computer Design
Logic Design Combinational Circuits Digital Computer Design Topics Combinational Logic Karnaugh Maps Combinational uilding locks Timing 2 Logic Circuit logic circuit is composed of: Inputs Outputs Functional
Possible logic functions of two variables
ombinational logic asic logic oolean algebra, proofs by re-writing, proofs by perfect induction logic functions, truth tables, and switches NOT, ND, OR, NND, NOR, OR,..., minimal set Logic realization
Discrete Mathematics. CS204: Spring, Jong C. Park Computer Science Department KAIST
Discrete Mathematics CS204: Spring, 2008 Jong C. Park Computer Science Department KAIST Today s Topics Combinatorial Circuits Properties of Combinatorial Circuits Boolean Algebras Boolean Functions and
L2: Combinational Logic Design (Construction and Boolean Algebra)
L2: Combinational Logic Design (Construction and oolean lgebra) cknowledgements: Lecture material adapted from Chapter 2 of R. Katz, G. orriello, Contemporary Logic Design (second edition), Pearson Education,
for Digital Systems Simplification of logic functions Tajana Simunic Rosing Sources: TSR, Katz, Boriello & Vahid
SE140: omponents and Design Techniques for Digital Systems Simplification of logic functions Tajana Simunic Rosing 1 What we covered thus far: Number representations Where we are now inary, Octal, Hex,
Number System. Decimal to binary Binary to Decimal Binary to octal Binary to hexadecimal Hexadecimal to binary Octal to binary
Number System Decimal to binary Binary to Decimal Binary to octal Binary to hexadecimal Hexadecimal to binary Octal to binary BOOLEAN ALGEBRA BOOLEAN LOGIC OPERATIONS Logical AND Logical OR Logical COMPLEMENTATION
COS 140: Foundations of Computer Science
COS 140: Foundations of Computer Science Boolean Algebra Fall 2018 Introduction 3 Problem................................................................. 3 Boolean algebra...........................................................
UC Berkeley College of Engineering, EECS Department CS61C: Representations of Combinational Logic Circuits
2 Wawrzynek, Garcia 2004 c UCB UC Berkeley College of Engineering, EECS Department CS61C: Representations of Combinational Logic Circuits 1 Introduction Original document by J. Wawrzynek (2003-11-15) Revised
Logic 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
Chapter 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
Lecture 4: More Boolean Algebra
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
Chapter 2 Part 7 Combinational Logic Circuits
University of Wisconsin - Madison EE/omp Sci 352 Digital Systems Fundamentals Kewal K. Saluja and u Hen Hu Spring 2002 hapter 2 Part 7 ombinational Logic ircuits Originals by: harles R. Kime and Tom Kamisnski
Chapter 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 =
Logic. Basic Logic Functions. Switches in series (AND) Truth Tables. Switches in Parallel (OR) Alternative view for OR
TOPIS: Logic Logic Expressions Logic Gates Simplifying Logic Expressions Sequential Logic (Logic with a Memory) George oole (85-864), English mathematician, oolean logic used in digital computers since
Chapter 2 Combinational Logic Circuits
Logic and Computer Design Fundamentals Chapter 2 Combinational Logic Circuits Part 3 Additional Gates and Circuits Overview Part 1 Gate Circuits and Boolean Equations Binary Logic and Gates Boolean Algebra
This 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
CS61c: Representations of Combinational Logic Circuits
CS61c: Representations of Combinational Logic Circuits J. Wawrzynek March 5, 2003 1 Introduction Recall that synchronous systems are composed of two basic types of circuits, combination logic circuits,
1 Boolean Algebra Simplification
cs281: Computer Organization Lab3 Prelab Our objective in this prelab is to lay the groundwork for simplifying boolean expressions in order to minimize the complexity of the resultant digital logic circuit.
Digital Logic. Lecture 5 - Chapter 2. Outline. Other Logic Gates and their uses. Other Logic Operations. CS 2420 Husain Gholoom - lecturer Page 1
Lecture 5 - Chapter 2 Outline Other Logic Gates and their uses Other Logic Operations CS 2420 Husain Gholoom - lecturer Page 1 Digital logic gates CS 2420 Husain Gholoom - lecturer Page 2 Buffer A buffer
L2: Combinational Logic Design (Construction and Boolean Algebra)
L2: Combinational Logic Design (Construction and oolean lgebra) cknowledgements: Materials in this lecture are courtesy of the following people and used with permission. - Randy H. Katz (University of
CSE 140, Lecture 2 Combinational Logic CK Cheng CSE Dept. UC San Diego
CSE 140, Lecture 2 Combinational Logic CK Cheng CSE Dept. UC San Diego 1 Combinational Logic Outlines 1. Introduction 1. Scope 2. Review of Boolean lgebra 3. Review: Laws/Theorems and Digital Logic 2.
