Understanding Logic Design

Size: px
Start display at page:

Download "Understanding Logic Design"

Transcription

1 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 dder R0 R2 What kind of hardware can DD two binary integers? We need to learn about GTES and BOOLEN LGEBR that are foundations of logic design.

2 ND gate X Y X.Y X X.Y Y OR gate X Y X+Y X X+Y Y NOT gate ( x = x ) X X 0 1 X X 1 0 Typically, logical 1 = +3.5 volt, and logical 0 = 0 volt. Other representations are possible.

3 nalysis of logical circuits X X.Y F Y X.Y What is the value of F when X=0 and Y=1? Draw a truth table. X Y F This is the exclusive or (XOR) function. In algebraic form F= X.Y + X.Y

4 More practice 1. Let.B +.C = 0. What are the values of, B, C? 2. Let ( + B + C).( + B + C) = 0. What are the possible values of, B, C? Draw truth tables. Draw the logic circuits for the above two functions. B C

5 Boolean lgebra + 0 = + = 1. 1 =. = = 1 + B = B + 0. = 0. B = B. + (B + C) = ( + B) + C. (B. C) = (. B). C + =. =. (B + C) =.B +.C Distributive Law + B.C = (+B). (+C). B = + B De Morgan s theorem + B =. B

6 De Morgan s theorem. B = + B + B =. B Thus, is equivalent to Verify it using truth tables. Similarly, is equivalent to These can be generalized to more than two variables: to. B. C = + B + C + B + C =. B. C

7 Synthesis of logic circuits Many problems of logic design can be specified using a truth table. Give such a table, can you design the logic circuit? Design a logic circuit with three inputs, B, C and one output F such that F=1 only when a majority of the inputs is equal to 1. B C F Sum of product form F =.B.C +.B.C +.B.C +.B.C Draw a logic circuit to generate F

8 Simplification of Boolean functions Using the theorems of Boolean lgebra, the algebraic forms of functions can often be simplified, which leads to simpler (and cheaper) implementations. Example 1 F =.B +.B + B.C =. (B + B) + B.C How many gates do you save =.1 + B.C from this simplification? = + B.C F B B C F C

9 Example 2 F =.B.C +.B.C +.B.C +.B.C =.B.C +.B.C +.B.C +.B.C +.B.C +.B.C = (.B.C +.B.C) + (.B.C +.B.C) + (.B.C +.B.C) = ( + ). B.C + (B + B). C. + (C + C)..B = B.C + C. +.B Example 3 Show that +.B = + B =.1 +.B =. (1 + B) =. 1 =

10 Other types of gates.b B +B B NND gate NOR gate Be familiar with the truth tables of these gates. B + B =.B +.B Exclusive OR (XOR) gate

11 NND and NOR are universal gates ny function can be implemented using only NND or only NOR gates. How can we prove this? (Proof for NND gates) ny boolean function can be implemented using ND, OR and NOT gates. So if ND, OR and NOT gates can be implemented using NND gates only, then we prove our point. 1. Implement NOT using NND

12 2. Implementation of ND using NND.B B 3. Implementation of OR using NND.B = +B B B Exercise. Prove that NOR is a universal gate.

13 Logic Design (continued) XOR Revisited XOR is also called modulo-2 addition. B C F B = 1 only when there are an odd number of 1 s in (,B). The same is true for B C also = Why? 0 =

14 Logic Design Examples Half dder B S C Half dder Sum (S) B Carry (C) S = B C =.B Carry B Sum

15 Full dder Sum (S) B C in S C out Full dder B C in Carry (C out ) S = B C in C out =.B + B.C in +.C in Design a full adder using two half-adders (and a few gates if necessary) Can you design a 1-bit subtracter?

16 Decoders typical decoder has n inputs and 2 n outputs. Enable B D3 D2 D1 D0 D D B D D to-4 decoder and its truth table D3 =.B Draw the circuit of this decoder. D2 =.B D1 =.B The decoder works per specs D0 =.B when (Enable = 1). When Enable = 0, all the outputs are 0. Exercise. Design a 3-to-8 decoder. Question. Where are decoders used? Can you design a 2-4 decoder using 1-2 decoders?

