Henry Lin, Department of Electrical and Computer Engineering, California State University, Bakersfield Lecture 7 (Digital Logic) July 24 th, 2012


 Richard Lloyd
 2 years ago
 Views:
Transcription
1 Henry Lin, Department of Electrical and Computer Engineering, California State University, Bakersfield Lecture 7 (Digital Logic) July 24 th,
2 Digital vs Analog Digital signals are binary; analog signals are realvalued numbers 2
3 Integrated Circuits The building blocks of computers Designed for specialized functions Examples: the CPU, bus interface, memory management unit Transistors: primary components of Ics Motorola MPC 7400 PowerPC modules: 6.5 million transistors in less than in² 3
4 Transistors Boolean algebra: basis for computer logic design Transistors: means for implementing Boolean algebra Switches: on/off to represent the 0 s and 1 s of binary digital circuits Combined to form logic gates 4
5 Combinatorial logic Digital Circuits Results of an operation depend only on the present inputs to the operation Uses: perform arithmetic, control data movement, compare values for decision making Sequential logic Results depend on both the inputs to the operation and the result of the previous operation Uses: counter 5
6 Boolean Algebra Rules that govern constants and variables that can take on 2 values True/false; on/off; yes/no; 0/1 Boolean logic Rules for handling Boolean constants and variables 3 fundamental operations: AND, OR and NOT Truth Table: specifies results for all possible input combinations 6
7 Logic Functions Logical functions can be expressed in several ways: Truth table Logical expressions Graphical form 7
8 AND Boolean Operators Result TRUE if and only if both input 0 0 operands 0 are true C = A B INCLUSIVEOR Result TRUE if any input operands are true C = A + B A B C A B C
9 NOT Boolean Operators Result TRUE if single input value is FALSE C = A A C
10 Switching Circuits 10
11 AND Operator Similar Examples If the car is fueled AND the engine works, then the engine works, then the engine will start. AND means that both conditions must be true in order for the conclusion to be true. OR Operator If I have cash or a credit card, then I can pay the bill. OR works such that the output is true, if either of the two inputs is true. 11
12 Similar Examples XOR (Exclusive OR) Operator If gender A XOR gender B, then reproduction is possible. XOR works such that output is activated (equal to one) if both inputs are of a different value. 12
13 EXCLUSIVEOR Boolean Operators Result TRUE if either A or B is TRUE but not both C = A B Can be derived from INCLUSIVEOR, AND and NOT A xor B equals A or B but not both A and B A B = (A + B) ( A B ) A xor B = either A and not B or B and not A A B = (A B ) + ( B A ) 13
14 Boolean Algebra Operations Valid for INCLUSIVEOR, AND, XOR Associative A + ( B + C ) = ( A + B ) + C Distributive A ( B + C ) = A B + A C Commutative A + B = B + A DeMorgan s Theorems A + B = A B A B = A + B 14
15 Gates and Combinatorial Logic Many computer functions defined in terms of Boolean equations Example: sum of 2 single binary digit numbers Truth table for sum Truth table for carry XOR AND A B C A B C
16 Computer Implementation Gates or logical gates Integrated circuits constructed from transistor switches and other electronic components VLSI: very largescale integration 16
17 Level of Integration An IC (a chip) Examples: Smallscale Integration (SSI): < 10 gates Mediumscale Integration (MSI): 10 ~ 100 gates Largescale Integration (LSI): 100 ~ xk gates Very Largescale Integration (VLSI): > xk gates VLSI Small size (compact size) Low cost Low power consumption High reliability High speed 17
18 Boolean Algebra Implementation Single type of gate appropriately combined 2 possibilities NAND gate: AND operation followed by a NOT operation NOR gate: INCLUSIVEOR followed by a NOT operation Note: indicates a NOT operation 18
19 NAND gate Proving NAND gate is universal 19
20 NOR gate Proving NOR gate is universal 20
21 Gates with multiple inputs Graphic symbols and inputoutput signals for logic gates with multiple inputs 21
22 MultiInput AND Gate AND gates can be built with any number of inputs Consider the symbol for the 4input AND gate F is true only when all the inputs are true (1 s) 22
23 MultiInput AND Gate Using 3 twoinput AND gates, we could build the same 4input AND gate. 23
24 Majority function Output is one whenever majority of inputs is 1. We use 3input majority function. 24
25 Majority function 25
