Karnaugh Maps (K Maps) K Maps with 3 and 4 Variables


 Esther Simon
 2 years ago
 Views:
Transcription
1 Karnaugh Maps (K Maps) Karnugh map is a graphical representation of a truth table The map contains one cell for each possible minterm adjacent cells differ in onl one literal, i.e., or Two variables, F =f(,) m m m2 m3 Function is plotted b placing in cells corresponding to minterms of function Eample, F = 7 of 92 K Maps with 3 and 4 Variables 3 variables, F = f(,,z); 4 variables, F = f(w,,,z) m m m3 m2 z z m4 m5 m7 m6 z z z z w m m m3 m2 m4 m5 m7 m6 w m2 m3 m5 m4 m8 m9 m m z 7 of 92
2 Eamples F = w = (+ )(+ )(z+z ) w F = w F = w z w 72 of 92 K Map oolean Funct. Simplification To write simplified function, find maimum size groups (minimum literals) that cover all s in map 8 cells > single literal 4 cells > two literals 2 cells > three literals cell > four literals Guidelines for logic snthesis Fewer groups: fewer ND gates and fewer input to the OR gate Fewer literals (larger group): fewer inputs to ND gate Snthesis (design) objectives Smallest number of logic gates Number of inputs to logic gate 73 of 92
3 Eample Consider the following K map Nothing must be a single cell Four groups of two cells each nothing left uncovered The group of 4 (z) term is not needed F = w + w + w + w z w 74 of 92 Product of Sum Epression Recall: Let F be the function F = (all minterms not in F) F = Π (all minterms not in F) (de morgan s theorem) Therefore, one can obtain F b grouping all s on K map, and then taking the complement to obtain productofsum form Hence, F = (w + )( + z )( + z) in sumofproduct form Should check both, sum of products, and product of sums One is often simpler than the other F = z + + w z w F = w + + z 75 of 92
4 Plotting Product of Sum Given, F = (w + )( + + z)( + z) F = w + + z w 76 of 92 Don t Care (Incompletel Specified) Conditions Some times, not all values of a function are defined Some input conditions will never occur We don t care what the output is for that input condition In these cases, we can choose the output to be either or, whichever simplifies the circuit Eample: a circuit is to have an output of if a binar coded decimal (CD) digit is a multiple of 3 digit w z F 77 of 92
5 don t care condition ,, ,, ,, ,, ,, F = (3,6,9) + d(,,2,3,4,5) 78 of 92 Don t Care: Plotting Don t cares are plotted as in the K map Sum of products: treat as if it allows a larger group Product of sums: Treat as of it allows a larger group F = wz + + (sum of products, (a)) F2 = z + w + z (recall F = (all minterms not in F) F2 = ( + z )(w + )( + z) w w (a) (b) 79 of 92
6 Observation: In general, F is not equal to F2 due to different values chosen for don t care cells 8 of 92 More Logic Gates NOT gate ND gate uffer gate NND gate OR gate OR gate NOR gate NOR gate 8 of 92
7 NND and NOR Implementation set of logic gates are functionall complete if an boolean function can be implemented b just these gates ND, OR, NOT ND, NOT ( ) = + ==> OR gate OR, NOT NND NOR NND and NOR gates are easier to implement (smaller area, less power consumption, faster) than ND and OR gates 82 of 92 Logic Implementation with NND/NOR F = () F = + = () Given F = z + w all implementations represent the same function Function can be implemented with NND gates onl Procedure from K map = NDInvert InvertOR gate F = z + w z w present the simplified function in sum of product form (NDOR) use De morgan s theorem to represent the function in NNDNND form F = z + w z w Similar steps for NOR implementation starting from product of sums form F = z + w z w 83 of 92
8 Other TwoLevel Implementations Wired Logic, TransistorTransistor Logic (TTL) Wired logic: if outputs of two logic gates are shorted together TTL stle implementation allows wired connection + 5 V + 5 V + 5 V R R R Out Input Out Inputs ND logic Out NOT gate NND gate wired ND gate Other two level implementations are NDORINVERT and ORNDINVERT 84 of 92 Simplest TwoLevel Epression Some definitions Implicant: a grouping of one or more K map cells Prime implicant: an implicant that is not a subset of another implicant Essential prime implicant: a prime implicant that covers at least one minterm not covered b another prime implicant Eample, f(w,,,z) = (,,2,5,6,7,9,4) + d(3) w w essential prime implicants prime implicants 85 of 92
