CS/COE1541: Introduction to Computer Architecture. Logic Design Review. Sangyeun Cho. Computer Science Department University of Pittsburgh

Size: px
Start display at page:

Download "CS/COE1541: Introduction to Computer Architecture. Logic Design Review. Sangyeun Cho. Computer Science Department University of Pittsburgh"

Transcription

1 CS/COE54: Introduction to Computer Architecture Logic Design Review Sangyeun Cho Computer Science Department Logic design? Digital hardware is implemented by way of logic design Digital circuits process and produce two discrete values: 0 and Example: -bit full adder (FA)

2 Layered design approach Logic design is done using logic gates Often we design desired function using high-level languages and somewhat higher level than logic gates Two approaches in design Top down Bottom up Microarchitecture Function blocks Logic gates Transistors Transistor as a switch X X X G G= G=0 N -type TR X X X G G=0 G= P -type TR

3 An inverter P -type TR A N -type TR 0 When A = P -type TR OFF A= =0 N -type TR ON 0

4 When A = 0 P -type TR ON A=0 = N -type TR OFF 0 Abstraction P -type TR A A N -type TR 0

5 Logic gates 2-input AND A B =A & B 2-input OR A B =A B 2-input NAND A B =~(A & B) 2-input NOR A B =~(A B) Describing a function Output A = F(Input 0, Input,, Input N ) Output B = F (Input 0, Input,, Input N ) Output C = F (Input 0, Input,, Input N ) Methods Truth table Sum of products Product of sums

6 Truth table Input Output A B C in S C out Sum of products Input Output A B C in S C out S = A B C in + A BC in + AB C in + ABC in C out = A BC in + AB C in + ABC in + ABC in

7 Combinational vs. sequential logic Combinational logic = function A function whose outputs are dependent only on the current inputs As soon as inputs are known, outputs can be determined Sequential logic = combinational logic + memory Some memory elements (i.e., state ) Outputs are dependent on the current state and the current inputs Next state is dependent on the current state and the current inputs Combinational logic inputs outputs

8 Sequential logic inputs outputs current state next state clock Combinational logic Any combinational logic can be implemented using sum of products or product of sums Input-output relationship can be defined in the truth table format From the truth table, each output function can be derived Boolean expressions can be further manipulated (e.g., to reduce cost) using various Boolean algebraic rules

9 Boolean algebra Boole, George (85~864): mathematician and philosopher; inventor of Boolean Algebra, the basis of all computer arithmetic Binary values: {0,} Two binary operations: AND ( / ), OR (+) One unary operation: NOT (~) Boolean algebra Binary operations: AND ( / ), OR (+) Idempotent a a = a+a= a Commutative a b = b a a+b = b+a Associative a (b c) = (a b) c a+(b+c) = (a+b)+c Distributive a (b+c) = a b + a c a+(b c) = (a+b) (a+c)

10 Boolean algebra De Morgan s laws ~(a+b) = ~a ~b ~(a b) = ~a+~b More a+(a b) = a a (a+b) = a ~~a = a a+~a = a (~a) = 0 Expressive power With AND/OR/NOT, we can express any function in Boolean algebra Sum (+) of products ( ) What if we have NAND/NOR/NOT? What if we have NAND only? What if we have NOR only?

11 Multiplexor (aka MUX) A 0 B S = (S)? B:A; A 32-bit MUX

12 Simplifying expressions Input Output A B C in S C out C out = A BC in + AB C in + ABC in + ABC in C out = BC in + AC in + AB Karnaugh map BC in A AC in BC in 0 0 AB C out = BC in +AB+AC in

13 Building a -bit ALU ALU = arithmetic logic unit = arithmetic unit + logic unit Building a 32-bit ALU

14 Implementing sub Implementing NAND and NOR

15 Implementing SLT (set-less-than) -bit ALU for bits 0~30 -bit ALU for bit 3 Implementing SLT (set-less-than)

16 Supporting BEQ and BNE zero detector Abstracting ALU Note that ALU is a combinational logic

17 RS latch Beware of the feedback! RS latch When R=0, S=

18 RS latch When R=, S=0 RS latch When R=0, S=0, and Q was 0

19 RS latch When R=0, S=0, and Q was RS latch What happens if R=S=

20 D latch Note that we have an RS latch in the back-end of this design D latch R S Note that R, S inputs always get opposite values when C= When C=0, S=R=0 RS latch remembers the previous value

