Learning Objectives 10/7/2010. CE 411 Digital System Design. Fundamental of Logic Design. Review the basic concepts of logic circuits. Dr.

Size: px
Start display at page:

Download "Learning Objectives 10/7/2010. CE 411 Digital System Design. Fundamental of Logic Design. Review the basic concepts of logic circuits. Dr."

Transcription

1 /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 gates ynthesis Create CMO logic gates = = Battery ight (a) Two states of a switch (a) imple connection to a battery (b) ymbol for a switch (b) Using a ground connection as the return path Figure.. A binary switch. Figure.. A light controlled by a switch. ight (a) The logical AND function (series connection) ight ight (b) The logical OR function (parallel connection) Figure.. Two basic functions. Figure.4. A series-parallel connection.

2 /7/ R Figure.5. An inverting circuit. Figure.6. A truth table for AND and OR. Basic Gates AND, OR, NOT n n (a) AND gates + n n (b) OR gates Figure.7. Three-input AND and OR. (c) NOT gate Basic Gates NAND, NOR n n (a) NAND gates f = n n (b) NOR gates Figure.9. An OR-AND function.

3 /7/ DeMorgan s Theorem and other symbols for NAND, NOR A B f Time (a) = + (c) Timing diagram g (d) Network that implements g = + (b) + = Figure.b. ogic network. Basic Gates XOR f = f = (a) Truth table (b) Graphical symbol f = Figure.. Proof of DeMorgan s theorem. (c) um-of-products implementation Basic Gates XNOR f = f = =. Variables and Functions n Function y=f(,...n) y (a) Truth table (b) Graphical symbol f = A function is defined as the dependency of output y on the n inputs (,, n) The n inputs (,, n) are variables The function of a combinational logic circuit can be epressed by a Boolean logic function For a Boolean logic function, output and inputs are binary, and the basic operators include AND, OR, NOT. (c) um-of-products implementation Eample f (,, )

4 /7/ Basic functions ummary of basic logic functions Inversion, AND, OR Can be used to implement logic function of any compleity ogic gates The basic logic function (operation) can be implemented electronically with transistors, which is called a logic gate A logic gate has one or more inputs and one output schematics + NOT Truth Table Karnaugh Map f (,, ) y Representations of a logic function: -- mathematic Algebra epression -- Truth Table -- Karnaugh map (net page) Observations for an n-variable function: n ) rows in truth table ( ) n ) different n-variable functions totally 4 different -variable functions: f()=, f()=, f()=, f()= 6 different -variable functions 56 different -variable functions m m m m m 4 m 5 m 6 m 7 (a) Truth table m m m m m 6 m 7 (b) Karnaugh map m 4 m 5 f = = 5 = Boolean Algebra Aioms of Boolean Algebra =, =, =, = +=, +=, +=, += If =, then =; if =, then = ingle-variable theorems X =, =, +=, +=, +=, = Multiple-Variable Properties Commutative, associative, distributive, absorption, combining, DeMorgan s theorem f =

5 /7/ Commutative Associative Distributive Absorption Combining Properties y y ( y z) ( y) z DeMorgan s theorem y z y z y y y y y ynthesis using basic logic gates ynthesis: begin with a description of the desired behavior, and then generate a circuit that realizes this behavior. Eample of synthesis, ) f (, ) f ( um-of-products Minterm: any function can be epressed as the sum of some minterms. For a function of n variables, a product term in which each of the n variables appears once Variables either in uncomplemented or complemented form For a given row of a truth table, i of i=, i if i = Materm: any function can be epressed as the product of some materms. For a function of n variables, a sum term in which each of the n variables appears once Variables either in uncomplemented or complemented form For a given row of a truth table, i of =, i i if i = Three-variable minterms and materms um-of-products, Product-of-sums Transistor as a switch Concept of switch ignals are assumed to have only possible values(, and ) The basic element is a switch which has two states The switch state is controlled by an input variable witch is open if =; closed if = OP PO f (,, ) m(,4,5,6 ) f,, ) (,,,7) ( M 5