9 Essential prime implicants: z, Prime implicants: w, w z, w z, w, w z (,5,9,3) (6,4) w (,) w z (,2) w z (5,7) w (6,7) w (2,6) minterms covered * * C D E 86 of 92 ll minterms must be covered Essential prime imlicants must be included (*) Different combinations of prime implicants are: + C; or + D; or + C + E; or + D + E + C or + D are the simplest, hence the simplest function implementation is F = z + + w z + w z or z + + w z + w 87 of 92
10 Tabulation (QuineMcCluske) Method The map method of simplification is convenient if number of variables does not eceed beond 4 or 5 Tabulation method is preferred for a function with large number of variables for F = f(w,,,z) consider two adjacent minterms let a = m4 + m5 = w z + w z = w or = + =  similarl, let b = m2 + m3 = w z + w z = w or = + =  similarl, c = m4 + m5 + m2 + m3 = a + b = w + w = = = of 92 djacent minterms differ b a single bit in their binar representation Tabulation method consists of grouping minterms and sstematicall checking for single bit differences Eample, f(w,,,z) = (,3,4,6,7,8,,,5) + d(5,9) Group minterms according to number of s in binar representation Each element of each section is compared with each element of the section below it; all reductions are recorded in net column Mark terms that combine ll unmarked terms are prime implicants 89 of 92
11 w z of 92,4 (4) 4,5,6,7 (,2) ,8 (8) 8,9,, (,2) ,5 () 3,7,,5 (4,8) ,6 (2) 3 8,9 () 5 8, (2) ,7 (4) 3, (8) ,7 (2) 7 6,7 () 9, (2) , () ,5 (8),5 (4) 9 of 92
12 Prime implicants 3 minterms covered ,4,8 4,5,6,7 8,9,, 3,7,,5 F(w,,,z) =,4 + 4,5,6,7 + 8,9,, + 3,7,, w z + w + w + or F(w,,,z) =,8 + 4,5,6,7 + 8,9,, + 3,7,, z + w + w + 92 of 92
Karnaugh Maps & Combinational Logic Design. ECE 152A Winter 2012
Karnaugh Maps & Combinational Logic Design ECE 52A Winter 22 Reading Assignment Brown and Vranesic 4 Optimized Implementation of Logic Functions 4. Karnaugh Map 4.2 Strategy for Minimization 4.2. Terminology
More informationKarnaugh Map. Alternative way to Boolean Function Simplification. Karnaugh Map. Description of Kmap & Terminology
Alternative way to Boolean Function Simplification Karnaugh Map CIT 595 Spring 2010 Simplification of Boolean functions leads to simpler (and usually faster) digital circuits Simplifying Boolean functions
More information1. Digital Logic Circuits
1 Digital Logic ircuits 1. Digital Logic ircuits Many scientific, industrial and commercial advances have been made possible by the advent of computers. Digital Logic ircuits form the basis of any digital
More information2 1 Implementation using NAND gates: We can write the XOR logical expression A B + A B using double negation as
Chapter 2 Digital Logic asics 2 Implementation using NND gates: We can write the XOR logical expression + using double negation as + = + = From this logical expression, we can derive the following NND
More informationDigital Fundamentals
Digital Fundamentals Tenth Edition Floyd hapter 5 2009 Pearson Education, Upper 2008 Pearson Saddle River, Education NJ 07458. ll Rights Reserved Summary ombinational Logic ircuits In SumofProducts (SOP)
More informationBOOLEAN ALGEBRA & LOGIC GATES
BOOLEAN ALGEBRA & LOGIC GATES Logic gates are electronic circuits that can be used to implement the most elementary logic expressions, also known as Boolean expressions. The logic gate is the most basic
More informationCSEE 3827: Fundamentals of Computer Systems. Standard Forms and Simplification with Karnaugh Maps
CSEE 3827: Fundamentals of Computer Systems Standard Forms and Simplification with Karnaugh Maps Agenda (M&K 2.32.5) Standard Forms ProductofSums (PoS) SumofProducts (SoP) converting between Minterms
More informationENGIN 112 Intro to Electrical and Computer Engineering
ENGIN 112 Intro to Electrical and omputer Engineering Lecture 11 NND and XOR Implementations Overview Developing NND circuits from Kmaps Twolevel implementations onvert from ND/OR to NND (again!) Multilevel
