Boolean Algebra and Digital Circuits Part 3: Logic Gates and Combinatorial Circuits

Save this PDF as:

Size: px
Start display at page:

Download "Boolean Algebra and Digital Circuits Part 3: Logic Gates and Combinatorial Circuits"

Transcription

1 Boolean Algebra and Digital Circuits Part 3: Logic Gates and Combinatorial Circuits

2 Logic Gates a gate implements a simple boolean function such as AND, OR or NOT constructed using a few transistors basic building block of digital design AND. OR + NOT XOR (the circle in the NOT gate represents complement)

3 Universal Gates recall that all other gates can be constructed using NAND gates alone, or NOR gates alone so these are our universal gates NAND. NOR +

4 Multiple Inputs and Outputs z OR ++z three input OR gate z AND..z three input AND gate AND Q =. Q =. two output AND gate adapted from figs , Computer Organization & Architecture

5 Digital Circuits we can build boolean functions using gates: F(,, z) = +.z z F and sum of products can make construction simple: F = z + z + z F and for efficienc we could alwas simplif further b using kmaps before construction z

6 Subtle Uses of Logic Gates the functionalit we see in high-level languages is built upon lower level circuits and sometimes this can be eploited to improve efficienc and performance: using XOR to swap 2 variables' values: = XOR = XOR = XOR using AND to mask bits: for a bte z, to find if its 4th bit is set use z AND in general, set the bits ou want to keep to 1, set others to 0, then AND with our bte (/word)

7 Integrated Circuits a modular approach we've seen that individual gates can be combined to perform more comple functions however gates aren't usuall manufactured individuall but instead a collection of them are etched onto an integrated circuit we use one or man of these ICs to create a boolean function

8 IC Small Scale Integration (SSI) Eample here's an integrated chip with just four NAND gates (note that modern chips have VLSI or ULSI) figure 3.10, Computer Organization & Architecture

9 Implementing a Function on the Simple IC F F(,) = + converted to just NANDs = (. ). (. )

10 Combinatorial Circuits the eamples we've seen so far are combinatorial circuits the output is based entirel upon the input values the produce an output at the (notional) instant when the input values are specified so all input values must arrive at the same time for them to work the can't 'remember' the inputs if some arrive later than others we'll see later what to do if the inputs arrive sequentiall for now we'll look at some useful combinatorial circuits

11 Half-Adder we want to be able to add binar numbers in the Arithmetic Logic Unit (ALU) let's start with a half-adder which can add two bits together: so could we simpl combine a set of half-adders to perform addition on words of an size we choose? no, because we need to account for the carr in table 3.9, figure 3.11, Computer Organization & Architecture

12 Full-Adder a full-adder takes account of the carr in......and we see how the half-adder got it name figure 3.12, Computer Organization & Architecture

13 Ripple-Carr Adder the full-adder can be combined to create a ripple-carradder which can add words together figure 3.13, Computer Organization & Architecture note that in realit we now have far more efficient adders (40%-90% faster!) through the use of optimisations based upon parallelisation and handling of the carr bit

14 Decoder uses the combination of the input values to select one specific output line so, with two inputs and, there are 4 possible combinations:.,.,.,. and we create an output line for each: figure 3.14, Computer Organization & Architecture this is useful for building circuits which can determine which memor address to access, or which function to perform based upon the input

15 Multipleer selects a single output from several inputs uses control lines to determine which input to route like the inputs & output of a home theatre receiver figure 3.14, Computer Organization & Architecture

16 Simple 2-bit ALU control codes: 00 = A + B 01 = NOT A 10 = A OR B 11 = A AND B figure 3.15, Computer Organization & Architecture

17 Simple 2-bit ALU OR function enabled (code 10) with inputs of 01 & 10 and an output of 11 figure 3.15, Computer Organization & Architecture

18 To Conclude we can build comple circuits in a modular fashion either b combining individual gates or b combining integrated circuits but so far these circuits require that the inputs arrive and are handled at the same time the are memorless so net lecture we'll see how to account for memor and timing needs

19 References & Further Learning outline primaril based upon: Chapter 3, Computer Organization & Architecture (3rd Edition), Null & Lobur other material used for reference: Chapter 3, Fundamentals of Computer Architecture, Burrell suggested learning activities: make sure that ou understand how the full adder works perhaps trace the flow for a 4-bit adder tr to follow instructions through the simple 2-bit ALU