21 D latch latched mode R C D Q(t) 0 0 Q(t-) 0 Q(t-) S 0 0 transparent mode D latch D C D Latch Q Q

22 D flip-flop (D-FF) Two cascaded D latches; C input of the second is inverted This is a negative edge triggered D-FF D flip-flop D Q D-FF C Q

23 Finite state machine (FSM) Traffic light control example Two states NSlite: green light on North-South road EWlite: green light on East-West road Current state goes for 30 seconds, then Switch to the other state if there is a car waiting Current state goes for another 30 seconds if not We use /30 Hz clock

24 Traffic light control example Traffic light control example

25 Traffic light control example Let s assign 0 to NSlite and to EWlite initially NextState = CurrentState EWcar + CurrentState NScar NSlite = CurrentState EWlite = CurrentState To wrap up In digital logic, transistors are used as simple switches Logic gates are an abstraction of a transistor network A combinational logic block has inputs and outputs whose values are immediately determined as inputs become known A sequential logic block is composed of a combinational logic block and memory elements

26 To wrap up Boolean algebra provides a theoretical foundation for digital logic Starting from two transistors (N-type and P-type), we ve built logic gates and more complex structures (bottom up) An ALU for the MIPS architecture has been built! To wrap up Flip-flops (FFs) were used as a memory element A finite state machine (FSM) can be implemented using FFs and some combinational logic

Logic design? Transistor as a switch. Layered design approach. CS/COE1541: Introduction to Computer Architecture. Logic Design Review.

Logic design? Transistor as a switch. Layered design approach. CS/COE1541: Introduction to Computer Architecture. Logic Design Review. Logic design? CS/COE54: Introduction to Computer rchitecture Digital hardware is implemented by way of logic design Digital circuits process and produce two discrete values: and Example: -bit full adder

More information

CS/COE0447: Computer Organization

CS/COE0447: Computer Organization CS/COE0447: Computer Organization and Assembly Language Logic Design Review Sangyeun Cho Dept. of Computer Science Logic design? Digital hardware is implemented by way of logic design Digital circuits

More information

CS/COE0447: Computer Organization

CS/COE0447: Computer Organization Logic design? CS/COE0447: Computer Organization and Assembly Language Logic Design Review Digital hardware is implemented by way of logic design Digital circuits process and produce two discrete values:

More information

CS/COE0447: Computer Organization and Assembly Language

CS/COE0447: Computer Organization and Assembly Language CS/COE0447: Computer Organization and Assembly Language Logic Design Introduction (Brief?) Appendix B: The Basics of Logic Design Dept. of Computer Science Logic design? Digital hardware is implemented

More information

Digital Logic: Boolean Algebra and Gates. Textbook Chapter 3

Digital Logic: Boolean Algebra and Gates. Textbook Chapter 3 Digital Logic: Boolean Algebra and Gates Textbook Chapter 3 Basic Logic Gates XOR CMPE12 Summer 2009 02-2 Truth Table The most basic representation of a logic function Lists the output for all possible

More information

Lecture 7: Logic design. Combinational logic circuits

Lecture 7: Logic design. Combinational logic circuits /24/28 Lecture 7: Logic design Binary digital circuits: Two voltage levels: and (ground and supply voltage) Built from transistors used as on/off switches Analog circuits not very suitable for generic

More information

Boolean Algebra and Digital Logic 2009, University of Colombo School of Computing

Boolean Algebra and Digital Logic 2009, University of Colombo School of Computing IT 204 Section 3.0 Boolean Algebra and Digital Logic Boolean Algebra 2 Logic Equations to Truth Tables X = A. B + A. B + AB A B X 0 0 0 0 3 Sum of Products The OR operation performed on the products of

More information

Latches. October 13, 2003 Latches 1

Latches. October 13, 2003 Latches 1 Latches The second part of CS231 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 how primitive memory