17 Encoders typical encoder has 2 n inputs and n outputs. D0 D1 D2 D3 B D D D2 B D to-2 encoder and its truth table = D1 + D3 B = D2 + D3

18 Multiplexor It is a many-to-one switch, also called a selector. 0 F S = 0, F = B 1 S = 1, F = B Control S Specifications of the mux 2-to-1 mux F = S. + S. B Exercise. Design a 4-to-1 multiplexor using two 2-to- 1 multiplexors.

19 Demultiplexors demux is a one-to-many switch. 0 X S = 0, X = 1 Y S = 1, Y = S 1-to-2 demux, and its specification. So, X = S., and Y = S. Exercise. Design a 1-4 demux using 1-2 demux.

20 1-bit LU Operation Operation = 00 implies ND Result Operation = 01 implies OR B Operation = 10 implies DD? Operation Carry in B Result dder 10 Carry out Understand how this circuit works.

21 Converting an adder into a subtractor - B (here - means arithmetic subtraction) = + 2 s complement of B = + 1 s complement of B + 1 operation Carry in B Result 0 10 dder 1 11 B invert Carry out 1-bit adder/subtractor For subtraction, B invert = 1 and Carry in = 1

22 32-bit LU B invert C in operation 0 LU B0 Result 0 Cout C in 1 LU B1 Result 1 Cout LU B31 Result 31 Cout overflow

23 Combinational vs. Sequential Circuits Combinational circuits The output depends only on the current values of the inputs and not on the past values. Examples are adders, subtractors, and all the circuits that we have studied so far Sequential circuits The output depends not only on the current values of the inputs, but also on their past values. These hold the secret of how to memorize information. We will study sequential circuits later.

Binary Adders: Half Adders and Full Adders

Binary 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 information

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

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

More information

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

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

More information

Boolean Algebra Part 1

Boolean 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 information

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

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

More information

COMBINATIONAL CIRCUITS

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

More information

5 Combinatorial Components. 5.0 Full adder. Full subtractor

5 Combinatorial Components. 5.0 Full adder. Full subtractor 5 Combatorial Components Use for data transformation, manipulation, terconnection, and for control: arithmetic operations - addition, subtraction, multiplication and division. logic operations - AND, OR,

More information

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

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

More information

Let s put together a Manual Processor

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

More information

CHAPTER 3 Boolean Algebra and Digital Logic

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

More information

Two-level logic using NAND gates

Two-level logic using NAND gates CSE140: Components and Design Techniques for Digital Systems Two and Multilevel logic implementation Tajana Simunic Rosing 1 Two-level logic using NND gates Replace minterm ND gates with NND gates Place

More information

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

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.

More information

earlier in the semester: The Full adder above adds two bits and the output is at the end. So if we do this eight times, we would have an 8-bit adder.

earlier in the semester: The Full adder above adds two bits and the output is at the end. So if we do this eight times, we would have an 8-bit adder. The circuit created is an 8-bit adder. The 8-bit adder adds two 8-bit binary inputs and the result is produced in the output. In order to create a Full 8-bit adder, I could use eight Full -bit adders and

More information

Logic in Computer Science: Logic Gates

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

More information

CSE140: Components and Design Techniques for Digital Systems

CSE140: 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 information

Combinational circuits

Combinational circuits Combinational circuits Combinational circuits are stateless The outputs are functions only of the inputs Inputs Combinational circuit Outputs 3 Thursday, September 2, 3 Enabler Circuit (High-level view)

More information

Combinational Logic Design

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

More information

Figure 8-1 Four Possible Results of Adding Two Bits

Figure 8-1 Four Possible Results of Adding Two Bits CHPTER EIGHT Combinational Logic pplications Thus far, our discussion has focused on the theoretical design issues of computer systems. We have not yet addressed any of the actual hardware you might find

More information

DEPARTMENT OF INFORMATION TECHNLOGY

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

More information

Gates, Circuits, and Boolean Algebra

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

More information

EE 261 Introduction to Logic Circuits. Module #2 Number Systems

EE 261 Introduction to Logic Circuits. Module #2 Number Systems EE 261 Introduction to Logic Circuits Module #2 Number Systems Topics A. Number System Formation B. Base Conversions C. Binary Arithmetic D. Signed Numbers E. Signed Arithmetic F. Binary Codes Textbook