More informationCAS 701. Boolean Algebra. Mahnaz Ahmadi Oct. 14, 2004 McMaster University. References
S 701 oolean lgebra Mahna hmadi Oct. 14 2004 McMaster Universit References J. Eldon whitesitt oolean lgebra and its pplications Ralph P. Grimaldi Discrete and ombinational Mathematics Kenneth H.Rosen Discrete
More informationThe equation for the 3input XOR gate is derived as follows
The equation for the 3input XOR gate is derived as follows The last four product terms in the above derivation are the four 1minterms in the 3input XOR truth table. For 3 or more inputs, the XOR gate
More informationNAND and NOR Implementation
University of Wisconsin  Madison EE/omp ci 352 Digital ystems Fundamentals harles R. Kime ection 2 Fall 200 hapter 2 ombinational Logic ircuits Part 7 harles Kime & Thomas Kaminski NND and NOR Implementation
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 informationChapter 4: Combinational Logic Solutions to Problems: [1, 5, 9, 12, 23, 30]
Chapter 4: Combinational Logic Solutions to Problems: [, 5, 9, 2, 23, 3] Problem: 4 Consider the combinational circuit shown in Fig. P4. (a) Derive the Boolean epressions for T through T 4. Evaluate
More informationComputer Organization I. Lecture 8: Boolean Algebra and Circuit Optimization
Computer Organization I Lecture 8: Boolean Algebra and Circuit Optimization Overview The simplification from SOM to SOP and their circuit implementation Basics of Logic Circuit Optimization: Cost Criteria
More informationGateLevel Minimization
Chapter 3 GateLevel Minimization 3 Outline! Karnaugh Map Method! NAND and NOR Implementations! Other TwoLevel Implementations! ExclusiveOR Function! Hardware Description Language 32 Why Logic Minimization?!
More informationPoints Addressed in this Lecture. Standard form of Boolean Expressions. Lecture 5: Logic Simplication & Karnaugh Map
Points Addressed in this Lecture Lecture 5: Logic Simplication & Karnaugh Map Professor Peter Cheung Department of EEE, Imperial College London (Floyd 4.54.) (Tocci 4.4.5) Standard form of Boolean Expressions
More informationElementary Logic Gates
Elementary Logic Gates Name Symbol Inverter (NOT Gate) ND Gate OR Gate Truth Table Logic Equation = = = = = + C. E. Stroud Combinational Logic Design (/6) Other Elementary Logic Gates NND Gate NOR Gate
More informationKarnaugh Maps (Kmap) Alternate representation of a truth table
Karnaugh Maps (Kmap) lternate representation of a truth table Red decimal = minterm value Note that is the MS for this minterm numbering djacent squares have distance = 1 Valuable tool for logic minimization
More informationTwolevel logic using NAND gates
CSE140: Components and Design Techniques for Digital Systems Two and Multilevel logic implementation Tajana Simunic Rosing 1 Twolevel logic using NND gates Replace minterm ND gates with NND gates Place
More informationBoolean Algebra And Its Applications
oolean lgebra nd Its pplications Introduction Let Ω be a set consisting of two elements denoted by the symbols 0 and 1, i.e. Ω = {0, 1}. Suppose that three operations has been defined: the logical sum
More informationDigital Circuits and Systems
Spring 2015 Week 1 odule 4 Digital Circuits and Sstems interms, aterms SoP and PoS forms Shankar Balachandran* Associate Professor, CSE Department Indian Institute of Technolog adras *Currentl a Visiting
More informationComp 150 Booleans and Digital Logic
Comp 150 Booleans and Digital Logic Recall the bool date type in Python has the two literals True and False and the three operations: not, and, or. The operations are defined by truth tables (see page
More informationChapter 2: Boolean Algebra and Logic Gates. Boolean Algebra
The Universit Of Alabama in Huntsville Computer Science Chapter 2: Boolean Algebra and Logic Gates The Universit Of Alabama in Huntsville Computer Science Boolean Algebra The algebraic sstem usuall used
More informationLogic Design 2013/9/5. Introduction. Logic circuits operate on digital signals
Introduction Logic Design Chapter 2: Introduction to Logic Circuits Logic circuits operate on digital signals Unlike continuous analog signals that have an infinite number of possible values, digital signals