6 /7/ Implementation of ogic gates () Transistor switches Implementation of ogic gates () CMO logic gates (as networks of transistors) PUN T T T V V T T T T T 4 f T V T 4 PDN on on off off on off off on off on on off off off on on (a) Circuit (b) Truth table and transistor states Implementation of ogic gates () PUN: PMO PDN: NMO Output Vf is selectively connected either to Vdd through PUN or to Gnd through PDN, depending on inputs VDD=5V witch network GND V V n y Pull-up network (PUN) Pull-down network (PDN) Comple CMO logic gate Eample. f f ( ) For f= For f= V V V Procedures for comple logic gates Epress a function so that all variables appear in their complemented form e.g. f (,, ) Derive the PUN based on f (,, ) Products transistors (or branches) in series ums transistors (or branches) in parallel Derive a complemented function so that all variables appear in their uncomplemented form e. g. f (,, ) Derive the PDN based on f (,, ) Products transistors (or branches) in series ums transistors (or branches) in parallel Eercise? Create CMO gate for function f ( ) 4 6

7 /7/ Analysis of comple CMO gate Derive epression from circuit based on PUN Branches in parallel sums Branches in series products All variables in complemented form Derive PDN from PUN, or derive PUN from PDN For branches in parallel in PDN, there are branches in series in PUN; vice versa. For branches in series in PDN, there are branches in parallel in PUN; vice versa. Problem.6 to. Problem.7 to. Homework 7

CS 226: Digital Logic Design

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

More information

University of Technology

University 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 information

Ex: Boolean expression for majority function F = A'BC + AB'C + ABC ' + ABC.

Ex: 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 information

Logic Design. Chapter 2: Introduction to Logic Circuits

Logic 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 information

Digital Design. Digital Design

Digital 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 information

XI STANDARD [ COMPUTER SCIENCE ] 5 MARKS STUDY MATERIAL.

XI STANDARD [ COMPUTER SCIENCE ] 5 MARKS STUDY MATERIAL. 2017-18 XI STANDARD [ COMPUTER SCIENCE ] 5 MARKS STUDY MATERIAL HALF ADDER 1. The circuit that performs addition within the Arithmetic and Logic Unit of the CPU are called adders. 2. A unit that adds two

More information

ECE 342 Electronic Circuits. Lecture 34 CMOS Logic

ECE 342 Electronic Circuits. Lecture 34 CMOS Logic ECE 34 Electronic Circuits Lecture 34 CMOS Logic Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois jesa@illinois.edu 1 De Morgan s Law Digital Logic - Generalization ABC... ABC...

More information

Lecture 4: More Boolean Algebra

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

More information

CPE100: Digital Logic Design I

CPE100: Digital Logic Design I Professor Brendan Morris, SEB 3216, brendan.morris@unlv.edu CPE100: Digital Logic Design I Midterm01 Review http://www.ee.unlv.edu/~b1morris/cpe100/ 2 Logistics Thursday Oct. 5 th In normal lecture (13:00-14:15)

More information

Chapter 2 Boolean Algebra and Logic Gates

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 =

More information

Chapter 2 Combinational Logic Circuits

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

More information

EEE130 Digital Electronics I Lecture #4

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

More information

Boolean Algebra and Logic Simplification

Boolean 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 information

This form sometimes used in logic circuit, example:

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

More information

LOGIC GATES. Basic Experiment and Design of Electronics. Ho Kyung Kim, Ph.D.

LOGIC 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 information

Digital Logic. CS211 Computer Architecture. l Topics. l Transistors (Design & Types) l Logic Gates. l Combinational Circuits.

Digital Logic. CS211 Computer Architecture. l Topics. l Transistors (Design & Types) l Logic Gates. l Combinational Circuits. CS211 Computer Architecture Digital Logic l Topics l Transistors (Design & Types) l Logic Gates l Combinational Circuits l K-Maps Figures & Tables borrowed from:! http://www.allaboutcircuits.com/vol_4/index.html!

More information

Combinational Logic Circuits Part II -Theoretical Foundations

Combinational 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 information

L2: Combinational Logic Design (Construction and Boolean Algebra)

L2: Combinational Logic Design (Construction and Boolean Algebra) L2: Combinational Logic Design (Construction and Boolean Algebra) Acknowledgements: Lecture material adapted from Chapter 2 of R. Katz, G. Borriello, Contemporary Logic Design (second edition), Pearson

More information

Chapter 2: Boolean Algebra and Logic Gates

Chapter 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 information

Chapter 2: Princess Sumaya Univ. Computer Engineering Dept.