Algebraic Methods for the Analysis and Synthesis
lgebraic ethods for the nalysis and Synthesis Fundaentals of oolean lgebra asic Postulates. oolean algebra is closed algebraic syste containing a set K of two or ore eleents and two operators and, ND and
4 Switching Algebra 4.1 Axioms; Signals and Switching Algebra
4 Switching Algebra 4.1 Axioms; Signals and Switching Algebra To design a digital circuit that will perform a required function, it is necessary to manipulate and combine the various input signals in certain
CprE 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
Chapter 2. Digital Logic Basics
Chapter 2 Digital Logic Basics 1 2 Chapter 2 2 1 Implementation using NND gates: We can write the XOR logical expression B + B using double negation as B+ B = B+B = B B From this logical expression, we
Section 001. Read this before starting! You may use one sheet of scrap paper that you will turn in with your test.
Points missed: Student's Name: Total score: /100 points East Tennessee State University Department of Computer and Information Sciences CSCI 2150 (Tarnoff) Computer Organization TEST 1 for Spring Semester,
Computer Organization: Boolean Logic
Computer Organization: Boolean Logic Representing and Manipulating Data Last Unit How to represent data as a sequence of bits How to interpret bit representations Use of levels of abstraction in representing
ﻮﻧﺭﺎﮐ ﺔﺸﻘﻧ ﺎﺑ ﻱﺯﺎﺳ ﻪﻨﻴﻬﺑ
بهينه سازي با نقشة کارنو Karnaugh Map Karnaugh Map Method of graphically representing the truth table that helps visualize adjacencies 2-variable K-map 3-variable K-map 2 3 2 3 6 7 4 5 D 3 2 4 5 7 6 2
Combinational 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
Digital Electronics. Delay Max. FF Rate Power/Gate High Low (ns) (MHz) (mw) (V) (V) Standard TTL (7400)
P57/67 Lec9, P Digital Electronics Introduction: In electronics we can classify the building blocks of a circuit or system as being either analog or digital in nature. If we focus on voltage as the circuit
2 Application of Boolean Algebra Theorems (15 Points - graded for completion only)
CSE140 HW1 Solution (100 Points) 1 Introduction The purpose of this assignment is three-fold. First, it aims to help you practice the application of Boolean Algebra theorems to transform and reduce Boolean
Lecture 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
II. 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
CS 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
CMSC 313 Lecture 16 Announcement: no office hours today. Good-bye Assembly Language Programming Overview of second half on Digital Logic DigSim Demo
CMSC 33 Lecture 6 nnouncement: no office hours today. Good-bye ssembly Language Programming Overview of second half on Digital Logic DigSim Demo UMC, CMSC33, Richard Chang Good-bye ssembly
Boolean Algebra and Digital Logic 2009, University of Colombo School of Computing
IT 204 Section 3.0 Boolean Algebra and Digital Logic Boolean Algebra 2 Logic Equations to Truth Tables X = A. B + A. B + AB A B X 0 0 0 0 3 Sum of Products The OR operation performed on the products of
Lecture 9: Digital Electronics
Introduction: We can classify the building blocks of a circuit or system as being either analog or digital in nature. If we focus on voltage as the circuit parameter of interest: nalog: The voltage can
Combinational Logic (mostly review!)
ombinational Logic (mostly review!)! Logic functions, truth tables, and switches " NOT, N, OR, NN, NOR, OR,... " Minimal set! xioms and theorems of oolean algebra " Proofs by re-writing " Proofs by perfect
EECS150 - 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
ECE 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
Chapter 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
Lecture 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
Textbook: 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
Appendix A: Digital Logic. CPSC 352- Computer Organization
- CPSC 352- Computer Organization -2 Chapter Contents. Introduction.2 Combinational Logic.3 Truth Tables.4 Logic Gates.5 Properties of oolean lgebra.6 The Sum-of-Products Form, and Logic Diagrams.7 The
DIGITAL CIRCUIT LOGIC BOOLEAN ALGEBRA (CONT.)
DIGITAL CIRCUIT LOGIC BOOLEAN ALGEBRA (CONT.) 1 Learning Objectives 1. Apply the laws and theorems of Boolean algebra to to the manipulation of algebraic expressions to simplifying an expression, finding
DIGITAL 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
Boolean algebra. Examples of these individual laws of Boolean, rules and theorems for Boolean algebra are given in the following table.
The Laws of Boolean Boolean algebra As well as the logic symbols 0 and 1 being used to represent a digital input or output, we can also use them as constants for a permanently Open or Closed circuit or
Standard 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
CMSC 313 Lecture 15 Good-bye Assembly Language Programming Overview of second half on Digital Logic DigSim Demo
CMSC 33 Lecture 5 Good-bye ssembly Language Programming Overview of second half on Digital Logic DigSim Demo UMC, CMSC33, Richard Chang Good-bye ssembly Language What a pain! Understand