26 Practice Problem Find the output of the following circuit Answer: (x+y)y x+y (x+y)y y 26
27 Practice Problem Find the output of the following circuit x y x y x y Answer: 27
28 Practice Problem Write the circuits for the following Boolean algebraic expressions x x+y 28
29 Practice Problem Write the circuits for the following Boolean algebraic expressions x x+y x+y (x+y)x y 29
30 Logical Equivalence All three circuits implement F=AB function. 30
31 Logical Equivalence Proving logical equivalence of two circuits Derive the logical expression for the output of each circuit. Show that these two expressions are equivalent. Two ways: You can use the truth table method For every combination of inputs, if both expressions yield the same output, they are equivalent. Good for logical expressions with small number of variables. You can also use algebraic manipulation Need Boolean identities 31
32 Logical Equivalence Derivation of logical expression from a circuit Trace from the input to output Write down intermediate logical expressions along the path. 32
33 Logical Equivalence Proving logical equivalence: Truth table method A B F1 = A B F3 = (A + B) (A + B) (A + B)
34 Boolean Algebra 34
35 Boolean Algebra 35
36 Boolean Algebra Proving logical equivalence: Boolean algebra method To prove that two logical functions F1 and F2 are equivalent Start with one function and apply Boolean laws to derive the other function Needs intuition as to which laws should be applied and when Practice helps Sometimes it may be convenient to reduce both functions to the same expression Example: F1=AB and F3=(A+B)(A+B)(A+B) are equivalent. 36
37 Logical Expression Simplification One method is algebraic manipulation Use Boolean laws to simplify the expression. Difficult to use Don t know if you have the simplified form 37
38 Algebraic Manipulation Majority function example A B C + A B C + A B C + A B C = Added extra A B C + A B C + A B C + A B C + A B C + A B C We can now simplify this expression as B C + A C + A B A difficult method to use for complex expressions 38
39 Logic Circuit Design Process A simple logic design process involves Problem specification Truth table derivation Derivation of logical expression Simplification of logical expression Implementation 39
40 Selector or Multiplexer Switch input back and forth between inputs Logic circuits that make up a computer Are relatively simple but Look complicated because many circuits required 40
41 How to add binary numbers Consider adding two 1bit binary numbers x and y = = = = 10 Carry is x AND y Sum is x XOR y The circuit to compute this is called a halfadder. 41
42 HalfAdder 42
43 Using half adders We can then use a halfadder to compute the sum of two Boolean numbers. 43
44 How to fix this We need to create an adder that can take a carry bit as an additional input. Inputs: x, y, carry in Outputs: sum, carry out This is called a full adder. Will add x and y with a halfadder Will add the sum of that to the carry in What about the carry out? It s 1 if either (or both): X + y = 10 X + y = 01 and carry in
45 Truth Table for Full Adder 45
46 Full Adder Handles possible carry from previous bit Half adder shown as block to simplify 2bit adder contains 32 circuits Also called ripple adder because the carry ripples through 32 bits 46
47 Carry lookahead adders Ripplecarry adders can be slow Delay proportional to number of bits Carry lookahead adders Eliminate the delay of ripplecarry adders Carryins are generated independently C 0 = A 0 B 0 C 1 = A 0 B 0 A 1 + A 0 B 0 B 1 + A 1 B 1 Requires complex circuits Usually, a combination of carry lookahead and ripplecarry techniques are used 47
48 Sequential Logic Circuits Output depends on Input Previous state of the circuit Flipflop: basic memory element State table: output for all combinations of input and previous states 48
49 Sequential Logic Circuits Main components of a sequential circuit 49
50 Clock Signal 50
51 Clock Signal Clock serves two distinct purposes Synchronization point Start of a cycle End of a cycle Intermediate point at which the clock signal changes levels Timing information Clock period, ON, and OFF periods Propagation delay Time required for the output to react to changes in the inputs 51
52 Clock Signal 52
53 FlipFlop Types with State Tables 53
54 Register COPY Operation Uses both sequential and combinatorial logic 54
55 Steps in a LOAD Instruction 55
56 56
Lecture (05) Boolean Algebra and Logic Gates