More information

Two's Complement Adder/Subtractor Lab L03

Two's Complement Adder/Subtractor Lab L03 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,

More information

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

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,

More information

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

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

More information

Sistemas Digitais I LESI - 2º ano

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

More information

Systems I: Computer Organization and Architecture

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

More information

Binary full adder. 2-bit ripple-carry adder. CSE 370 Spring 2006 Introduction to Digital Design Lecture 12: Adders

Binary full adder. 2-bit ripple-carry adder. CSE 370 Spring 2006 Introduction to Digital Design Lecture 12: Adders SE 370 Spring 2006 Introduction to Digital Design Lecture 12: dders Last Lecture Ls and Ls Today dders inary full 1-bit full omputes sum, carry-out arry-in allows cascaded s = xor xor = + + 32 ND2 11 ND2

More information

Counters and Decoders

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

More information

EE360: Digital Design I Course Syllabus

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

More information

Take-Home Exercise. z y x. Erik Jonsson School of Engineering and Computer Science. The University of Texas at Dallas

Take-Home Exercise. z y x. Erik Jonsson School of Engineering and Computer Science. The University of Texas at Dallas Take-Home Exercise Assume you want the counter below to count mod-6 backward. That is, it would count 0-5-4-3-2-1-0, etc. Assume it is reset on startup, and design the wiring to make the counter count

More information

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

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,

More information

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 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

More information

Lecture 4: Binary. CS442: Great Insights in Computer Science Michael L. Littman, Spring 2006. I-Before-E, Continued

Lecture 4: Binary. CS442: Great Insights in Computer Science Michael L. Littman, Spring 2006. I-Before-E, Continued Lecture 4: Binary CS442: Great Insights in Computer Science Michael L. Littman, Spring 26 I-Before-E, Continued There are two ideas from last time that I d like to flesh out a bit more. This time, let

More information

Lab 1: Full Adder 0.0

Lab 1: Full Adder 0.0 Lab 1: Full Adder 0.0 Introduction In this lab you will design a simple digital circuit called a full adder. You will then use logic gates to draw a schematic for the circuit. Finally, you will verify

More information

Digital Logic Elements, Clock, and Memory Elements

Digital Logic Elements, Clock, and Memory Elements Physics 333 Experiment #9 Fall 999 Digital Logic Elements, Clock, and Memory Elements Purpose This experiment introduces the fundamental circuit elements of digital electronics. These include a basic set

More information

Karnaugh Maps & Combinational Logic Design. ECE 152A Winter 2012

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 information

C H A P T E R. Logic Circuits

C H A P T E R. Logic Circuits C H A P T E R Logic Circuits Many important functions are naturally computed with straight-line programs, programs without loops or branches. Such computations are conveniently described with circuits,

More information

Elementary Logic Gates

Elementary 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 information

Digital Design. Assoc. Prof. Dr. Berna Örs Yalçın

Digital Design. Assoc. Prof. Dr. Berna Örs Yalçın Digital Design Assoc. Prof. Dr. Berna Örs Yalçın Istanbul Technical University Faculty of Electrical and Electronics Engineering Office Number: 2318 E-mail: siddika.ors@itu.edu.tr Grading 1st Midterm -

More information

COMBINATIONAL and SEQUENTIAL LOGIC CIRCUITS Hardware implementation and software design

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

More information

Unit 3 Boolean Algebra (Continued)

Unit 3 Boolean Algebra (Continued) Unit 3 Boolean Algebra (Continued) 1. Exclusive-OR Operation 2. Consensus Theorem Department of Communication Engineering, NCTU 1 3.1 Multiplying Out and Factoring Expressions Department of Communication

More information

BOOLEAN ALGEBRA & LOGIC GATES

BOOLEAN 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 information

plc numbers - 13.1 Encoded values; BCD and ASCII Error detection; parity, gray code and checksums

plc numbers - 13.1 Encoded values; BCD and ASCII Error detection; parity, gray code and checksums plc numbers - 3. Topics: Number bases; binary, octal, decimal, hexadecimal Binary calculations; s compliments, addition, subtraction and Boolean operations Encoded values; BCD and ASCII Error detection;