More informationKarnaugh Maps. Circuitwise, this leads to a minimal twolevel implementation
Karnaugh Maps Applications of Boolean logic to circuit design The basic Boolean operations are AND, OR and NOT These operations can be combined to form complex expressions, which can also be directly translated
More informationChapter 1: Number Systems and Conversion
Chapter : Number Systems and Conversion.6 Subtract in binary. Place a over each column from which it was necessary to borrow. (a) (b) (c).7 dd the following numbers in binary using 2 s complement to represent
More informationCSE140: Midterm 1 Solution and Rubric
CSE140: Midterm 1 Solution and Rubric April 23, 2014 1 Short Answers 1.1 True or (6pts) 1. A maxterm must include all input variables (1pt) True 2. A canonical product of sums is a product of minterms
More information4 BOOLEAN ALGEBRA AND LOGIC SIMPLIFICATION
4 BOOLEAN ALGEBRA AND LOGIC SIMPLIFICATION BOOLEAN OPERATIONS AND EXPRESSIONS Variable, complement, and literal are terms used in Boolean algebra. A variable is a symbol used to represent a logical quantity.
More informationCSE 220: Systems Fundamentals I Unit 7: Logic Gates; Digital Logic Design: Boolean Equations and Algebra
CSE 220: Systems Fundamentals I Unit 7: Logic Gates; Digital Logic Design: Boolean Equations and Algebra Logic Gates Logic gatesare simple digital circuits that take one or more binary inputs and produce
More informationLAB 2: BOOLEAN THEOREMS
LAB 2: BOOLEAN THEOREMS OBJECTIVES 1. To implement DeMorgan's theorems in circuit simplification. 2. To design a combinational logic circuit with simplest logic gates representation using Karnaugh Mapping
More information4.203 Write the truth table for each of the following logic functions:
3e4.5 4.201 According to DeMorgan s theorem, the complement of X + Y Z is X Y +Z. Yet both functions are 1 for XYZ = 110. How can both a function and its complement be 1 for the same input combination?
More informationWEEK 2.2 CANONICAL FORMS
WEEK 2.2 CANONICAL FORMS 1 Canonical SumofProducts (SOP) Given a truth table, we can ALWAYS write a logic expression for the function by taking the OR of the minterms for which the function is a 1. This
More informationA Little Perspective Combinational Logic Circuits
A Little Perspective Combinational Logic Circuits COMP 251 Computer Organization and Architecture Fall 2009 Motivating Example Recall our machine s architecture: A Simple ALU Consider an ALU that can perform
More informationDigital Logic Design 1. Truth Tables. Truth Tables. OR Operation With OR Gates
2007 oolean Constants and Variables K TP.HCM Tran Ngoc Thinh HCMC University of Technology http://www.cse.hcmut.edu.vn/~tnthinh oolean algebra is an important tool in describing, analyzing, designing,
More informationCSE140: Components and Design Techniques for Digital Systems
CSE4: Components and Design Techniques for Digital Systems Tajana Simunic Rosing What we covered thus far: Number representations Logic gates Boolean algebra Introduction to CMOS HW#2 due, HW#3 assigned
More informationAnalog & Digital Electronics Course No: PH218
Analog & Digital Electronics Course No: PH218 Lec29: Combinational Logic Modules Course Instructor: Dr. A. P. VAJPEYI Department of Physics, Indian Institute of Technology Guwahati, India 1 Combinational
More informationGates & Boolean Algebra. Boolean Operators. Combinational Logic. Introduction
Introduction Gates & Boolean lgebra Boolean algebra: named after mathematician George Boole (85 864). 2valued algebra. digital circuit can have one of 2 values. Signal between and volt =, between 4 and
More informationENEE244 (sec ) Spring Time alloted: 50 minutes. Student ID: Maximum score: 50 points
ENEE244 (sec 4) Spring 26 Midterm Examination II Pages: 7 printed sides Name: Answer key Time alloted: 5 minutes. Student ID: Maximum score: 5 points University rules dictate strict penalties for any
More informationDigital Circuit and Logic Design /2