More information

Lecture 13: Sequential Circuits, FSM

Lecture 13: Sequential Circuits, FSM Lecture 13: Sequential Circuits, FSM Today s topics: Sequential circuits Finite state machines 1 Clocks A microprocessor is composed of many different circuits that are operating simultaneously if each

More information

Fundamentals of Digital Design

Fundamentals of Digital Design Fundamentals of Digital Design Digital Radiation Measurement and Spectroscopy NE/RHP 537 1 Binary Number System The binary numeral system, or base-2 number system, is a numeral system that represents numeric

More information

Lecture 13: Sequential Circuits, FSM

Lecture 13: Sequential Circuits, FSM Lecture 13: Sequential Circuits, FSM Today s topics: Sequential circuits Finite state machines Reminder: midterm on Tue 2/28 will cover Chapters 1-3, App A, B if you understand all slides, assignments,

More information

Chapter 4. Sequential Logic Circuits

Chapter 4. Sequential Logic Circuits Chapter 4 Sequential Logic Circuits 1 2 Chapter 4 4 1 The defining characteristic of a combinational circuit is that its output depends only on the current inputs applied to the circuit. The output of

More information

Sequential Logic Circuits

Sequential Logic Circuits Chapter 4 Sequential Logic Circuits 4 1 The defining characteristic of a combinational circuit is that its output depends only on the current inputs applied to the circuit. The output of a sequential circuit,

More information

CS61C : Machine Structures

CS61C : Machine Structures inst.eecs.berkeley.edu/~cs61c/su05 CS61C : Machine Structures Lecture #15: Combinational Logic Blocks 2005-07-14 CS 61C L15 Blocks (1) Andy Carle Outline CL Blocks Latches & Flip Flops A Closer Look CS

More information

Digital Logic Appendix A

Digital Logic Appendix A Digital Logic Appendix A Boolean Algebra Gates Combinatorial Circuits Sequential Circuits 1 Boolean Algebra George Boole ideas 1854 Claude Shannon, apply to circuit design, 1938 Describe digital circuitry

More information

Sequential Logic. Rab Nawaz Khan Jadoon DCS. Lecturer COMSATS Lahore Pakistan. Department of Computer Science

Sequential Logic. Rab Nawaz Khan Jadoon DCS. Lecturer COMSATS Lahore Pakistan. Department of Computer Science Sequential Logic Rab Nawaz Khan Jadoon DCS COMSATS Institute of Information Technology Lecturer COMSATS Lahore Pakistan Digital Logic and Computer Design Sequential Logic Combinational circuits with memory

More information

CS61C : Machine Structures

CS61C : Machine Structures CS 61C L15 Blocks (1) inst.eecs.berkeley.edu/~cs61c/su05 CS61C : Machine Structures Lecture #15: Combinational Logic Blocks Outline CL Blocks Latches & Flip Flops A Closer Look 2005-07-14 Andy Carle CS

More information

Boolean Algebra. Digital Logic Appendix A. Postulates, Identities in Boolean Algebra How can I manipulate expressions?

Boolean Algebra. Digital Logic Appendix A. Postulates, Identities in Boolean Algebra How can I manipulate expressions? Digital Logic Appendix A Gates Combinatorial Circuits Sequential Circuits Other operations NAND A NAND B = NOT ( A ANDB) = AB NOR A NOR B = NOT ( A ORB) = A + B Truth tables What is the result of the operation

More information

EE40 Lec 15. Logic Synthesis and Sequential Logic Circuits

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

More information

XI STANDARD [ COMPUTER SCIENCE ] 5 MARKS STUDY MATERIAL.