More information

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

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

More information

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

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

More information

CSE140: Components and Design Techniques for Digital Systems. Introduction. Prof. Tajana Simunic Rosing

CSE140: Components and Design Techniques for Digital Systems. Introduction. Prof. Tajana Simunic Rosing CSE4: Components and Design Techniques for Digital Systems Introduction Prof. Tajana Simunic Rosing Welcome to CSE 4! Instructor: Tajana Simunic Rosing Email: tajana@ucsd.edu; please put CSE4 in the subject

More information

Digital Electronics Detailed Outline

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

More information

Lecture 8: Synchronous Digital Systems

Lecture 8: Synchronous Digital Systems Lecture 8: Synchronous Digital Systems The distinguishing feature of a synchronous digital system is that the circuit only changes in response to a system clock. For example, consider the edge triggered

More information

Digital circuits make up all computers and computer systems. The operation of digital circuits is based on

Digital circuits make up all computers and computer systems. The operation of digital circuits is based on Digital Logic Circuits Digital circuits make up all computers and computer systems. The operation of digital circuits is based on Boolean algebra, the mathematics of binary numbers. Boolean algebra is

More information

CSE140: Midterm 1 Solution and Rubric

CSE140: 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 information

Chapter 3 Digital Basics

Chapter 3 Digital Basics Chapter 3 Digital asics We conclude our review of basic concepts with a survey of topics from digital electronics. We confine our attention to aspects that are important in the understanding of simple

More information

3.Basic Gate Combinations

3.Basic Gate Combinations 3.Basic Gate Combinations 3.1 TTL NAND Gate In logic circuits transistors play the role of switches. For those in the TTL gate the conducting state (on) occurs when the baseemmiter signal is high, and

More information

SECTION C [short essay] [Not to exceed 120 words, Answer any SIX questions. Each question carries FOUR marks] 6 x 4=24 marks

SECTION C [short essay] [Not to exceed 120 words, Answer any SIX questions. Each question carries FOUR marks] 6 x 4=24 marks UNIVERSITY OF KERALA First Degree Programme in Computer Applications Model Question Paper Semester I Course Code- CP 1121 Introduction to Computer Science TIME : 3 hrs Maximum Mark: 80 SECTION A [Very

More information

List of Experiment. 8. To study and verify the BCD to Seven Segments DECODER.(IC-7447).

List of Experiment. 8. To study and verify the BCD to Seven Segments DECODER.(IC-7447). G. H. RAISONI COLLEGE OF ENGINEERING, NAGPUR Department of Electronics & Communication Engineering Branch:-4 th Semester[Electronics] Subject: - Digital Circuits List of Experiment Sr. Name Of Experiment

More information

Simplifying Logic Circuits with Karnaugh Maps

Simplifying 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 information

The string of digits 101101 in the binary number system represents the quantity

The string of digits 101101 in the binary number system represents the quantity Data Representation Section 3.1 Data Types Registers contain either data or control information Control information is a bit or group of bits used to specify the sequence of command signals needed for

More information

Today. Binary addition Representing negative numbers. Andrew H. Fagg: Embedded Real- Time Systems: Binary Arithmetic

Today. Binary addition Representing negative numbers. Andrew H. Fagg: Embedded Real- Time Systems: Binary Arithmetic Today Binary addition Representing negative numbers 2 Binary Addition Consider the following binary numbers: 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 1 How do we add these numbers? 3 Binary Addition 0 0 1 0 0 1 1

More information

1.4. Arithmetic of Algebraic Fractions. Introduction. Prerequisites. Learning Outcomes

1.4. Arithmetic of Algebraic Fractions. Introduction. Prerequisites. Learning Outcomes Arithmetic of Algebraic Fractions 1.4 Introduction Just as one whole number divided by another is called a numerical fraction, so one algebraic expression divided by another is known as an algebraic fraction.