Homework# Digital Circuit and Logic Design / Page / Solution of Homework# () Draw block diagram to show how to use to8 lines decoders to produce the following: (ll decoders have one activelow ENBLE
More informationWorking with combinational logic. Design example: 2x2bit multiplier
Working with combinational logic Simplification twolevel simplification exploiting don t cares algorithm for simplification Logic realization twolevel logic and canonical forms realized with NNs and
More informationCDA 3200 Digital Systems. Instructor: Dr. Janusz Zalewski Developed by: Dr. Dahai Guo Spring 2012
CDA 3200 Digital Systems Instructor: Dr. Janusz Zalewski Developed by: Dr. Dahai Guo Spring 2012 Outline MultiLevel Gate Circuits NAND and NOR Gates Design of TwoLevel Circuits Using NAND and NOR Gates
More informationL2: 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 sources and are used with permission. Prof. Randy Katz (Unified
More informationBoolean Algebra Part 1
Boolean Algebra Part 1 Page 1 Boolean Algebra Objectives Understand Basic Boolean Algebra Relate Boolean Algebra to Logic Networks Prove Laws using Truth Tables Understand and Use First Basic Theorems
More informationWorking with combinational logic
Working with combinational logic Simplification twolevel simplification exploiting don t cares algorithm for simplification Logic realization twolevel logic and canonical forms realized with NNs and
More informationCombinational Logic Circuits
Chapter 2 Combinational Logic Circuits J.J. Shann Chapter Overview 21 Binary Logic and Gates 22 Boolean Algebra 23 Standard Forms 24 TwoLevel Circuit Optimization 25 Map Manipulation 補 充 資 料 :QuineMcCluskey
More informationCHAPTER 3 Boolean Algebra and Digital Logic
CHAPTER 3 Boolean Algebra and Digital Logic 3.1 Introduction 121 3.2 Boolean Algebra 122 3.2.1 Boolean Expressions 123 3.2.2 Boolean Identities 124 3.2.3 Simplification of Boolean Expressions 126 3.2.4
More informationConversion between number systems:
Conversion between number systems: Radixr to decimal. Decimal to binary. Decimal to Radixr Binary to Octal Binary to Hex Binary arithmetic operations. Negative number representations. Switching Algebra
More informationIntroduction to Logic Circuits
April 5, 999 4:05 g02ch2 Sheet number Page number 7 black chapter 2 Introduction to Logic Circuits 2. d2 d4, d7 d5 7 April 5, 999 4:05 g02ch2 Sheet number 2 Page number 8 black 8 CHAPTER 2 Introduction
More informationReading and construction of logic gates
Reading and construction of logic gates A Boolean function is an expression formed with binary variables, a binary variable can take a value of 1 or 0. Boolean function may be represented as an algebraic
More informationIntroduction. Digital Logic Design 1. Simplifying Logic Circuits. SumofProducts Form. Algebraic Simplification
2007 Introduction BK TP.HCM Tran Ngoc Thinh HCMC University of Technology http://www.cse.hcmut.edu.vn/~tnthinh Basic logic gate functions will be combined in combinational logic circuits. Simplification
More informationState Reduction and State Assignment Techniques. Derek Hildreth and Timothy Price Brigham Young University  Idaho
State Reduction and Assignment Running head: STATE REDUCTION AND ASSIGNMENT State Reduction and State Assignment Techniques Derek Hildreth and Timothy Price Brigham Young University  Idaho State Reduction
More informationUnderstanding Logic Design
Understanding Logic Design ppendix of your Textbook does not have the needed background information. This document supplements it. When you write add DD R0, R1, R2, you imagine something like this: R1
More information3.2 Simplify the following Boolean functions, using threevariable maps: (ay F(x, y, z) = L(o, 1,5,7)
Answers to problems marked with ~,appear at the end of the book. 3.1'~ Simplify the following Boolean functions, using threevariable maps: (a) F(x, y, z) = L(o, 2,6,7) (b) F(x, y, z) = L(o, 1,2,3,7) 3.2
More informationChapter 4 Boolean Algebra and Logic Simplification
ETEC 23 Programmable Logic Devices Chapter 4 Boolean Algebra and Logic Simplification Shawnee State University Department of Industrial and Engineering Technologies Copyright 27 by Janna B. Gallaher Boolean