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

More information

CSC9R6 Computer Design. Practical Digital Logic

CSC9R6 Computer Design. Practical Digital Logic CSC9R6 Computer Design Practical Digital Logic 1 References (for this part of CSC9R6) Hamacher et al: Computer Organization App A. In library Floyd: Digital Fundamentals Ch 1, 3-6, 8-10 web page: www.prenhall.com/floyd/

More information

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

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

More information

Philadelphia University Student Name: Student Number:

Philadelphia University Student Name: Student Number: Philadelphia University Student Name: Student Number: Faculty of Engineering Serial Number: Final Exam, First Semester: 2017/2018 Dept. of Computer Engineering Course Title: Logic Circuits Date: 29/01/2018

More information

ELCT201: DIGITAL LOGIC DESIGN

ELCT201: DIGITAL LOGIC DESIGN ELCT201: DIGITAL LOGIC DESIGN Dr. Eng. Haitham Omran, haitham.omran@guc.edu.eg Dr. Eng. Wassim Alexan, wassim.joseph@guc.edu.eg Lecture 6 Following the slides of Dr. Ahmed H. Madian محرم 1439 ه Winter

More information

Number System. Decimal to binary Binary to Decimal Binary to octal Binary to hexadecimal Hexadecimal to binary Octal to binary

Number System. Decimal to binary Binary to Decimal Binary to octal Binary to hexadecimal Hexadecimal to binary Octal to binary Number System Decimal to binary Binary to Decimal Binary to octal Binary to hexadecimal Hexadecimal to binary Octal to binary BOOLEAN ALGEBRA BOOLEAN LOGIC OPERATIONS Logical AND Logical OR Logical COMPLEMENTATION

More information

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

Boolean algebra. Examples of these individual laws of Boolean, rules and theorems for Boolean algebra are given in the following table. The Laws of Boolean Boolean algebra As well as the logic symbols 0 and 1 being used to represent a digital input or output, we can also use them as constants for a permanently Open or Closed circuit or

More information

Principles of Computer Architecture. Appendix B: Reduction of Digital Logic. Chapter Contents

Principles of Computer Architecture. Appendix B: Reduction of Digital Logic. Chapter Contents B-1 Principles of Computer Architecture Miles Murdocca and Vincent Heuring Appendix B: Reduction of Digital Logic B-2 Chapter Contents B.1 Reduction of Combinational Logic and Sequential Logic B.2 Reduction

More information

WORKBOOK. Try Yourself Questions. Electrical Engineering Digital Electronics. Detailed Explanations of

WORKBOOK. Try Yourself Questions. Electrical Engineering Digital Electronics. Detailed Explanations of 27 WORKBOOK Detailed Eplanations of Try Yourself Questions Electrical Engineering Digital Electronics Number Systems and Codes T : Solution Converting into decimal number system 2 + 3 + 5 + 8 2 + 4 8 +

More information

Appendix B. Review of Digital Logic. Baback Izadi Division of Engineering Programs

Appendix B. Review of Digital Logic. Baback Izadi Division of Engineering Programs Appendix B Review of Digital Logic Baback Izadi Division of Engineering Programs bai@engr.newpaltz.edu Elect. & Comp. Eng. 2 DeMorgan Symbols NAND (A.B) = A +B NOR (A+B) = A.B AND A.B = A.B = (A +B ) OR

More information

Switches: basic element of physical implementations

Switches: basic element of physical implementations Combinational logic Switches Basic logic and truth tables Logic functions Boolean algebra Proofs by re-writing and by perfect induction Winter 200 CSE370 - II - Boolean Algebra Switches: basic element

More information

Review for Final Exam

Review for Final Exam CSE140: Components and Design Techniques for Digital Systems Review for Final Exam Mohsen Imani CAPE Please submit your evaluations!!!! RTL design Use the RTL design process to design a system that has

More information

EEE130 Digital Electronics I Lecture #4

EEE130 Digital Electronics I Lecture #4 EEE130 Digital Electronics I Lecture #4 - Boolean Algebra and Logic Simplification - By Dr. Shahrel A. Suandi Topics to be discussed 4-1 Boolean Operations and Expressions 4-2 Laws and Rules of Boolean

More information

Hakim Weatherspoon CS 3410 Computer Science Cornell University

Hakim Weatherspoon CS 3410 Computer Science Cornell University Hakim Weatherspoon CS 3410 Computer Science Cornell University The slides are the product of many rounds of teaching CS 3410 by Professors Weatherspoon, Bala, Bracy, and Sirer. memory inst 32 register

More information

Systems I: Computer Organization and Architecture

Systems I: Computer Organization and Architecture Systems I: Computer Organization and Architecture Lecture 6 - Combinational Logic Introduction A combinational circuit consists of input variables, logic gates, and output variables. The logic gates accept