Chapter 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 information

XOR - XNOR Gates. The graphic symbol and truth table of XOR gate is shown in the figure.

XOR - XNOR Gates. The graphic symbol and truth table of XOR gate is shown in the figure. XOR - XNOR Gates Lesson Objectives: In addition to AND, OR, NOT, NAND and NOR gates, exclusive-or (XOR) and exclusive-nor (XNOR) gates are also used in the design of digital circuits. These have special

More information

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 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

More information

2009 Spring CS211 Digital Systems & Lab CHAPTER 2: INTRODUCTION TO LOGIC CIRCUITS

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

More information

MC9211 Computer Organization

MC9211 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 information

Lecture 2 Review on Digital Logic (Part 1)

Lecture 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 information

Chapter 2 Combinational Logic Circuits

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

More information

Lecture 5: NAND, NOR and XOR Gates, Simplification of Algebraic Expressions

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

More information

CS 121 Digital Logic Design. Chapter 2. Teacher Assistant. Hanin Abdulrahman

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

More information

Floating Point Representation and Digital Logic. Lecture 11 CS301

Floating Point Representation and Digital Logic. Lecture 11 CS301 Floating Point Representation and Digital Logic Lecture 11 CS301 Administrative Daily Review of today s lecture w Due tomorrow (10/4) at 8am Lab #3 due Friday (9/7) 1:29pm HW #5 assigned w Due Monday 10/8

More information

Logic Gate Level. Part 2

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

More information

Chapter 2. Boolean Algebra and Logic Gates

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

More information

Chapter 7 Logic Circuits

Chapter 7 Logic Circuits Chapter 7 Logic Circuits Goal. Advantages of digital technology compared to analog technology. 2. Terminology of Digital Circuits. 3. Convert Numbers between Decimal, Binary and Other forms. 5. Binary

More information

ECE 20B, Winter 2003 Introduction to Electrical Engineering, II LECTURE NOTES #2

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

More information

Lecture 22 Chapters 3 Logic Circuits Part 1

Lecture 22 Chapters 3 Logic Circuits Part 1 Lecture 22 Chapters 3 Logic Circuits Part 1 LC-3 Data Path Revisited How are the components Seen here implemented? 5-2 Computing Layers Problems Algorithms Language Instruction Set Architecture Microarchitecture

More information

Unit 8A Computer Organization. Boolean Logic and Gates

Unit 8A Computer Organization. Boolean Logic and Gates Unit 8A Computer Organization Boolean Logic and Gates Announcements Bring ear buds or headphones to lab! 15110 Principles of Computing, Carnegie Mellon University - CORTINA 2 Representing and Manipulating

More information

WEEK 2.1 BOOLEAN ALGEBRA

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

More information

211: Computer Architecture Summer 2016

211: 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 information

CprE 281: Digital Logic

CprE 281: Digital Logic CprE 28: Digital Logic Instructor: Alexander Stoytchev http://www.ece.iastate.edu/~alexs/classes/ Examples of Solved Problems CprE 28: Digital Logic Iowa State University, Ames, IA Copyright Alexander

More information

Combinational Logic Design Principles

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

More information

Chapter 2 Combinational Logic Circuits

Chapter 2 Combinational Logic Circuits Logic and Computer Design Fundamentals Chapter 2 Combinational Logic Circuits Part 3 Additional Gates and Circuits Charles Kime & Thomas Kaminski 2008 Pearson Education, Inc. (Hyperlinks are active in

More information

Boolean Algebra & Logic Gates. By : Ali Mustafa

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

More information

Logic 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 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 information

Cs302 Quiz for MID TERM Exam Solved

Cs302 Quiz for MID TERM Exam Solved Question # 1 of 10 ( Start time: 01:30:33 PM ) Total Marks: 1 Caveman used a number system that has distinct shapes: 4 5 6 7 Question # 2 of 10 ( Start time: 01:31:25 PM ) Total Marks: 1 TTL based devices

More information

CMSC 313 Lecture 17. Focus Groups. Announcement: in-class lab Thu 10/30 Homework 3 Questions Circuits for Addition Midterm Exam returned