More informationSumofProducts and ProductofSums expressions
SumofProducts and ProductofSums expressions This worksheet and all related files are licensed under the reative ommons ttribution License, version.. To view a copy of this license, visit http://creativecommons.org/licenses/by/./,
More informationCS61c: Representations of Combinational Logic Circuits
CS61c: Representations of Combinational Logic Circuits J. Wawrzynek October 12, 2007 1 Introduction In the previous lecture we looked at the internal details of registers. We found that every register,
More informationExclusive OR/Exclusive NOR (XOR/XNOR)
Exclusive OR/Exclusive NOR (XOR/XNOR) XOR and XNOR are useful logic functions. Both have two or more inputs. The truth table for two inputs is shown at right. a XOR b = 1 if and only if (iff) a b. a XNOR
More informationDigital Logic and Design (EEE241) Lecture
Digital Logic and Design (EEE241) Lecture Dr. M. G. Abbas Malik abbas.malik@ciitlahore.edu.pk edu Picture Source: http://www.vanoast.com/oldportfolio/digitaldesignlogoone%5ba%5d.jpg Previous lecture
More informationFORDHAM UNIVERSITY CISC 3593. Dept. of Computer and Info. Science Spring, 2011. The Binary Adder
FORDHAM UNIVERITY CIC 3593 Fordham College Lincoln Center Computer Organization Dept. of Computer and Info. cience pring, 2011 1 Introduction The Binar Adder The binar adder circuit is an important building
More informationLogic gate implementation and circuit minimization
Logic gate implementation and circuit minimization Lila Kari The University of Western Ontario Logic gate implementation and circuit minimization CS2209, Applied Logic for Computer Science 1 / 48 Why binary?
More informationDESIGN OF GATE NETWORKS
DESIGN OF GATE NETWORKS DESIGN OF TWOLEVEL NETWORKS: andor and orand NETWORKS MINIMAL TWOLEVEL NETWORKS KARNAUGH MAPS MINIMIZATION PROCEDURE AND TOOLS LIMITATIONS OF TWOLEVEL NETWORKS DESIGN OF TWOLEVEL
More informationLogic Gates. Is the front door open? Is the back door open? Are both doors open?
Logic Gates Logic gates are used in electronic circuits when decisions need to be made. For example, suppose we make an intruder alarm for which we want the alarm to sound when the front door or back door
More informationCombinational Functions and Circuits
Introduction to Digital Logic Prof. Nizamettin DIN naydin@yildiz.edu.tr naydin@ieee.org ourse Outline. Digital omputers, Number Systems, rithmetic Operations, Decimal, lphanumeric, and Gray odes. inary
More informationIntroduction. The QuineMcCluskey Method Handout 5 January 21, 2016. CSEE E6861y Prof. Steven Nowick
CSEE E6861y Prof. Steven Nowick The QuineMcCluskey Method Handout 5 January 21, 2016 Introduction The QuineMcCluskey method is an exact algorithm which finds a minimumcost sumofproducts implementation
More information22 Chapter 2 Gates, Circuits, and Combinational Logic. 24 Chapter 2 Gates, Circuits, and Combinational Logic
 hapter Gates, ircuits, and ombinational Logic hapter : Gates, ircuits, and ombinational Logic  hapter Gates, ircuits, and ombinational Logic nalog and Digital Systems Dr. Tim McGuire Sam Houston State
More informationTakeHome Exercise. z y x. Erik Jonsson School of Engineering and Computer Science. The University of Texas at Dallas
TakeHome Exercise Assume you want the counter below to count mod6 backward. That is, it would count 0543210, etc. Assume it is reset on startup, and design the wiring to make the counter count
More informationDigital Circuits. Frequently Asked Questions
Digital Circuits Frequently Asked Questions Module 1: Digital & Analog Signals 1. What is a signal? Signals carry information and are defined as any physical quantity that varies with time, space, or any
More informationChapter 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. Overview Part 1 Gate Circuits
More informationCOMBINATIONAL LOGIC CIRCUITS
COMBINATIONAL LOGIC CIRCUITS 4.1 INTRODUCTION The digital system consists of two types of circuits, namely: (i) Combinational circuits and (ii) Sequential circuits A combinational circuit consists of logic