More information

Synchronous Sequential Logic

Synchronous Sequential Logic 1 IT 201 DIGITAL SYSTEMS DESIGN MODULE4 NOTES Synchronous Sequential Logic Sequential Circuits - A sequential circuit consists of a combinational circuit and a feedback through the storage elements in

More information

Lecture 3 Review on Digital Logic (Part 2)

Lecture 3 Review on Digital Logic (Part 2) Lecture 3 Review on Digital Logic (Part 2) Xuan Silvia Zhang Washington University in St. Louis http://classes.engineering.wustl.edu/ese461/ ircuit Optimization Simplest implementation ost criterion literal

More information

Sample Test Paper - I

Sample Test Paper - I Scheme G Sample Test Paper - I Course Name : Computer Engineering Group Marks : 25 Hours: 1 Hrs. Q.1) Attempt any THREE: 09 Marks a) Define i) Propagation delay ii) Fan-in iii) Fan-out b) Convert the following:

More information

Chapter 3 Digital Logic Structures

Chapter 3 Digital Logic Structures Chapter 3 Digital Logic Structures Original slides from Gregory Byrd, North Carolina State University Modified by C. Wilcox, M. Strout, Y. Malaiya Colorado State University Computing Layers Problems Algorithms

More information

Chapter 7 Logic Circuits

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

More information

CSE140: Components and Design Techniques for Digital Systems. Midterm Information. Instructor: Mohsen Imani. Sources: TSR, Katz, Boriello & Vahid

CSE140: Components and Design Techniques for Digital Systems. Midterm Information. Instructor: Mohsen Imani. Sources: TSR, Katz, Boriello & Vahid CSE140: Components and Design Techniques for Digital Systems Midterm Information Instructor: Mohsen Imani Midterm Topics In general: everything that was covered in homework 1 and 2 and related lectures,

More information

Review for B33DV2-Digital Design. Digital Design

Review for B33DV2-Digital Design. Digital Design Review for B33DV2 The Elements of Modern Behaviours Design Representations Blocks Waveforms Gates Truth Tables Boolean Algebra Switches Rapid Prototyping Technologies Circuit Technologies TTL MOS Simulation

More information

Boolean Algebra. Digital Logic Appendix A. Boolean Algebra Other operations. Boolean Algebra. Postulates, Identities in Boolean Algebra

Boolean Algebra. Digital Logic Appendix A. Boolean Algebra Other operations. Boolean Algebra. Postulates, Identities in Boolean Algebra Digital Logic Appendix A Gates Combinatorial Circuits Sequential Circuits George Boole ideas 1854 Claude Shannon, apply to circuit design, 1938 (piirisuunnittelu) Describe digital circuitry function programming

More information

UNIVERSITY OF WISCONSIN MADISON

UNIVERSITY OF WISCONSIN MADISON CS/ECE 252: INTRODUCTION TO COMPUTER ENGINEERING UNIVERSITY OF WISCONSIN MADISON Prof. Gurindar Sohi TAs: Minsub Shin, Lisa Ossian, Sujith Surendran Midterm Examination 2 In Class (50 minutes) Friday,

More information

ECE/CS 250 Computer Architecture

ECE/CS 250 Computer Architecture ECE/CS 250 Computer Architecture Basics of Logic Design: Boolean Algebra, Logic Gates (Combinational Logic) Tyler Bletsch Duke University Slides are derived from work by Daniel J. Sorin (Duke), Alvy Lebeck

More information

ECE 250 / CPS 250 Computer Architecture. Basics of Logic Design Boolean Algebra, Logic Gates

ECE 250 / CPS 250 Computer Architecture. Basics of Logic Design Boolean Algebra, Logic Gates ECE 250 / CPS 250 Computer Architecture Basics of Logic Design Boolean Algebra, Logic Gates Benjamin Lee Slides based on those from Andrew Hilton (Duke), Alvy Lebeck (Duke) Benjamin Lee (Duke), and Amir