Boolean Algebra and Digital Logic

Null3 /7/3 4:35 PM Page 93 I ve alwas loved that word, Boolean. Claude Shannon CHAPTER 3 3. Boolean Algebra and Digital Logic INTRODUCTION eorge Boole lived in England during the time Abraham Lincoln was

Digital Logic Design. Basics Combinational Circuits Sequential Circuits. Pu-Jen Cheng

Digital Logic Design Basics Combinational Circuits Sequential Circuits Pu-Jen Cheng Adapted from the slides prepared by S. Dandamudi for the book, Fundamentals of Computer Organization and Design. Introduction

CHAPTER 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

Exclusive 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

4 Combinational Components

Chapter 4 Combinational Components Page of 8 4 Combinational Components In constructing large digital circuits, instead of starting with the basic gates as building blocks, we often start with larger building

Chapter 4. Gates and Circuits. Chapter Goals. Chapter Goals. Computers and Electricity. Computers and Electricity. Gates

Chapter Goals Chapter 4 Gates and Circuits Identify the basic gates and describe the behavior of each Describe how gates are implemented using transistors Combine basic gates into circuits Describe the

1. True or False? A voltage level in the range 0 to 2 volts is interpreted as a binary 1.

File: chap04, Chapter 04 1. True or False? A voltage level in the range 0 to 2 volts is interpreted as a binary 1. 2. True or False? A gate is a device that accepts a single input signal and produces one

Experiment 5. Arithmetic Logic Unit (ALU)

Experiment 5 Arithmetic Logic Unit (ALU) Objectives: To implement and test the circuits which constitute the arithmetic logic circuit (ALU). Background Information: The basic blocks of a computer are central

Understanding 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

Combinational Logic. Combinational Circuits in Computers (Examples) Design of Combinational Circuits. CC Design Example

Combinational Circuits in Computers (Examples) Combinational Logic Translates a set of Boolean n input variables ( or ) by a mapping function (using Boolean operations) to produce a set of Boolean m output

Gates, 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

Let s put together a Manual Processor

Lecture 14 Let s put together a Manual Processor Hardware Lecture 14 Slide 1 The processor Inside every computer there is at least one processor which can take an instruction, some operands and produce

1. Realization of gates using Universal gates

1. Realization of gates using Universal gates Aim: To realize all logic gates using NAND and NOR gates. Apparatus: S. No Description of Item Quantity 1. IC 7400 01 2. IC 7402 01 3. Digital Trainer Kit

FORDHAM 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

Chapter 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

FORDHAM UNIVERSITY CISC 3593. Dept. of Computer and Info. Science Spring, 2011. Lab 2. The Full-Adder

FORDHAM UNIVERSITY CISC 3593 Fordham College Lincoln Center Computer Organization Dept. of Computer and Info. Science Spring, 2011 Lab 2 The Full-Adder 1 Introduction In this lab, the student will construct

Chapter 4 Register Transfer and Microoperations. Section 4.1 Register Transfer Language

Chapter 4 Register Transfer and Microoperations Section 4.1 Register Transfer Language Digital systems are composed of modules that are constructed from digital components, such as registers, decoders,

Chapter 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

(Or Gate) (And Gate) (Not Gate)

6 March 2015 Today we will be abstracting away the physical representation of logical gates so we can more easily represent more complex circuits. Specifically, we use the shapes themselves to represent

Systems I: Computer Organization and Architecture

Systems I: Computer Organization and Architecture Lecture 9 - Register Transfer and Microoperations Microoperations Digital systems are modular in nature, with modules containing registers, decoders, arithmetic

Arithmetic-logic units

Arithmetic-logic units An arithmetic-logic unit, or ALU, performs many different arithmetic and logic operations. The ALU is the heart of a processor you could say that everything else in the CPU is there

Logic 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

Digital Logic: Boolean Algebra and Gates

Digital Logic: Boolean Algebra and Gates Textbook Chapter 3 CMPE2 Summer 28 Basic Logic Gates CMPE2 Summer 28 Slides by ADB 2 Truth Table The most basic representation of a logic function Lists the output

COMBINATIONAL and SEQUENTIAL LOGIC CIRCUITS Hardware implementation and software design

PH-315 COMINATIONAL and SEUENTIAL LOGIC CIRCUITS Hardware implementation and software design A La Rosa I PURPOSE: To familiarize with combinational and sequential logic circuits Combinational circuits

Reading 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

Circuits and Boolean Expressions

Circuits and Boolean Expressions Provided by TryEngineering - Lesson Focus Boolean logic is essential to understanding computer architecture. It is also useful in program construction and Artificial Intelligence.