More informationProgrammable Logic Devices (PLDs)
Programmable Logic Devices (PLDs) Lesson Objectives: In this lesson you will be introduced to some types of Programmable Logic Devices (PLDs): PROM, PAL, PLA, CPLDs, FPGAs, etc. How to implement digital
More informationArithmetic Circuits Addition, Subtraction, & Multiplication
Arithmetic Circuits Addition, Subtraction, & Multiplication The adder is another classic design example which we are obliged look at. Simple decimal arithmetic is something which we rarely give a second
More informationMultiplexers and Demultiplexers
8 Multiplexers and Demultiplexers In the previous chapter, we described at length those combinational logic circuits that can be used to perform arithmetic and related operations. This chapter takes a
More informationBasics of Digital Logic Design
CSE 675.2: Introduction to Computer Architecture Basics of Digital Logic Design Presentation D Study: B., B2, B.3 Slides by Gojko Babi From transistors to chips Chips from the bottom up: Basic building
More informationBasics of Digital Systems. Boolean algebra Truth tables Karnaugh maps
Basics of Digital Systems Boolean algebra Truth tables Karnaugh maps Boolean Algebra In digital systems we deal with the binary number system. This means that the value of an element can be either 0 or
More informationLecture 7: Signed Numbers & Arithmetic Circuits. BCD (Binary Coded Decimal) Points Addressed in this Lecture
Points ddressed in this Lecture Lecture 7: Signed Numbers rithmetic Circuits Professor Peter Cheung Department of EEE, Imperial College London (Floyd 2.52.7, 6.16.7) (Tocci 6.16.11, 9.19.2, 9.4) Representing
More informationBasics of Digital Logic Design
Basics of Digital Logic Design Dr. Arjan Durresi Louisiana State University Baton Rouge, LA 70810 Durresi@Csc.LSU.Edu LSUEd These slides are available at: http://www.csc.lsu.edu/~durresi/csc3501_07/ Louisiana
More informationSwitching Circuits & Logic Design
Switching Circuits & Logic Design JieHong Roland Jiang 江介宏 Department of Electrical Engineering National Taiwan University Fall 23 2 oolean lgebra 2 Outline Introduction asic operations oolean expressions
More informationBinary Adders: Half Adders and Full Adders
Binary Adders: Half Adders and Full Adders In this set of slides, we present the two basic types of adders: 1. Half adders, and 2. Full adders. Each type of adder functions to add two binary bits. In order
More informationAljabar Boolean, Penyederhanaan Logika dan Peta Karnaugh
Aljabar Boolean, Penyederhanaan Logika dan Peta Karnaugh ENDY SA ENDY SA Program Studi Teknik Elektro Fakultas Teknik Universitas Muhammadiyah Prof. Dr. HAMKA Slide  6 1 Standard Forms of Boolean Expressions
More informationModule 3 Digital Gates and Combinational Logic
Introduction to Digital Electronics, Module 3: Digital Gates and Combinational Logic 1 Module 3 Digital Gates and Combinational Logic INTRODUCTION: The principles behind digital electronics were developed
More informationDigital Logic Circuits
Digital Logic Circuits Digital describes any system based on discontinuous data or events. Typically digital is computer data or electronic sampling of an analog signal. Computers are digital machines
More information2.0 Chapter Overview. 2.1 Boolean Algebra
Thi d t t d ith F M k 4 2 Boolean Algebra hapter Two Logic circuits are the basis for modern digital computer systems. To appreciate how computer systems operate you will need to understand digital logic
More informationGates, Circuits, and Boolean Algebra
Gates, Circuits, and Boolean Algebra Computers and Electricity A gate is a device that performs a basic operation on electrical signals Gates are combined into circuits to perform more complicated tasks
More informationTheory of Logic Circuits. Laboratory manual. Exercise 11
Zakła Mikroinformatyki i Teorii Automatów Cyfrowych Theory of Logic Circuits Laboratory manual Exercise mplementing Logic Functions Using M Multiplexers an emultiplexers 8 Tomasz Poeszwa, Piotr Czekalski
More informationDECODERS. A binary code of n bits is capable of representing up to 2^n distinct elements of coded information.