Lecture (05) Boolean Algebra and Logic Gates By: Dr. Ahmed ElShafee ١ Minterms and Maxterms consider two binary variables x and y combined with an AND operation. Since eachv ariable may appear in either
More informationQUESTION BANK FOR TEST
CSCI 2121 Computer Organization and Assembly Language PRACTICE QUESTION BANK FOR TEST 1 Note: This represents a sample set. Please study all the topics from the lecture notes. Question 1. Multiple Choice
More informationDigital Logic Design Exercises. Assignment 1
Assignment 1 For Exercises 15, match the following numbers with their definition A Number Natural number C Integer number D Negative number E Rational number 1 A unit of an abstract mathematical system
More informationChapter 2 Logic Gates and Introduction to Computer Architecture
Chapter 2 Logic Gates and Introduction to Computer Architecture 2.1 Introduction The basic components of an Integrated Circuit (IC) is logic gates which made of transistors, in digital system there are
More informationObjectives: 1 Bolean Algebra. Eng. Ayman Metwali
Objectives: Chapter 3 : 1 Boolean Algebra Boolean Expressions Boolean Identities Simplification of Boolean Expressions Complements Representing Boolean Functions 2 Logic gates 3 Digital Components 4
More informationLecture 21: Combinational Circuits. Integrated Circuits. Integrated Circuits, cont. Integrated Circuits Combinational Circuits
Lecture 21: Combinational Circuits Integrated Circuits Combinational Circuits Multiplexer Demultiplexer Decoder Adders ALU Integrated Circuits Circuits use modules that contain multiple gates packaged
More informationPhiladelphia University Student Name: Student Number:
Philadelphia University Student Name: Student Number: Faculty of Engineering Serial Number: Final Exam, First Semester: 2018/2019 Dept. of Computer Engineering Course Title: Logic Circuits Date: 03/01/2019
More informationDIGITAL CIRCUIT LOGIC UNIT 9: MULTIPLEXERS, DECODERS, AND PROGRAMMABLE LOGIC DEVICES
DIGITAL CIRCUIT LOGIC UNIT 9: MULTIPLEXERS, DECODERS, AND PROGRAMMABLE LOGIC DEVICES 1 Learning Objectives 1. Explain the function of a multiplexer. Implement a multiplexer using gates. 2. Explain the
More informationChap2 Boolean Algebra
Chap2 Boolean Algebra Contents: My name Outline: My position, contact Basic information theorem and postulate of Boolean Algebra. or project description Boolean Algebra. Canonical and Standard form. Digital
More informationR10. II B. Tech I Semester, Supplementary Examinations, May
SET  1 1. a) Convert the following decimal numbers into an equivalent binary numbers. i) 53.625 ii) 4097.188 iii) 167 iv) 0.4475 b) Add the following numbers using 2 s complement method. i) 48 and +31
More informationChapter 2. Boolean Algebra and Logic Gates
Chapter 2. Boolean Algebra and Logic Gates Tong In Oh 1 Basic Definitions 2 3 2.3 Axiomatic Definition of Boolean Algebra Boolean algebra: Algebraic structure defined by a set of elements, B, together
More information1. Mark the correct statement(s)
1. Mark the correct statement(s) 1.1 A theorem in Boolean algebra: a) Can easily be proved by e.g. logic induction b) Is a logical statement that is assumed to be true, c) Can be contradicted by another
More information6.1 Combinational Circuits. George Boole ( ) Claude Shannon ( )
6. Combinational Circuits George Boole (85 864) Claude Shannon (96 2) Digital signals Binary (or logical ) values: or, on or off, high or low voltage Wires. Propagate logical values from place to place.
More information01 Introduction to Digital Logic. ENGR 3410 Computer Architecture Mark L. Chang Fall 2008
Introduction to Digital Logic ENGR 34 Computer Architecture Mark L. Chang Fall 28 Acknowledgements Patterson & Hennessy: Book & Lecture Notes Patterson s 997 course notes (U.C. Berkeley CS 52, 997) Tom
More informationBoolean Logic CS.352.F12
Boolean Logic CS.352.F12 Boolean Algebra Boolean Algebra Mathematical system used to manipulate logic equations. Boolean: deals with binary values (True/False, yes/no, on/off, 1/0) Algebra: set of operations
More information2.1 Binary Logic and Gates
1 EED2003 Digital Design Presentation 2: Boolean Algebra Asst. Prof.Dr. Ahmet ÖZKURT Asst. Prof.Dr Hakkı T. YALAZAN Based on the Lecture Notes by Jaeyoung Choi choi@comp.ssu.ac.kr Fall 2000 2.1 Binary
More informationVon Neumann Architecture
Von Neumann Architecture Assist lecturer Donya A. Khalid Lecture 2 2/29/27 Computer Organization Introduction In 945, just after the World War, Jon Von Neumann proposed to build a more flexible computer.