Digital 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

Gate Count Comparison of Different 16-Bit Carry Select Adders

DOI: 10.15662/ijareeie.2014.0307034 Gate Count Comparison of Different 16-Bit Carry Select Adders M.Lavanya 1 Assistant professor, Dept. of ECE, Vardhaman College of Engineering, Telangana, India 1 ABSTRACT:

l What have discussed up until now & why: l C Programming language l More low-level then Java. l Better idea about what s really going on.

CS211 Computer Architecture l Topics Digital Logic l Transistors (Design & Types) l Logic Gates l Combinational Circuits l K-Maps Class Checkpoint l What have discussed up until now & why: l C Programming

ECE3281 Electronics Laboratory

ECE328 Electronics Laboratory Experiment #4 TITLE: EXCLUSIVE-OR FUNCTIONS and INRY RITHMETIC OJECTIVE: Synthesize exclusive-or and the basic logic functions necessary for execution of binary arithmetic.

Lecture 8 Binary Numbers & Logic Operations The focus of the last lecture was on the microprocessor

Lecture 8 Binary Numbers & Logic Operations The focus of the last lecture was on the microprocessor During that lecture we learnt about the function of the central component of a computer, the microprocessor

Binary Adder. sum of 2 binary numbers can be larger than either number need a carry-out to store the overflow

Binary Addition single bit addition Binary Adder sum of 2 binary numbers can be larger than either number need a carry-out to store the overflow Half-Adder 2 inputs (x and y) and 2 outputs (sum and carry)

Chapter 6 Digital Arithmetic: Operations & Circuits

Chapter 6 Digital Arithmetic: Operations & Circuits Chapter 6 Objectives Selected areas covered in this chapter: Binary addition, subtraction, multiplication, division. Differences between binary addition

2 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

4 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.

UNIT I NUMBER SYSTEM AND BINARY CODES

1 UNIT I NUMBER SYSTEM AND BINARY CODES 1.0 Aims and Objectives 1.1 Introduction 1.2 Number System 1.2.1 Decimal Number System 1.2.2 Bi-stable Devices 1.2.3 Binary Number System 1.2.4 Octal number System

CSE140 Homework #7 - Solution

CSE140 Spring2013 CSE140 Homework #7 - Solution You must SHOW ALL STEPS for obtaining the solution. Reporting the correct answer, without showing the work performed at each step will result in getting

Logic in Computer Science: Logic Gates

Logic in Computer Science: Logic Gates Lila Kari The University of Western Ontario Logic in Computer Science: Logic Gates CS2209, Applied Logic for Computer Science 1 / 49 Logic and bit operations Computers

Counters and Decoders

Physics 3330 Experiment #10 Fall 1999 Purpose Counters and Decoders In this experiment, you will design and construct a 4-bit ripple-through decade counter with a decimal read-out display. Such a counter

Module 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

Digital Systems CCPS1573

1. Name of Course 2. Course Code 3. Name(s) of academic staff 4. Rationale for the inclusion of the course/module in the programme Digital Systems CCPS1573 Faculty This module provides foundation knowledge

Two's Complement Adder/Subtractor Lab L03 Introduction Computers are usually designed to perform indirect subtraction instead of direct subtraction. Adding -B to A is equivalent to subtracting B from A,

The equation for the 3-input XOR gate is derived as follows

The equation for the 3-input XOR gate is derived as follows The last four product terms in the above derivation are the four 1-minterms in the 3-input XOR truth table. For 3 or more inputs, the XOR gate

Chapter 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

International Journal of Electronics and Computer Science Engineering 1482

International Journal of Electronics and Computer Science Engineering 1482 Available Online at www.ijecse.org ISSN- 2277-1956 Behavioral Analysis of Different ALU Architectures G.V.V.S.R.Krishna Assistant

2 hrs lecture 2 hrs lab 2 hrs section

Arab Academy for Science and Technology & Maritime Transport University/Academy: Arab Academy for Science and Technology & Maritime Transport Faculty/Institute: College of Computing and Information Technology

Digital Logic cct. Lec. (6)

THE NAND GATE The NAND gate is a popular logic element because it can be used as a universal gate: that is, NAND gates can be used in combination to perform the AND, OR, and inverter operations. The term

ENEE 244 (01**). Spring 2006. Homework 4. Due back in class on Friday, April 7.