CMSC 313 Lecture 17. Focus Groups. Announcement: in-class lab Thu 10/30 Homework 3 Questions Circuits for Addition Midterm Exam returned Focus Groups CMSC 33 Lecture 7 Need good sample of all types of CS students Mon /7 & Thu /2, 2:3p-2:p & 6:p-7:3p Announcement: in-class lab Thu /3 Homework 3 Questions Circuits for Addition Midterm Exam

More information

E40M. Binary Numbers. M. Horowitz, J. Plummer, R. Howe 1

E40M. Binary Numbers. M. Horowitz, J. Plummer, R. Howe 1 E40M Binary Numbers M. Horowitz, J. Plummer, R. Howe 1 Reading Chapter 5 in the reader A&L 5.6 M. Horowitz, J. Plummer, R. Howe 2 Useless Box Lab Project #2 Adding a computer to the Useless Box alows us

More information

CHAPTER1: Digital Logic Circuits Combination Circuits

CHAPTER1: 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 information

Digital Logic (2) Boolean Algebra

Digital Logic (2) Boolean Algebra Digital Logic (2) Boolean Algebra Boolean algebra is the mathematics of digital systems. It was developed in 1850 s by George Boole. We will use Boolean algebra to minimize logic expressions. Karnaugh

More information

Boolean algebra. Examples of these individual laws of Boolean, rules and theorems for Boolean algebra are given in the following table.

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

More information

4 Switching Algebra 4.1 Axioms; Signals and Switching Algebra

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

More information

DIGITAL LOGIC CIRCUITS

DIGITAL LOGIC CIRCUITS DIGITAL LOGIC CIRCUITS Introduction Logic Gates Boolean Algebra Map Specification Combinational Circuits Flip-Flops Sequential Circuits Memory Components Integrated Circuits Digital Computers 2 LOGIC GATES

More information

Chapter 2 Combinational

Chapter 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 information

ELCT201: DIGITAL LOGIC DESIGN

ELCT201: 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 information

In Module 3, we have learned about Exclusive OR (XOR) gate. Boolean Expression AB + A B = Y also A B = Y. Logic Gate. Truth table

In Module 3, we have learned about Exclusive OR (XOR) gate. Boolean Expression AB + A B = Y also A B = Y. Logic Gate. Truth table Module 8 In Module 3, we have learned about Exclusive OR (XOR) gate. Boolean Expression AB + A B = Y also A B = Y Logic Gate Truth table A B Y 0 0 0 0 1 1 1 0 1 1 1 0 In Module 3, we have learned about

More information

Computer Organization: Boolean Logic

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

More information

Every time has a value associated with it, not just some times. A variable can take on any value within a range

Every time has a value associated with it, not just some times. A variable can take on any value within a range Digital Logic Circuits Binary Logic and Gates Logic Simulation Boolean Algebra NAND/NOR and XOR gates Decoder fundamentals Half Adder, Full Adder, Ripple Carry Adder Analog vs Digital Analog Continuous»

More information

Switches: basic element of physical implementations

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

More information

Digital Circuit And Logic Design I. Lecture 3

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

More information

Digital Logic. Lecture 5 - Chapter 2. Outline. Other Logic Gates and their uses. Other Logic Operations. CS 2420 Husain Gholoom - lecturer Page 1

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

More information

Chapter 2 Boolean Algebra and Logic Gates

Chapter 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 information

II. COMBINATIONAL LOGIC DESIGN. - algebra defined on a set of 2 elements, {0, 1}, with binary operators multiply (AND), add (OR), and invert (NOT):

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

More information

7.1. 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 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 information

Circuits & Boolean algebra.

Circuits & 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

DIGITAL CIRCUIT LOGIC BOOLEAN ALGEBRA

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

More information

Combinatorial Logic Design Principles

Combinatorial 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 information

ESE 570: Digital Integrated Circuits and VLSI Fundamentals

ESE 570: Digital Integrated Circuits and VLSI Fundamentals ESE 570: Digital Integrated Circuits and VLSI Fundamentals Lec 2: January 17, 2017 MOS Fabrication pt. 1: Physics and Methodology Lecture Outline! Digital CMOS Basics! VLSI Fundamentals! Fabrication Process

More information

L2: Combinational Logic Design (Construction and Boolean Algebra)

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,

More information

L2: Combinational Logic Design (Construction and Boolean Algebra)

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

More information

1 Boolean Algebra Simplification

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.