More informationBawar Abid Abdalla. Assistant Lecturer Software Engineering Department Koya University
Logic Design First Stage Lecture No.5 Boolean Algebra Bawar Abid Abdalla Assistant Lecturer Software Engineering Department Koya University Boolean Operations Laws of Boolean Algebra Rules of Boolean Algebra
More informationCS 261 Fall Mike Lam, Professor. Combinational Circuits
CS 261 Fall 2017 Mike Lam, Professor Combinational Circuits The final frontier Java programs running on Java VM C programs compiled on Linux Assembly / machine code on CPU + memory??? Switches and electric
More information(ii) Simplify and implement the following SOP function using NOR gates:
DHANALAKSHMI COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING EE6301 DIGITAL LOGIC CIRCUITS UNIT I NUMBER SYSTEMS AND DIGITAL LOGIC FAMILIES PART A 1. How can an OR gate be
More informationComputer Organization and Levels of Abstraction
Computer Organization and Levels of Abstraction Announcements Today: PS 7 Lab 8: Sound Lab tonight bring machines and headphones! PA 7 Tomorrow: Lab 9 Friday: PS8 Today (Short) Floating point review Boolean
More informationLecture #21 March 31, 2004 Introduction to Gates and Circuits
Lecture #21 March 31, 2004 Introduction to Gates and Circuits To this point we have looked at computers strictly from the perspective of assembly language programming. While it is possible to go a great
More information3. The high voltage level of a digital signal in positive logic is : a) 1 b) 0 c) either 1 or 0
1. The number of level in a digital signal is: a) one b) two c) four d) ten 2. A pure sine wave is : a) a digital signal b) analog signal c) can be digital or analog signal d) neither digital nor analog
More informationLECTURE 4. Logic Design
LECTURE 4 Logic Design LOGIC DESIGN The language of the machine is binary that is, sequences of 1 s and 0 s. But why? At the hardware level, computers are streams of signals. These signals only have two
More informationBasic Arithmetic (adding and subtracting)
Basic Arithmetic (adding and subtracting) Digital logic to show add/subtract Boolean algebra abstraction of physical, analog circuit behavior 1 0 CPU components ALU logic circuits logic gates transistors
More informationElectronic Engineering Part 1 Laboratory Experiment. Digital Circuit Design 1 Combinational Logic. (3 hours)
Electronic Engineering Part 1 Laboratory Experiment Digital Circuit Design 1 Combinational Logic (3 hours) 1. Introduction These days most signal processing is done digitally. Electronic signals (representing
More information01 Introduction to Digital Logic. ENGR 3410 Computer Architecture Mark L. Chang Fall 2006
Introduction to Digital Logic ENGR 34 Computer Architecture Mark L. Chang Fall 26 Acknowledgements Patterson & Hennessy: Book & Lecture Notes Patterson s 997 course notes (U.C. Berkeley CS 52, 997) Tom
More informationDigital logic fundamentals. Question Bank. Unit I
Digital logic fundamentals Question Bank Subject Name : Digital Logic Fundamentals Subject code: CA102T Staff Name: R.Roseline Unit I 1. What is Number system? 2. Define binary logic. 3. Show how negative
More informationInjntu.com Injntu.com Injntu.com R16
1. a) What are the three methods of obtaining the 2 s complement of a given binary (3M) number? b) What do you mean by Kmap? Name it advantages and disadvantages. (3M) c) Distinguish between a halfadder
More informationCombinational Circuits
Combinational Circuits Q. What is a combinational circuit? A. Digital: signals are or. A. No feedback: no loops. analog circuits: signals vary continuously sequential circuits: loops allowed (stay tuned)
More informationSUBJECT CODE: IT T35 DIGITAL SYSTEM DESIGN YEAR / SEM : 2 / 3
UNIT  I PART A (2 Marks) 1. Using Demorgan s theorem convert the following Boolean expression to an equivalent expression that has only OR and complement operations. Show the function can be implemented
More informationEXPERIMENT #8: BINARY ARITHMETIC OPERATIONS
EE 2 Lab Manual, EE Department, KFUPM EXPERIMENT #8: BINARY ARITHMETIC OPERATIONS OBJECTIVES: Design and implement a circuit that performs basic binary arithmetic operations such as addition, subtraction,
More informationCode No: 07A3EC03 Set No. 1
Code No: 07A3EC03 Set No. 1 II B.Tech I Semester Regular Examinations, November 2008 SWITCHING THEORY AND LOGIC DESIGN ( Common to Electrical & Electronic Engineering, Electronics & Instrumentation Engineering,
More informationChapter 3. Boolean Algebra and Digital Logic
Chapter 3 Boolean Algebra and Digital Logic Chapter 3 Objectives Understand the relationship between Boolean logic and digital computer circuits. Learn how to design simple logic circuits. Understand how
More informationLecture 4: Implementation AND, OR, NOT Gates and Complement
EE210: Switching Systems Lecture 4: Implementation AND, OR, NOT Gates and Complement Prof. YingLi Tian Feb. 13, 2018 Department of Electrical Engineering The City College of New York The City University
More informationBoolean Algebra and Logic Gates
Boolean Algebra and Logic Gates Binary logic is used in all of today's digital computers and devices Cost of the circuits is an important factor Finding simpler and cheaper but equivalent circuits can
More informationComputer Organization and Levels of Abstraction
Computer Organization and Levels of Abstraction Announcements PS8 Due today PS9 Due July 22 Sound Lab tonight bring machines and headphones! Binary Search Today Review of binary floating point notation
More informationLAB #1 BASIC DIGITAL CIRCUIT
LAB #1 BASIC DIGITAL CIRCUIT OBJECTIVES 1. To study the operation of basic logic gates. 2. To build a logic circuit from Boolean expressions. 3. To introduce some basic concepts and laboratory techniques
More information2008 The McGrawHill Companies, Inc. All rights reserved.