ENEE 244 (**). Spring 26 Homework 4 Due back in class on Friday, April 7.. Implement the following Boolean expression with exclusive-or and AND gates only: F = AB'CD' + A'BCD' + AB'C'D + A'BC'D. F = AB

2012-13 Department of Electronics & Communication

(A constituent college of Sri Siddhartha University) 2012-13 Department of Electronics & Communication LOGIC DESIGN LAB MANUAL III SEM BE Name : Sem :. Sec: Logic Design Lab Manual Contents Exp No Title

Design and Development of Virtual Instrument (VI) Modules for an Introductory Digital Logic Course

Session ENG 206-6 Design and Development of Virtual Instrument (VI) Modules for an Introductory Digital Logic Course Nikunja Swain, Ph.D., PE South Carolina State University swain@scsu.edu Raghu Korrapati,

Electronic Design Automation Prof. Indranil Sengupta Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur

Electronic Design Automation Prof. Indranil Sengupta Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Lecture - 10 Synthesis: Part 3 I have talked about two-level

Chapter 4 BOOLEAN ALGEBRA AND THEOREMS, MIN TERMS AND MAX TERMS

Chapter 4 BOOLEAN ALGEBRA AND THEOREMS, MIN TERMS AND MAX TERMS Lesson 5 BOOLEAN EXPRESSION, TRUTH TABLE and product of the sums (POSs) [MAXTERMS] 2 Outline POS two variables cases POS for three variable

COMBINATIONAL CIRCUITS

COMBINATIONAL CIRCUITS http://www.tutorialspoint.com/computer_logical_organization/combinational_circuits.htm Copyright tutorialspoint.com Combinational circuit is a circuit in which we combine the different

LOGIC DESIGN LABORATORY MANUAL

LOGIC DESIGN LABORATORY MANUAL Logic Design Laboratory Manual 1 EXPERIMENT: 1 LOGIC GATES AIM: To study and verify the truth table of logic gates LEARNING OBJECTIVE: Identify various ICs and their specification.

NOT AND OR XOR NAND NOR

NOT AND OR XOR NAND NOR Expression 1: It is raining today Expression 2: Today is my birthday X Meaning True False It is raining today It is not raining Binary representation of the above: X Meaning 1 It

ELG3331: Lab 3 Digital Logic Circuits

ELG3331: Lab 3 Digital Logic Circuits What does Digital Means? Digital describes any system based on discontinuous data or events. Typically digital is computer data or electronic sampling of an analog

Sistemas Digitais I LESI - 2º ano

Sistemas Digitais I LESI - 2º ano Lesson 6 - Combinational Design Practices Prof. João Miguel Fernandes (miguel@di.uminho.pt) Dept. Informática UNIVERSIDADE DO MINHO ESCOLA DE ENGENHARIA - PLDs (1) - The

A single register, called the accumulator, stores the. operand before the operation, and stores the result. Add y # add y from memory to the acc

Other architectures Example. Accumulator-based machines A single register, called the accumulator, stores the operand before the operation, and stores the result after the operation. Load x # into acc

Chapter 5: Sequential Circuits (LATCHES)

Chapter 5: Sequential Circuits (LATCHES) Latches We focuses on sequential circuits, where we add memory to the hardware that we ve already seen Our schedule will be very similar to before: We first show

Introduction. Logic. Most Difficult Reading Topics. Basic Logic Gates Truth Tables Logical Functions. COMP370 Introduction to Computer Architecture

Introduction LOGIC GATES COMP370 Introduction to Computer Architecture Basic Logic Gates Truth Tables Logical Functions Truth Tables Logical Expression Graphical l Form Most Difficult Reading Topics Logic

In this chapter we are concerned with basic architecture and the. different operations related to explain the proper functioning of the

CHAPTER I CONTENTS: 1.1 INTRODUCTION 1.2 STORED PROGRAM ORGANIZATION 1.3 INDIRECT ADDRESS 1.4 COMPUTER REGISTERS 1.5 COMMON BUS SYSTEM SUMMARY SELF ASSESSMENT OBJECTIVE: In this chapter we are concerned