DECODERS A binary code of n bits is capable of representing up to 2^n distinct elements of coded information. A decoder is a combinational circuit that converts binary information from n input lines to
More informationSteps of sequential circuit design (cont'd)
Design of Clocked Synchronous Sequential Circuits Design of a sequential circuit starts with the verbal description of the problem (scenario). Design process is similar to computer programming. First,
More informationCombinational logic lab
ECE2883 HP: Lab 3 Logic Experts (LEs) Combinational logic lab Implementing combinational logic with Quartus We should be starting to realize that you, the SMEs in this course, are just a specific type
More informationBasic Logic Gates Richard E. Haskell
BASIC LOGIC GATES 1 E Basic Logic Gates Richard E. Haskell All digital systems are made from a few basic digital circuits that we call logic gates. These circuits perform the basic logic functions that
More informationKarnaugh Maps. Example A B C X 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 0 1 1 0 1 1 1 1 1. each 1 here gives a minterm e.g.
Karnaugh Maps Yet another way of deriving the simplest Boolean expressions from behaviour. Easier than using algebra (which can be hard if you don't know where you're going). Example A B C X 0 0 0 0 0
More informationRita Lovassy. Digital Technics
Rita Lovassy Digital Technics Kandó Kálmán Faculty of Electrical Engineering Óbuda University Budapest, 2013 Preface Digital circuits address the growing need for computer networking communications in
More informationImplementation of SOP and POS Form Logic Functions
Implementation of SOP and POS Form Logic Functions By: Dr. A. D. Johnson Lab Assignment #3 EECS: 1100 Digital Logic Design The University of Toledo 1. Objectives  becoming familiar with two standard forms
More informationDigital Electronics Detailed Outline
Digital Electronics Detailed Outline Unit 1: Fundamentals of Analog and Digital Electronics (32 Total Days) Lesson 1.1: Foundations and the Board Game Counter (9 days) 1. Safety is an important concept
More informationDigital Logic Design. Basics Combinational Circuits Sequential Circuits. PuJen Cheng
Digital Logic Design Basics Combinational Circuits Sequential Circuits PuJen Cheng Adapted from the slides prepared by S. Dandamudi for the book, Fundamentals of Computer Organization and Design. Introduction
More informationExp. No. (2) Exclusive OR Gate and it's Applications
University of Technology Laser & Optoelectronics Engineering Department Digital Electronics lab. Object Exp. No. (2) Exclusive OR Gate and it's pplications To study the logic function of exclusive OR (OR)
More informationTutorial 5 Special Combinational Logic Circuit
Tutorial 5 Special Combinational Logic Circuit Question 1 a) What is the function of an adder circuit? b) A halfadder adds two binary bits, true or false? c) A halfadder has a sum output only, true or
More informationCounters and Decoders
Physics 3330 Experiment #10 Fall 1999 Purpose Counters and Decoders In this experiment, you will design and construct a 4bit ripplethrough decade counter with a decimal readout display. Such a counter
More informationModule3 SEQUENTIAL LOGIC CIRCUITS
Module3 SEQUENTIAL LOGIC CIRCUITS Till now we studied the logic circuits whose outputs at any instant of time depend only on the input signals present at that time are known as combinational circuits.
More informationChapter 1 Design Concepts. Fundamentals of DIGITAL LOGIC with VHDL design. Chapter 2 Introduction to Logic Circuits. 2.1 Variables and Functions
Fundamentals o DIGITA OGIC with VHD design Chapter Design Concepts tephen Brown and Zvonko Vranesic McGrawHill, 2 Read as introduction lides prepared b P.J. Bakkes (2) (Edited in June 23) 2 Chapter 2
More informationFundamentals of Computer Systems
Fundamentals of Computer Systems Combinational Logic Martha A. Kim Columbia University Fall 23 / Combinational Circuits Combinational circuits are stateless. Their output is a function only of the current
More informationLogic Reference Guide
Logic eference Guide Advanced Micro evices INTOUCTION Throughout this data book and design guide we have assumed that you have a good working knowledge of logic. Unfortunately, there always comes a time
More information