28 The McGrawHill Companies, Inc. All rights reserved. 28 The McGrawHill Companies, Inc. All rights reserved. All or Nothing Gate Boolean Expression: A B = Y Truth Table (ee next slide) or AB = Y 28
More informationKING FAHD UNIVERSITY OF PETROLEUM & MINERALS COMPUTER ENGINEERING DEPARTMENT
KING FAHD UNIVERSITY OF PETROLEUM & MINERALS COMPUTER ENGINEERING DEPARTMENT COE 202: Digital Logic Design Term 162 (Spring 2017) Instructor: Dr. Abdulaziz Barnawi Class time: U.T.R.: 11:0011:50AM Class
More informationReference Sheet for C112 Hardware
Reference Sheet for C112 Hardware 1 Boolean Algebra, Gates and Circuits Autumn 2016 Basic Operators Precedence : (strongest),, + (weakest). AND A B R 0 0 0 0 1 0 1 0 0 1 1 1 OR + A B R 0 0 0 0 1 1 1 0
More information6.1 Combinational Circuits. George Boole ( ) Claude Shannon ( )
6. Combinational Circuits George Boole (85 864) Claude Shannon (96 2) Signals and Wires Digital signals Binary (or logical ) values: or, on or off, high or low voltage Wires. Propagate digital signals
More informationCode No: R Set No. 1
Code No: R059210504 Set No. 1 II B.Tech I Semester Regular Examinations, November 2006 DIGITAL LOGIC DESIGN ( Common to Computer Science & Engineering, Information Technology and Computer Science & Systems
More informationParallel logic circuits
Computer Mathematics Week 9 Parallel logic circuits College of Information cience and Engineering Ritsumeikan University last week the mathematics of logic circuits the foundation of all digital design
More informationCombinational Circuits
Combinational Circuits Jason Filippou CMSC250 @ UMCP 06022016 ason Filippou (CMSC250 @ UMCP) Circuits 06022016 1 / 1 Outline ason Filippou (CMSC250 @ UMCP) Circuits 06022016 2 / 1 Hardware design
More informationReview. EECS Components and Design Techniques for Digital Systems. Lec 05 Boolean Logic 9/404. Seq. Circuit Behavior. Outline.
Review EECS 150  Components and Design Techniques for Digital Systems Lec 05 Boolean Logic 9404 David Culler Electrical Engineering and Computer Sciences University of California, Berkeley Design flow
More information6. Combinational Circuits. Building Blocks. Digital Circuits. Wires. Q. What is a digital system? A. Digital: signals are 0 or 1.
Digital Circuits 6 Combinational Circuits Q What is a digital system? A Digital: signals are or analog: signals vary continuously Q Why digital systems? A Accurate, reliable, fast, cheap Basic abstractions
More informationBoolean Algebra. BME208 Logic Circuits Yalçın İŞLER
Boolean Algebra BME28 Logic Circuits Yalçın İŞLER islerya@yahoo.com http://me.islerya.com 5 Boolean Algebra /2 A set of elements B There exist at least two elements x, y B s. t. x y Binary operators: +
More informationGC03 Boolean Algebra
Why study? GC3 Boolean Algebra Computers transfer and process binary representations of data. Binary operations are easily represented and manipulated in Boolean algebra! Digital electronics is binary/boolean
More informationECE 341 Midterm Exam
ECE 341 Midterm Exam Time allowed: 75 minutes Total Points: 75 Points Scored: Name: Problem No. 1 (8 points) For each of the following statements, indicate whether the statement is TRUE or FALSE: (a) A
More informationCS 31: Intro to Systems Digital Logic. Kevin Webb Swarthmore College February 3, 2015
CS 31: Intro to Systems Digital Logic Kevin Webb Swarthmore College February 3, 2015 Reading Quiz Today Hardware basics Machine memory models Digital signals Logic gates Circuits: Borrow some paper if
More informationMark Redekopp, All rights reserved. EE 352 Unit 8. HW Constructs
EE 352 Unit 8 HW Constructs Logic Circuits Combinational logic Perform a specific function (mapping of 2 n input combinations to desired output combinations) No internal state or feedback Given a set of
More informationSIR C.R.REDDY COLLEGE OF ENGINEERING, ELURU DEPARTMENT OF INFORMATION TECHNOLOGY LESSON PLAN
SIR C.R.REDDY COLLEGE OF ENGINEERING, ELURU DEPARTMENT OF INFORMATION TECHNOLOGY LESSON PLAN SUBJECT: CSE 2.1.6 DIGITAL LOGIC DESIGN CLASS: 2/4 B.Tech., I SEMESTER, A.Y.201718 INSTRUCTOR: Sri A.M.K.KANNA
More informationENDTERM EXAMINATION
(Please Write your Exam Roll No. immediately) ENDTERM EXAMINATION DECEMBER 2006 Exam. Roll No... Exam Series code: 100919DEC06200963 Paper Code: MCA103 Subject: Digital Electronics Time: 3 Hours Maximum