2 Boolean Arithmetic. Counting is the religion of this generation, its hope and salvation. Gertrude Stein ( )

2 Boolean Arithmetic Counting is the religion of this generation, its hope and salvation. Gertrude Stein (1874 1946) In this chapter we build gate logic designs that represent numbers and perform arithmetic

DEPARTMENT OF INFORMATION TECHNLOGY

DRONACHARYA GROUP OF INSTITUTIONS, GREATER NOIDA Affiliated to Mahamaya Technical University, Noida Approved by AICTE DEPARTMENT OF INFORMATION TECHNLOGY Lab Manual for Computer Organization Lab ECS-453

Lab Manual. Digital System Design (Pr): COT-215 Digital Electronics (P): IT-211

Lab Manual Digital System Design (Pr): COT-215 Digital Electronics (P): IT-211 Lab Instructions Several practicals / programs? Whether an experiment contains one or several practicals /programs One practical

Combinational Logic Design

Chapter 4 Combinational Logic Design The foundations for the design of digital logic circuits were established in the preceding chapters. The elements of Boolean algebra (two-element switching algebra

Online Development of Digital Logic Design Course

Online Development of Digital Logic Design Course M. Mohandes, M. Dawoud, S. Al Amoudi, A. Abul Hussain Electrical Engineering Department & Deanship of Academic Development King Fahd University of Petroleum

NEW adder cells are useful for designing larger circuits despite increase in transistor count by four per cell.

CHAPTER 4 THE ADDER The adder is one of the most critical components of a processor, as it is used in the Arithmetic Logic Unit (ALU), in the floating-point unit and for address generation in case of cache

UNIT - II LOGIC GATES AND GATES CLASSIFICATION

UNIT - II Logic Gates: Gates Classifications: Basic Gates (AND, OR, NOT), Universal Gates (NAND, NOR), Exclusive Gates (XOR, XNOR)(except circuit diagram) Logic Symbols, Logic Operators, Logical expression

Three-Phase Dual-Rail Pre-Charge Logic

Infineon Page 1 CHES 2006 - Yokohama Three-Phase Dual-Rail Pre-Charge Logic L. Giancane, R. Luzzi, A. Trifiletti {marco.bucci, raimondo.luzzi}@infineon.com {giancane, trifiletti}@die.mail.uniroma1.it Summary

Digital Circuits Laboratory LAB no. 2. LOGIC GATES

Digital Circuits Labat. Introduction LOGIC GATES Combinational logic sstems, no matter how complicated the are, the are realized with logic gates. An elementar logic gate implements a two variables unction.

Circuit and System Representation. IC Designers must juggle several different problems

Circuit and System Representation IC Designers must juggle several different problems Multiple levels of abstraction IC designs requires refining an idea through many levels of detail, specification ->

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

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

Adder.T(//29) 5. Lecture 3 Adder ircuits Objectives Understand how to add both signed and unsigned numbers Appreciate how the delay of an adder circuit depends on the data values that are being added together

EXPERIMENT NO.1:INTRODUCTION TO BASIC GATES AND LOGIC SIMPLIFICATION TECHNIQUES

DEPARTMENT OF ELECTRICAL AND ELECTROINC ENGINEERING BANGLADESH UNIVERSITY OF ENGINEERING & TECHNOLOGY EEE 304 : Digital Electronics Laboratory EXPERIMENT NO.1:INTRODUCTION TO BASIC GATES AND LOGIC SIMPLIFICATION

EE360: Digital Design I Course Syllabus

: Course Syllabus Dr. Mohammad H. Awedh Fall 2008 Course Description This course introduces students to the basic concepts of digital systems, including analysis and design. Both combinational and sequential

exclusive-or and Binary Adder R eouven Elbaz reouven@uwaterloo.ca Office room: DC3576

exclusive-or and Binary Adder R eouven Elbaz reouven@uwaterloo.ca Office room: DC3576 Outline exclusive OR gate (XOR) Definition Properties Examples of Applications Odd Function Parity Generation and Checking

Gates & Boolean Algebra. Boolean Operators. Combinational Logic. Introduction

Introduction Gates & Boolean lgebra Boolean algebra: named after mathematician George Boole (85 864). 2-valued algebra. digital circuit can have one of 2 values. Signal between and volt =, between 4 and