More information

An Efficient RNS to Binary Converter Using the Moduli Set {2n + 1, 2n, 2n 1}

An Efficient RNS to Binary Converter Using the Moduli Set {2n + 1, 2n, 2n 1} An Efficient RNS to Binary Converter Using the oduli Set {n + 1, n, n 1} Kazeem Alagbe Gbolagade 1,, ember, IEEE and Sorin Dan Cotofana 1, Senior ember IEEE, 1. Computer Engineering Laboratory, Delft University

More information

2.0 Chapter Overview. 2.1 Boolean Algebra

2.0 Chapter Overview. 2.1 Boolean Algebra Thi d t t d ith F M k 4 0 2 Boolean Algebra Chapter Two Logic circuits are the basis for modern digital computer systems. To appreciate how computer systems operate you will need to understand digital

More information

DB19. 4-Bit Parallel Adder/ Subtractor. Digital Lab Experiment Board Ver. 1.0

DB19. 4-Bit Parallel Adder/ Subtractor. Digital Lab Experiment Board Ver. 1.0 4-Bit Parallel Adder/ Subtractor Digital Lab Experiment Board Ver. 1.0 QUALITY POLICY To be a Global Leader of Innovative, Competitive and Eco friendly Electronic Equipment, Software Products and Turn-key

More information

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 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

More information

CSE140 Homework #7 - Solution

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

More information

Multipliers. Introduction

Multipliers. Introduction Multipliers Introduction Multipliers play an important role in today s digital signal processing and various other applications. With advances in technology, many researchers have tried and are trying

More information

Design Example: Counters. Design Example: Counters. 3-Bit Binary Counter. 3-Bit Binary Counter. Other useful counters:

Design Example: Counters. Design Example: Counters. 3-Bit Binary Counter. 3-Bit Binary Counter. Other useful counters: Design Eample: ers er: a sequential circuit that repeats a specified sequence of output upon clock pulses. A,B,C,, Z. G, O, T, E, R, P, S,!.,,,,,,,7. 7,,,,,,,.,,,,,,,,,,,. Binary counter: follows the binary

More information

BINARY CODED DECIMAL: B.C.D.

BINARY CODED DECIMAL: B.C.D. BINARY CODED DECIMAL: B.C.D. ANOTHER METHOD TO REPRESENT DECIMAL NUMBERS USEFUL BECAUSE MANY DIGITAL DEVICES PROCESS + DISPLAY NUMBERS IN TENS IN BCD EACH NUMBER IS DEFINED BY A BINARY CODE OF 4 BITS.

More information

Basic Logic Gates Richard E. Haskell

Basic 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 information

INTRODUCTION TO DIGITAL SYSTEMS. IMPLEMENTATION: MODULES (ICs) AND NETWORKS IMPLEMENTATION OF ALGORITHMS IN HARDWARE

INTRODUCTION TO DIGITAL SYSTEMS. IMPLEMENTATION: MODULES (ICs) AND NETWORKS IMPLEMENTATION OF ALGORITHMS IN HARDWARE INTRODUCTION TO DIGITAL SYSTEMS 1 DESCRIPTION AND DESIGN OF DIGITAL SYSTEMS FORMAL BASIS: SWITCHING ALGEBRA IMPLEMENTATION: MODULES (ICs) AND NETWORKS IMPLEMENTATION OF ALGORITHMS IN HARDWARE COURSE EMPHASIS:

More information

CH3 Boolean Algebra (cont d)

CH3 Boolean Algebra (cont d) CH3 Boolean Algebra (cont d) Lecturer: 吳 安 宇 Date:2005/10/7 ACCESS IC LAB v Today, you ll know: Introduction 1. Guidelines for multiplying out/factoring expressions 2. Exclusive-OR and Equivalence operations

More information

Chapter 2: Boolean Algebra and Logic Gates. Boolean Algebra

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

More information

Sum-of-Products and Product-of-Sums expressions

Sum-of-Products and Product-of-Sums expressions Sum-of-Products and Product-of-Sums 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 information

Logic Reference Guide

Logic 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

Today s topics. Digital Computers. More on binary. Binary Digits (Bits)

Today s topics. Digital Computers. More on binary. Binary Digits (Bits) Today s topics! Binary Numbers! Brookshear.-.! Slides from Prof. Marti Hearst of UC Berkeley SIMS! Upcoming! Networks Interactive Introduction to Graph Theory http://www.utm.edu/cgi-bin/caldwell/tutor/departments/math/graph/intro