More informationNADAR SARASWATHI COLLEGE OF ENGINEERING AND TECHNOLOGY Vadapudupatti, Theni
NADAR SARASWATHI COLLEGE OF ENGINEERING AND TECHNOLOGY Vadapudupatti, Theni625531 Question Bank for the Units I to V SEMESTER BRANCH SUB CODE 3rd Semester B.E. / B.Tech. Electrical and Electronics Engineering
More informationUPY14602DIGITAL ELECTRONICS AND MICROPROCESSORS Lesson Plan
UPY14602DIGITAL ELECTRONICS AND MICROPROCESSORS Lesson Plan UNIT I  NUMBER SYSTEMS AND LOGIC GATES Introduction to decimal Binary Octal Hexadecimal number systemsinter conversionsbcd code Excess
More informationCS 31: Intro to Systems Digital Logic. Kevin Webb Swarthmore College February 2, 2016
CS 31: Intro to Systems Digital Logic Kevin Webb Swarthmore College February 2, 2016 Reading Quiz Today Hardware basics Machine memory models Digital signals Logic gates Circuits: Borrow some paper if
More informationCS470: Computer Architecture. AMD Quad Core
CS470: Computer Architecture Yashwant K. Malaiya, Professor malaiya@cs.colostate.edu AMD Quad Core 1 Architecture Layers Building blocks Gates, flipflops Functional bocks: Combinational, Sequential Instruction
More informationCOMP combinational logic 1 Jan. 18, 2016
In lectures 1 and 2, we looked at representations of numbers. For the case of integers, we saw that we could perform addition of two numbers using a binary representation and using the same algorithm that
More informationUNIT  V MEMORY P.VIDYA SAGAR ( ASSOCIATE PROFESSOR) Department of Electronics and Communication Engineering, VBIT
UNIT  V MEMORY P.VIDYA SAGAR ( ASSOCIATE PROFESSOR) contents Memory: Introduction, RandomAccess memory, Memory decoding, ROM, Programmable Logic Array, Programmable Array Logic, Sequential programmable
More informationLogic, Words, and Integers
Computer Science 52 Logic, Words, and Integers 1 Words and Data The basic unit of information in a computer is the bit; it is simply a quantity that takes one of two values, 0 or 1. A sequence of k bits
More informationCode No: R Set No. 1
Code No: R059210504 Set No. 1 II B.Tech I Semester Regular Examinations, November 2007 DIGITAL LOGIC DESIGN ( Common to Computer Science & Engineering, Information Technology and Computer Science & Systems
More informationIntroduction to Computer Architecture
Boolean Operators The Boolean operators AND and OR are binary infix operators (that is, they take two arguments, and the operator appears between them.) A AND B D OR E We will form Boolean Functions of
More informationPropositional Calculus. CS 270: Mathematical Foundations of Computer Science Jeremy Johnson
Propositional Calculus CS 270: Mathematical Foundations of Computer Science Jeremy Johnson Propositional Calculus Objective: To provide students with the concepts and techniques from propositional calculus
More informationBUILDING BLOCKS OF A BASIC MICROPROCESSOR. Part 1 PowerPoint Format of Lecture 3 of Book
BUILDING BLOCKS OF A BASIC MICROPROCESSOR Part PowerPoint Format of Lecture 3 of Book Decoder Tristate device Full adder, full subtractor Arithmetic Logic Unit (ALU) Memories Example showing how to write
More information1. Prove that if you have tristate buffers and inverters, you can build any combinational logic circuit. [4]
HW 3 Answer Key 1. Prove that if you have tristate buffers and inverters, you can build any combinational logic circuit. [4] You can build a NAND gate from tristate buffers and inverters and thus you
More informationregister:a group of binary cells suitable for holding binary information flipflops + gates
9 차시 1 Ch. 6 Registers and Counters 6.1 Registers register:a group of binary cells suitable for holding binary information flipflops + gates control when and how new information is transferred into the
More informationHonorary Professor Supercomputer Education and Research Centre Indian Institute of Science, Bangalore
COMPUTER ORGANIZATION AND ARCHITECTURE V. Rajaraman Honorary Professor Supercomputer Education and Research Centre Indian Institute of Science, Bangalore T. Radhakrishnan Professor of Computer Science
More informationHANSABA COLLEGE OF ENGINEERING & TECHNOLOGY (098) SUBJECT: DIGITAL ELECTRONICS ( ) Assignment
Assignment 1. What is multiplexer? With logic circuit and function table explain the working of 4 to 1 line multiplexer. 2. Implement following Boolean function using 8: 1 multiplexer. F(A,B,C,D) = (2,3,5,7,8,9,12,13,14,15)