ECE410 Design Project Spring 2008 Design and Characterization of a CMOS 8-bit Microprocessor Data Path

ECE410 Design Project Spring 2008 Design and Characterization of a CMOS 8-bit Microprocessor Data Path Project Summary This project involves the schematic and layout design of an 8-bit microprocessor data

2011, The McGraw-Hill Companies, Inc. Chapter 4

Chapter 4 4.1 The Binary Concept Binary refers to the idea that many things can be thought of as existing in only one of two states. The binary states are 1 and 0 The 1 and 0 can represent: ON or OFF Open

LogicBlocks Experiment Guide a learn.sparkfun.com

LogicBlocks Experiment Guide a learn.sparkfun.com tutorial Available online at: http://sfe.io/t216 Contents Introduction 1. 2-Input AND Gate 2. 3-Input AND Gate 3. NANDs, NORs, and DeMorgan's Laws 4. Combinational

4.203 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?

Arithmetic. Hakim Weatherspoon CS 3410, Spring 2012 Computer Science Cornell University. See P&H 2.4 (signed), 2.5, 2.6, C.6, and Appendix C.

Arithmetic Hakim Weatherspoon CS 3410, Spring 2012 Computer Science Cornell University See P&H 2.4 (signed), 2.5, 2.6, C.6, and Appendix C.6 Goals for today Binary (Arithmetic) Operations One-bit and four-bit

CSEE 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 2.3-2.5) Standard Forms Product-of-Sums (PoS) Sum-of-Products (SoP) converting between Min-terms

Chapter 2 Digital Components. Section 2.1 Integrated Circuits

Chapter 2 Digital Components Section 2.1 Integrated Circuits An integrated circuit (IC) is a small silicon semiconductor crystal, called a chip, containing the electronic components for the digital gates

Lecture 5: Gate Logic Logic Optimization

Lecture 5: Gate Logic Logic Optimization MAH, AEN EE271 Lecture 5 1 Overview Reading McCluskey, Logic Design Principles- or any text in boolean algebra Introduction We could design at the level of irsim

Digital Systems. Syllabus 8/18/2010 1

Digital Systems Syllabus 1 Course Description: This course covers the design and implementation of digital systems. Topics include: combinational and sequential digital circuits, minimization methods,

WEEK 2.2 CANONICAL FORMS

WEEK 2.2 CANONICAL FORMS 1 Canonical Sum-of-Products (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

ENGIN 112 Intro to Electrical and Computer Engineering

ENGIN 112 Intro to Electrical and Computer Engineering Lecture 19 Sequential Circuits: Latches Overview Circuits require memory to store intermediate data Sequential circuits use a periodic signal to determine

Digital Circuits. Electrical & Computer Engineering Department (ECED) Course Notes ECED2200. ECED2200 Digital Circuits Notes 2012 Dalhousie University

1 Digital Circuits Electrical & Computer Engineering Department (ECED) Course Notes ECED2200 2 Table of Contents Digital Circuits... 7 Logic Gates... 8 AND Gate... 8 OR Gate... 9 NOT Gate... 10 NOR Gate...

Gates, Circuits and Boolean Functions

Lecture 2 Gates, Circuits and Boolean Functions DOC 112: Hardware Lecture 2 Slide 1 In this lecture we will: Introduce an electronic representation of Boolean operators called digital gates. Define a schematic

Karnaugh Maps. Circuit-wise, this leads to a minimal two-level 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

United States Naval Academy Electrical and Computer Engineering Department. EC262 Exam 1

United States Naval Academy Electrical and Computer Engineering Department EC262 Exam 29 September 2. Do a page check now. You should have pages (cover & questions). 2. Read all problems in their entirety.

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

Keonics Certified Embedded System

Duration: 2 Months Basic Electronics Keonics Certified Embedded System 1. Semi Conductors Diodes and Applications 1.1 P-N Junction Diode 1.2 Characteristics and Parameters 1.3 The Diode Current Equation

Department of Computer Science & Technology o14

Department of Computer Science & Technology 23-2o4 64- Digital Electronics Unit : Codes Short Question Define signal. List out the advantages of using digital circuitry. What do you mean by radix of the

Chapter # 5: Arithmetic Circuits

Chapter # 5: rithmetic Circuits Contemporary Logic Design 5- Number ystems Representation of Negative Numbers Representation of positive numbers same in most systems Major differences are in how negative