More information

Lecture 5: Gate Logic Logic Optimization

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

More information

ASYNCHRONOUS COUNTERS

ASYNCHRONOUS COUNTERS LB no.. SYNCHONOUS COUNTES. Introduction Counters are sequential logic circuits that counts the pulses applied at their clock input. They usually have 4 bits, delivering at the outputs the corresponding

More information

RUTGERS UNIVERSITY Department of Electrical and Computer Engineering 14:332:233 DIGITAL LOGIC DESIGN LABORATORY

RUTGERS UNIVERSITY Department of Electrical and Computer Engineering 14:332:233 DIGITAL LOGIC DESIGN LABORATORY RUTGERS UNIVERSITY Department of Electrical and Computer Engineering 14:332:233 DIGITAL LOGIC DESIGN LABORATORY Fall 2012 Contents 1 LABORATORY No 1 3 11 Equipment 3 12 Protoboard 4 13 The Input-Control/Output-Display

More information

Switching Algebra and Logic Gates

Switching Algebra and Logic Gates Chapter 2 Switching Algebra and Logic Gates The word algebra in the title of this chapter should alert you that more mathematics is coming. No doubt, some of you are itching to get on with digital design

More information

Course Requirements & Evaluation Methods

Course Requirements & Evaluation Methods Course Title: Logic Circuits Course Prefix: ELEG Course No.: 3063 Sections: 01 & 02 Department of Electrical and Computer Engineering College of Engineering Instructor Name: Justin Foreman Office Location:

More information

Digital Logic Design:

Digital Logic Design: Digital Logic Design: A Rigorous Approach Guy Even and Moti Medina School of Electrical Engineering, Tel-Aviv University Revised 28 Feb. 2016 Guy Even and Moti Medina 2010, 2011, 2012, 2013, 2014 Thisistheauthorsversionofthebook.

More information

Circuits and Boolean Expressions

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.

More information

EXPERIMENT 4. Parallel Adders, Subtractors, and Complementors

EXPERIMENT 4. Parallel Adders, Subtractors, and Complementors EXPERIMENT 4. Parallel Adders, Subtractors, and Complementors I. Introduction I.a. Objectives In this experiment, parallel adders, subtractors and complementors will be designed and investigated. In the

More information

Levent EREN levent.eren@ieu.edu.tr A-306 Office Phone:488-9882 INTRODUCTION TO DIGITAL LOGIC

Levent EREN levent.eren@ieu.edu.tr A-306 Office Phone:488-9882 INTRODUCTION TO DIGITAL LOGIC Levent EREN levent.eren@ieu.edu.tr A-306 Office Phone:488-9882 1 Number Systems Representation Positive radix, positional number systems A number with radix r is represented by a string of digits: A n

More information

Logic gates. Chapter. 9.1 Logic gates. MIL symbols. Learning Summary. In this chapter you will learn about: Logic gates

Logic gates. Chapter. 9.1 Logic gates. MIL symbols. Learning Summary. In this chapter you will learn about: Logic gates Chapter 9 Logic gates Learning Summary In this chapter you will learn about: Logic gates Truth tables Logic circuits/networks In this chapter we will look at how logic gates are used and how truth tables

More information

FORDHAM UNIVERSITY CISC 3593. Dept. of Computer and Info. Science Spring, 2011. The Binary Adder

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

More information

Boolean Algebra. Boolean Algebra. Boolean Algebra. Boolean Algebra

Boolean Algebra. Boolean Algebra. Boolean Algebra. Boolean Algebra 2 Ver..4 George Boole was an English mathematician of XIX century can operate on logic (or Boolean) variables that can assume just 2 values: /, true/false, on/off, closed/open Usually value is associated

More information

6. BOOLEAN LOGIC DESIGN

6. BOOLEAN LOGIC DESIGN 6. OOLEN LOGI DESIGN 89 Topics: oolean algebra onverting between oolean algebra and logic gates and ladder logic Logic examples Objectives: e able to simplify designs with oolean algebra 6. INTRODUTION

More information

Lecture #21 April 2, 2004 Relays and Adder/Subtractors

Lecture #21 April 2, 2004 Relays and Adder/Subtractors Lecture #21 April 2, 2004 Relays and Adder/Subtractors In this lecture we look at a real technology for implementing gate circuits, as well as a more-or-less complete design for a general purpose adder/subtractor