More informationCS61C : Machine Structures
inst.eecs.berkeley.edu/~cs61c/su06 CS61C : Machine Structures Lecture #14: Combinational Logic, Gates, and State 20060720 CS 61C L14 Combinational Logic (1) Andy Carle What are Machine Structures? Software
More informationDIGITAL ELECTRONICS. Vayu Education of India
DIGITAL ELECTRONICS ARUN RANA Assistant Professor Department of Electronics & Communication Engineering Doon Valley Institute of Engineering & Technology Karnal, Haryana (An ISO 9001:2008 ) Vayu Education
More information(Refer Slide Time: 00:01:53)
Digital Circuits and Systems Prof. S. Srinivasan Department of Electrical Engineering Indian Institute of Technology Madras Lecture  36 Design of Circuits using MSI Sequential Blocks (Refer Slide Time:
More informationCONTENTS CHAPTER 1: NUMBER SYSTEM. Foreword...(vii) Preface... (ix) Acknowledgement... (xi) About the Author...(xxiii)
CONTENTS Foreword...(vii) Preface... (ix) Acknowledgement... (xi) About the Author...(xxiii) CHAPTER 1: NUMBER SYSTEM 1.1 Digital Electronics... 1 1.1.1 Introduction... 1 1.1.2 Advantages of Digital Systems...
More informationPropositional Calculus. Math Foundations of Computer Science
Propositional Calculus Math Foundations of Computer Science Propositional Calculus Objective: To provide students with the concepts and techniques from propositional calculus so that they can use it to
More informationArab Open University. Computer Organization and Architecture  T103
Arab Open University Computer Organization and Architecture  T103 Reference Book: Linda Null, Julia Lobur, The essentials of Computer Organization and Architecture, Jones & Bartlett, Third Edition, 2012.
More informationCAD4 The ALU Fall 2009 Assignment. Description
CAD4 The ALU Fall 2009 Assignment To design a 16bit ALU which will be used in the datapath of the microprocessor. This ALU must support two s complement arithmetic and the instructions in the baseline
More informationDE Solution Set QP Code : 00904
DE Solution Set QP Code : 00904 1. Attempt any three of the following: 15 a. Define digital signal. (1M) With respect to digital signal explain the terms digits and bits.(2m) Also discuss active high and
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 informationExperiment 4 Boolean Functions Implementation
Experiment 4 Boolean Functions Implementation Introduction: Generally you will find that the basic logic functions AND, OR, NAND, NOR, and NOT are not sufficient to implement complex digital logic functions.
More informationELCT 501: Digital System Design
ELCT 501: Digital System Lecture 4: CAD tools (Continued) Dr. Mohamed Abd El Ghany, Basic VHDL Concept Via an Example Problem: write VHDL code for 1bit adder 4bit adder 2 1bit adder Inputs: A (1 bit)
More informationComputer Systems. Binary Representation. Binary Representation. Logical Computation: Boolean Algebra
Binary Representation Computer Systems Information is represented as a sequence of binary digits: Bits What the actual bits represent depends on the context: Seminar 3 Numerical value (integer, floating
More informationCS 261 Fall Mike Lam, Professor. Logic Gates
CS 261 Fall 2016 Mike Lam, Professor Logic Gates The final frontier Java programs running on Java VM C programs compiled on Linux Assembly / machine code on CPU + memory??? Switches and electric signals
More informationHours / 100 Marks Seat No.
17333 13141 3 Hours / 100 Seat No. Instructions (1) All Questions are Compulsory. (2) Answer each next main Question on a new page. (3) Illustrate your answers with neat sketches wherever necessary. (4)
More informationIntroduction to Boole algebra. Binary algebra
Introduction to Boole algebra Binary algebra Boole algebra George Boole s book released in 1847 We have only two digits: true and false We have NOT, AND, OR, XOR etc operations We have axioms and theorems
More informationDLD VIDYA SAGAR P. potharajuvidyasagar.wordpress.com. Vignana Bharathi Institute of Technology UNIT 3 DLD P VIDYA SAGAR
DLD UNIT III Combinational Circuits (CC), Analysis procedure, Design Procedure, Combinational circuit for different code converters and other problems, Binary Adder Subtractor, Decimal Adder, Binary Multiplier,
More informationThis presentation will..