More information

Sequential Circuit Analysis

Sequential Circuit Analysis Sequential Circuit Analysis Last time we started talking about latches and flip-flops, which are basic one-bit memory units. Today we ll talk about sequential circuit analysis and design. First, we ll

More information

DIGITAL LOGIC CIRCUITS

DIGITAL LOGIC CIRCUITS DIGITAL LOGIC CIRCUITS Digital logic circuits BINARY NUMBER SYSTEM electronic circuits that handle information encoded in binary form (deal with signals that have only two values, and ) Digital. computers,

More information

Memory Elements I. CS31 Pascal Van Hentenryck. CS031 Lecture 6 Page 1

Memory Elements I. CS31 Pascal Van Hentenryck. CS031 Lecture 6 Page 1 Memory Elements I CS31 Pascal Van Hentenryck CS031 Lecture 6 Page 1 Memory Elements (I) Combinational devices are good for computing Boolean functions pocket calculator Computers also need to remember

More information

Lecture 22 Chapters 3 Logic Circuits Part 1

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

More information

UNIT 8A Computer Circuitry: Layers of Abstraction. Boolean Logic & Truth Tables

UNIT 8A Computer Circuitry: Layers of Abstraction. Boolean Logic & Truth Tables UNIT 8 Computer Circuitry: Layers of bstraction 1 oolean Logic & Truth Tables Computer circuitry works based on oolean logic: operations on true (1) and false (0) values. ( ND ) (Ruby: && ) 0 0 0 0 0 1

More information

2. Associative Law: A binary operator * on a set S is said to be associated whenever (A*B)*C = A*(B*C) for all A,B,C S.

2. Associative Law: A binary operator * on a set S is said to be associated whenever (A*B)*C = A*(B*C) for all A,B,C S. BOOLEAN ALGEBRA 2.1 Introduction Binary logic deals with variables that have two discrete values: 1 for TRUE and 0 for FALSE. A simple switching circuit containing active elements such as a diode and transistor

More information

Chapter 14 Sequential logic, Latches and Flip-Flops

Chapter 14 Sequential logic, Latches and Flip-Flops Chapter 14 Sequential logic, Latches and Flip-Flops Flops Lesson 4 JK Flip Flop Ch14L4-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006 2 JK Flip-Flop ve edge triggered Output Q and

More information

UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING BENG (HONS) ELECTRICAL & ELECTRONICS ENGINEERING EXAMINATION SEMESTER /2017

UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING BENG (HONS) ELECTRICAL & ELECTRONICS ENGINEERING EXAMINATION SEMESTER /2017 UNIVERSITY OF BOLTON TW35 SCHOOL OF ENGINEERING BENG (HONS) ELECTRICAL & ELECTRONICS ENGINEERING EXAMINATION SEMESTER 2-2016/2017 INTERMEDIATE DIGITAL ELECTRONICS AND COMMUNICATIONS MODULE NO: EEE5002

More information

Vidyalankar S.E. Sem. III [CMPN] Digital Logic Design and Analysis Prelim Question Paper Solution

Vidyalankar S.E. Sem. III [CMPN] Digital Logic Design and Analysis Prelim Question Paper Solution . (a) (i) ( B C 5) H (A 2 B D) H S.E. Sem. III [CMPN] Digital Logic Design and Analysis Prelim Question Paper Solution ( B C 5) H (A 2 B D) H = (FFFF 698) H (ii) (2.3) 4 + (22.3) 4 2 2. 3 2. 3 2 3. 2 (2.3)

More information

ENGG 1203 Tutorial_9 - Review. Boolean Algebra. Simplifying Logic Circuits. Combinational Logic. 1. Combinational & Sequential Logic

ENGG 1203 Tutorial_9 - Review. Boolean Algebra. Simplifying Logic Circuits. Combinational Logic. 1. Combinational & Sequential Logic ENGG 1203 Tutorial_9 - Review Boolean Algebra 1. Combinational & Sequential Logic 2. Computer Systems 3. Electronic Circuits 4. Signals, Systems, and Control Remark : Multiple Choice Questions : ** Check