More information

Chapter 2 Combinational Logic Circuits

Chapter 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 information

Chapter 2: Switching Algebra and Logic Circuits

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

More information

ESE 570: Digital Integrated Circuits and VLSI Fundamentals

ESE 570: Digital Integrated Circuits and VLSI Fundamentals ESE 570: Digital Integrated Circuits and VLSI Fundamentals Lec 2: January 19, 2016 MOS Fabrication pt. 1: Physics and Methodology Lecture Outline! Digital CMOS Basics! VLSI Fundamentals! Fabrication Process

More information

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) 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 information

CprE 281: Digital Logic

CprE 281: Digital Logic CprE 281: Digital Logic Instructor: Alexander Stoytchev http://www.ece.iastate.edu/~alexs/classes/ NAND and NOR Logic Networks CprE 281: Digital Logic Iowa State University, Ames, IA Copyright Alexander

More information

NAND, NOR and XOR functions properties

NAND, NOR and XOR functions properties Laboratory NAND, NOR and XOR functions properties. Laboratory work goals Enumeration of NAND, NOR and XOR functions properties Presentation of NAND, NOR and XOR modules Realisation of circuits with gates

More information

CprE 281: Digital Logic

CprE 281: Digital Logic CprE 281: Digital Logic Instructor: Alexander Stoytchev http://www.ece.iastate.edu/~alexs/classes/ NAND and NOR Logic Networks CprE 281: Digital Logic Iowa State University, Ames, IA Copyright Alexander

More information

ELEC Digital Logic Circuits Fall 2014 Switching Algebra (Chapter 2)

ELEC Digital Logic Circuits Fall 2014 Switching Algebra (Chapter 2) ELEC 2200-002 Digital Logic Circuits Fall 2014 Switching Algebra (Chapter 2) Vishwani D. Agrawal James J. Danaher Professor Department of Electrical and Computer Engineering Auburn University, Auburn,

More information

Gates and Logic: From switches to Transistors, Logic Gates and Logic Circuits

Gates and Logic: From switches to Transistors, Logic Gates and Logic Circuits Gates and Logic: From switches to Transistors, Logic Gates and Logic Circuits Hakim Weatherspoon CS 3410, Spring 2013 Computer Science Cornell University See: P&H ppendix C.2 and C.3 (lso, see C.0 and

More information

Outline. EECS150 - Digital Design Lecture 4 - Boolean Algebra I (Representations of Combinational Logic Circuits) Combinational Logic (CL) Defined

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:

More information

ENG2410 Digital Design Combinational Logic Circuits

ENG2410 Digital Design Combinational Logic Circuits ENG240 Digital Design Combinational Logic Circuits Fall 207 S. Areibi School of Engineering University of Guelph Binary variables Binary Logic Can be 0 or (T or F, low or high) Variables named with single

More information

CpE358/CS381. Switching Theory and Logical Design. Class 2

CpE358/CS381. Switching Theory and Logical Design. Class 2 CpE358/CS38 Switching Theor and Logical Design Class 2 CpE358/CS38 Switching Theor and Logical Design Summer- 24 Copright 24 Stevens Institute of Technolog -45 Toda s Material Fundamental concepts of digital

More information

Textbook: Digital Design, 3 rd. Edition M. Morris Mano

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

More information

ECE 545 Digital System Design with VHDL Lecture 1A. Digital Logic Refresher Part A Combinational Logic Building Blocks

ECE 545 Digital System Design with VHDL Lecture 1A. Digital Logic Refresher Part A Combinational Logic Building Blocks ECE 545 Digital System Design with VHDL Lecture A Digital Logic Refresher Part A Combinational Logic Building Blocks Lecture Roadmap Combinational Logic Basic Logic Review Basic Gates De Morgan s Laws

More information

EE40 Lec 15. Logic Synthesis and Sequential Logic Circuits

EE40 Lec 15. Logic Synthesis and Sequential Logic Circuits EE40 Lec 15 Logic Synthesis and Sequential Logic Circuits Prof. Nathan Cheung 10/20/2009 Reading: Hambley Chapters 7.4-7.6 Karnaugh Maps: Read following before reading textbook http://www.facstaff.bucknell.edu/mastascu/elessonshtml/logic/logic3.html