Component Identification: Digital Introduction to Logic Gates and Integrated Circuits Digital Electronics 2014 This presentation will.. Introduce transistors, logic gates, integrated circuits (ICs), and
More informationB.Tech II Year I Semester (R13) Regular Examinations December 2014 DIGITAL LOGIC DESIGN
B.Tech II Year I Semester () Regular Examinations December 2014 (Common to IT and CSE) (a) If 1010 2 + 10 2 = X 10, then X is  Write the first 9 decimal digits in base 3. (c) What is meant by don
More informationSoftware and Hardware
Software and Hardware Numbers At the most fundamental level, a computer manipulates electricity according to specific rules To make those rules produce something useful, we need to associate the electrical
More informationEE292: Fundamentals of ECE
EE292: Fundamentals of ECE Fall 2012 TTh 10:0011:15 SEB 1242 Lecture 22 121115 http://www.ee.unlv.edu/~b1morris/ee292/ 2 Outline Review Binary Number Representation Binary Arithmetic Combinatorial Logic
More informationChap.3 3. Chap reduces the complexity required to represent the schematic diagram of a circuit Library
3.1 Combinational Circuits 2 Chap 3. logic circuits for digital systems: combinational vs sequential Combinational Logic Design Combinational Circuit (Chap 3) outputs are determined by the present applied
More informationComputer Architecture
Computer Architecture Lecture 1: Digital logic circuits The digital computer is a digital system that performs various computational tasks. Digital computers use the binary number system, which has two
More informationAssignment (36) Boolean Algebra and Logic Simplification  General Questions
Assignment (36) Boolean Algebra and Logic Simplification  General Questions 1. Convert the following SOP expression to an equivalent POS expression. 2. Determine the values of A, B, C, and D that make
More information1 /8_ 2 /12 3 /12 4 /25 5 /12 6 /15 7 /16
M A S S A C H U S E T T S I N S T I T U T E O F T E C H N O L O G Y DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE 6.S084 Computation Structures Spring 2018 Practice Quiz #1 1 /8_ 2 /12 3 /12
More informationVALLIAMMAI ENGINEERING COLLEGE. SRM Nagar, Kattankulathur DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING EC6302 DIGITAL ELECTRONICS
VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur603 203 DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING EC6302 DIGITAL ELECTRONICS YEAR / SEMESTER: II / III ACADEMIC YEAR: 20152016 (ODD
More informationDepartment of Electrical Engineering McGill University ECSE 221 Introduction to Computer Engineering Assignment 2 Combinational Logic
Department of Electrical Engineering McGill University ECSE 221 Introduction to Computer Engineering Assignment 2 Combinational Logic Question 1: Due October 19 th, 2009 A convenient shorthand for specifying
More informationUniversity of Toronto Faculty of Applied Science and Engineering Edward S. Rogers Sr. Department of Electrical and Computer Engineering
University of Toronto Faculty of Applied Science and Engineering Edward S. Rogers Sr. Department of Electrical and Computer Engineering Final Examination ECE 241F  Digital Systems Examiners: S. Brown,
More informationChapter 2. Boolean Expressions:
Chapter 2 Boolean Expressions: A Boolean expression or a function is an expression which consists of binary variables joined by the Boolean connectives AND and OR along with NOT operation. Any Boolean
More informationSYNERGY INSTITUTE OF ENGINEERING & TECHNOLOGY,DHENKANAL LECTURE NOTES ON DIGITAL ELECTRONICS CIRCUIT(SUBJECT CODE:PCEC4202)
Lecture No:5 Boolean Expressions and Definitions Boolean Algebra Boolean Algebra is used to analyze and simplify the digital (logic) circuits. It uses only the binary numbers i.e. 0 and 1. It is also called
More informationMGUBCA205 Second Sem Core VI Fundamentals of Digital Systems MCQ s. 2. Why the decimal number system is also called as positional number system?
MGUBCA205 Second Sem Core VI Fundamentals of Digital Systems MCQ s Unit1 Number Systems 1. What does a decimal number represents? A. Quality B. Quantity C. Position D. None of the above 2. Why the
More informationReal Digital Problem Set #6
Real igital Problem et #6. (2 points) ketch a block diagram for a magnitude comparator bitslice circuit. Create Kmaps to define the bitslice circuit, and use them to find optimal logic equations. ketch
More information