More information

CS61c: Representations of Combinational Logic Circuits

CS61c: Representations of Combinational Logic Circuits CS61c: Representations of Combinational Logic Circuits J. Wawrzynek March 5, 2003 1 Introduction Recall that synchronous systems are composed of two basic types of circuits, combination logic circuits,

More information

Unit II Chapter 4:- Digital Logic Contents 4.1 Introduction... 4

Unit II Chapter 4:- Digital Logic Contents 4.1 Introduction... 4 Unit II Chapter 4:- Digital Logic Contents 4.1 Introduction... 4 4.1.1 Signal... 4 4.1.2 Comparison of Analog and Digital Signal... 7 4.2 Number Systems... 7 4.2.1 Decimal Number System... 7 4.2.2 Binary

More information

S.Y. Diploma : Sem. III [DE/ED/EI/EJ/EN/ET/EV/EX/IC/IE/IS/IU/MU] Principles of Digital Techniques

S.Y. Diploma : Sem. III [DE/ED/EI/EJ/EN/ET/EV/EX/IC/IE/IS/IU/MU] Principles of Digital Techniques S.Y. Diploma : Sem. III [DE/ED/EI/EJ/EN/ET/EV/EX/IC/IE/IS/IU/MU] Principles of Digital Techniques Time: 3 Hrs.] Prelim Question Paper Solution [Marks : 100 Q.1(a) Attempt any SIX of the following : [12]

More information

University 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 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: J. Rose and

More information

ECEN 248: INTRODUCTION TO DIGITAL SYSTEMS DESIGN. Week 7 Dr. Srinivas Shakkottai Dept. of Electrical and Computer Engineering

ECEN 248: INTRODUCTION TO DIGITAL SYSTEMS DESIGN. Week 7 Dr. Srinivas Shakkottai Dept. of Electrical and Computer Engineering ECEN 248: INTRODUCTION TO DIGITAL SYSTEMS DESIGN Week 7 Dr. Srinivas Shakkottai Dept. of Electrical and Computer Engineering SEQUENTIAL CIRCUITS: LATCHES Overview Circuits require memory to store intermediate

More information

Written reexam with solutions for IE1204/5 Digital Design Monday 14/

Written reexam with solutions for IE1204/5 Digital Design Monday 14/ Written reexam with solutions for IE204/5 Digital Design Monday 4/3 206 4.-8. General Information Examiner: Ingo Sander. Teacher: William Sandqvist phone 08-7904487 Exam text does not have to be returned

More information

ECE/CS 250: Computer Architecture. Basics of Logic Design: Boolean Algebra, Logic Gates. Benjamin Lee

ECE/CS 250: Computer Architecture. Basics of Logic Design: Boolean Algebra, Logic Gates. Benjamin Lee ECE/CS 250: Computer Architecture Basics of Logic Design: Boolean Algebra, Logic Gates Benjamin Lee Slides based on those from Alvin Lebeck, Daniel Sorin, Andrew Hilton, Amir Roth, Gershon Kedem Admin

More information

Boolean Algebra & Logic Gates. By : Ali Mustafa

Boolean Algebra & Logic Gates. By : Ali Mustafa Boolean Algebra & Logic Gates By : Ali Mustafa Digital Logic Gates There are three fundamental logical operations, from which all other functions, no matter how complex, can be derived. These Basic functions

More information

Time Allowed 3:00 hrs. April, pages

Time Allowed 3:00 hrs. April, pages IGITAL ESIGN COEN 32 Prof. r. A. J. Al-Khalili Time Allowed 3: hrs. April, 998 2 pages Answer All uestions No materials are allowed uestion a) esign a half subtractor b) esign a full subtractor c) Using

More information

Combinational Logic. Review of Combinational Logic 1

Combinational Logic. Review of Combinational Logic 1 Combinational Logic! Switches -> Boolean algebra! Representation of Boolean functions! Logic circuit elements - logic gates! Regular logic structures! Timing behavior of combinational logic! HDLs and combinational

More information

Boolean Algebra, Gates and Circuits

Boolean Algebra, Gates and Circuits Boolean Algebra, Gates and Circuits Kasper Brink November 21, 2017 (Images taken from Tanenbaum, Structured Computer Organization, Fifth Edition, (c) 2006 Pearson Education, Inc.) Outline Last week: Von