More information

Gates and Flip-Flops

Gates and Flip-Flops Gates and Flip-Flops Chris Kervick (11355511) With Evan Sheridan and Tom Power December 2012 On a scale of 1 to 10, how likely is it that this question is using binary?...4? What s a 4? Abstract The operation

More information

Designing Information Devices and Systems II Spring 2018 J. Roychowdhury and M. Maharbiz Discussion 1A

Designing Information Devices and Systems II Spring 2018 J. Roychowdhury and M. Maharbiz Discussion 1A EEC 16B esigning Information evices and ystems II pring 2018 J. Roychowdhury and M. Maharbiz iscussion 1A 1 igit Bases (N) p is used to indicate that the number N is expressed in base p. For example, (N)

More information

CprE 281: Digital Logic

CprE 281: Digital Logic CprE 281: Digital Logic Instructor: Alexander Stoytchev http://www.ece.iastate.edu/~alexs/classes/ Design Examples CprE 281: Digital Logic Iowa State University, Ames, IA Copyright Alexander Stoytchev

More information

Mark Redekopp, All rights reserved. Lecture 5 Slides. Canonical Sums and Products (Minterms and Maxterms) 2-3 Variable Theorems DeMorgan s Theorem

Mark 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 information

Additional Gates COE 202. Digital Logic Design. Dr. Muhamed Mudawar King Fahd University of Petroleum and Minerals

Additional Gates COE 202. Digital Logic Design. Dr. Muhamed Mudawar King Fahd University of Petroleum and Minerals Additional Gates COE 202 Digital Logic Design Dr. Muhamed Mudawar King Fahd University of Petroleum and Minerals Presentation Outline Additional Gates and Symbols Universality of NAND and NOR gates NAND-NAND

More information

Why digital? Overview. Number Systems. Binary to Decimal conversion

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

More information

Theorem/Law/Axioms Over (.) Over (+)

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

More information

Digital Circuit And Logic Design I. Lecture 4

Digital Circuit And Logic Design I. Lecture 4 Digital Circuit And Logic Design I Lecture 4 Outline Combinational Logic Design Principles (2) 1. Combinational-circuit minimization 2. Karnaugh maps 3. Quine-McCluskey procedure Panupong Sornkhom, 2005/2

More information

Digital Design 2. Logic Gates and Boolean Algebra

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,

More information

E&CE 223 Digital Circuits & Systems. Lecture Transparencies (Boolean Algebra & Logic Gates) M. Sachdev

E&CE 223 Digital Circuits & Systems. Lecture Transparencies (Boolean Algebra & Logic Gates) M. Sachdev E&CE 223 Digital Circuits & Systems Lecture Transparencies (Boolean Algebra & Logic Gates) M. Sachdev 4 of 92 Section 2: Boolean Algebra & Logic Gates Major topics Boolean algebra NAND & NOR gates Boolean

More information

CHAPTER 15 CMOS DIGITAL LOGIC CIRCUITS

CHAPTER 15 CMOS DIGITAL LOGIC CIRCUITS CHAPTER 5 CMOS DIGITAL LOGIC CIRCUITS Chapter Outline 5. CMOS Logic Gate Circuits 5. Digital Logic Inverters 5.3 The CMOS Inverter 5.4 Dynamic Operation of the CMOS Inverter 5.5 Transistor Sizing 5.6 Power

More information

UNIVERSITI TENAGA NASIONAL. College of Information Technology

UNIVERSITI TENAGA NASIONAL. College of Information Technology UNIVERSITI TENAGA NASIONAL College of Information Technology BACHELOR OF COMPUTER SCIENCE (HONS.) FINAL EXAMINATION SEMESTER 2 2012/2013 DIGITAL SYSTEMS DESIGN (CSNB163) January 2013 Time allowed: 3 hours

More information

Chapter 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. 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 information

University of Toronto Faculty of Applied Science and Engineering Department of Electrical and Computer Engineering Midterm Examination

University of Toronto Faculty of Applied Science and Engineering Department of Electrical and Computer Engineering Midterm Examination University of Toronto Faculty of Applied Science and Engineering Department of Electrical and Computer Engineering Midterm Eamination ECE 241F - Digital Systems Wednesday October 11, 2006, 6:00 7:30 pm

More information

Logic Gates and Boolean Algebra

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

More information

Boolean Algebra and Logic Gates

Boolean 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 information