More information

Read-only memory Implementing logic with ROM Programmable logic devices Implementing logic with PLDs Static hazards

Read-only memory Implementing logic with ROM Programmable logic devices Implementing logic with PLDs Static hazards Points ddressed in this Lecture Lecture 8: ROM Programmable Logic Devices Professor Peter Cheung Department of EEE, Imperial College London Read-only memory Implementing logic with ROM Programmable logic

More information

Discrete Structures. Rajmohan Rajaraman Eric Ropiak Chris Burrows Ravi Sundaram

Discrete Structures. Rajmohan Rajaraman Eric Ropiak Chris Burrows Ravi Sundaram Discrete Structures Harriet Fell Javed A. Aslam Rajmohan Rajaraman Eric Ropiak Chris Burrows Ravi Sundaram Discrete Structures Version 2.1 Harriet Fell Javed A. Aslam Rajmohan Rajaraman Eric Ropiak Chris

More information

Adder.PPT(10/1/2009) 5.1. Lecture 13. Adder Circuits

Adder.PPT(10/1/2009) 5.1. Lecture 13. Adder Circuits 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

More information

Solution for Homework 2

Solution for Homework 2 Solution for Homework 2 Problem 1 a. What is the minimum number of bits that are required to uniquely represent the characters of English alphabet? (Consider upper case characters alone) The number of

More information

THREE YEAR DEGREE (HONS.) COURSE BACHELOR OF COMPUTER APPLICATION (BCA) First Year Paper I Computer Fundamentals

THREE YEAR DEGREE (HONS.) COURSE BACHELOR OF COMPUTER APPLICATION (BCA) First Year Paper I Computer Fundamentals THREE YEAR DEGREE (HONS.) COURSE BACHELOR OF COMPUTER APPLICATION (BCA) First Year Paper I Computer Fundamentals Full Marks 100 (Theory 75, Practical 25) Introduction to Computers :- What is Computer?

More information

Lab 1: Study of Gates & Flip-flops

Lab 1: Study of Gates & Flip-flops 1.1 Aim Lab 1: Study of Gates & Flip-flops To familiarize with circuit implementations using ICs and test the behavior of different logic gates and Flip-flops. 1.2 Hardware Requirement a. Equipments -

More information

Operating Manual Ver.1.1

Operating Manual Ver.1.1 4 Bit Binary Ripple Counter (Up-Down Counter) Operating Manual Ver.1.1 An ISO 9001 : 2000 company 94-101, Electronic Complex Pardesipura, Indore- 452010, India Tel : 91-731- 2570301/02, 4211100 Fax: 91-731-

More information

Chapter 1. Computation theory

Chapter 1. Computation theory Chapter 1. Computation theory In this chapter we will describe computation logic for the machines. This topic is a wide interdisciplinary field, so that the students can work in an interdisciplinary context.

More information

ELEC 2210 - EXPERIMENT 1 Basic Digital Logic Circuits

ELEC 2210 - EXPERIMENT 1 Basic Digital Logic Circuits Objectives ELEC - EXPERIMENT Basic Digital Logic Circuits The experiments in this laboratory exercise will provide an introduction to digital electronic circuits. You will learn how to use the IDL-00 Bit

More information

Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan

Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan 3 Binary Operations We are used to addition and multiplication of real numbers. These operations combine two real numbers

More information

Properties of Real Numbers

Properties of Real Numbers 16 Chapter P Prerequisites P.2 Properties of Real Numbers What you should learn: Identify and use the basic properties of real numbers Develop and use additional properties of real numbers Why you should

More information

Upon completion of unit 1.1, students will be able to

Upon completion of unit 1.1, students will be able to Upon completion of unit 1.1, students will be able to 1. Demonstrate safety of the individual, class, and overall environment of the classroom/laboratory, and understand that electricity, even at the nominal

More information

(1) /30 (2) /30 (3) /40 TOTAL /100

(1) /30 (2) /30 (3) /40 TOTAL /100 Your Name: SI Number: UNIVERSITY OF CALIFORNIA AT BERKELEY BERKELEY AVIS IRVINE LOS ANGELES RIVERSIE SAN IEGO SAN FRANCISCO epartment of Electrical Engineering and Computer Sciences SANTA BARBARA SANTA

More information