More information

CSC 322: Computer Organization Lab

CSC 322: Computer Organization Lab CSC 322: Computer Organization Lab Lecture 3: Logic Design Dr. Haidar M. Harmanani CSC 322: Computer Organization Lab Part I: Combinational Logic Dr. Haidar M. Harmanani Logical Design of Digital Systems

More information

CS470: Computer Architecture. AMD Quad Core

CS470: 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, flip-flops Functional bocks: Combinational, Sequential Instruction

More information

UNIVERSITI TENAGA NASIONAL. College of Information Technology

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

More information

Chapter 7. Sequential Circuits Registers, Counters, RAM

Chapter 7. Sequential Circuits Registers, Counters, RAM Chapter 7. Sequential Circuits Registers, Counters, RAM Register - a group of binary storage elements suitable for holding binary info A group of FFs constitutes a register Commonly used as temporary storage

More information

Combinatorial Logic Design Multiplexers and ALUs CS 64: Computer Organization and Design Logic Lecture #13

Combinatorial Logic Design Multiplexers and ALUs CS 64: Computer Organization and Design Logic Lecture #13 Combinatorial Logic Design Multiplexers and ALUs CS 64: Computer Organization and Design Logic Lecture #13 Ziad Matni Dept. of Computer Science, UCSB Administrative Re: Midterm Exam #2 Graded! 5/22/18

More information

ELEC Digital Logic Circuits Fall 2014 Sequential Circuits (Chapter 6) Finite State Machines (Ch. 7-10)

ELEC Digital Logic Circuits Fall 2014 Sequential Circuits (Chapter 6) Finite State Machines (Ch. 7-10) ELEC 2200-002 Digital Logic Circuits Fall 2014 Sequential Circuits (Chapter 6) Finite State Machines (Ch. 7-10) Vishwani D. Agrawal James J. Danaher Professor Department of Electrical and Computer Engineering

More information

( c) Give logic symbol, Truth table and circuit diagram for a clocked SR flip-flop. A combinational circuit is defined by the function

( c) Give logic symbol, Truth table and circuit diagram for a clocked SR flip-flop. A combinational circuit is defined by the function Question Paper Digital Electronics (EE-204-F) MDU Examination May 2015 1. (a) represent (32)10 in (i) BCD 8421 code (ii) Excess-3 code (iii) ASCII code (b) Design half adder using only NAND gates. ( c)

More information

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

EECS150 - Digital Design Lecture 4 - Boolean Algebra I (Representations of Combinational Logic Circuits) EECS150 - Digital Design Lecture 4 - Boolean Algebra I (Representations of Combinational Logic Circuits) September 5, 2002 John Wawrzynek Fall 2002 EECS150 Lec4-bool1 Page 1, 9/5 9am Outline Review of

More information

DIGITAL LOGIC CIRCUITS

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

More information

CMPE12 - Notes chapter 1. Digital Logic. (Textbook Chapter 3)

CMPE12 - Notes chapter 1. Digital Logic. (Textbook Chapter 3) CMPE12 - Notes chapter 1 Digital Logic (Textbook Chapter 3) Transistor: Building Block of Computers Microprocessors contain TONS of transistors Intel Montecito (2005): 1.72 billion Intel Pentium 4 (2000):

More information

MAHARASHTRA STATE BOARD OF TECHNICAL EDUCATION (Autonomous) (ISO/IEC Certified)

MAHARASHTRA STATE BOARD OF TECHNICAL EDUCATION (Autonomous) (ISO/IEC Certified) WINTER 17 EXAMINATION Subject Name: Digital Techniques Model Answer Subject Code: 17333 Important Instructions to examiners: 1) The answers should be examined by key words and not as word-to-word as given

More information

on candidate s understanding. 7) For programming language papers, credit may be given to any other program based on equivalent concept.

on candidate s understanding. 7) For programming language papers, credit may be given to any other program based on equivalent concept. WINTER 17 EXAMINATION Subject Name: Digital Techniques Model Answer Subject Code: 17333 Important Instructions to examiners: 1) The answers should be examined by key words and not as word-to-word as given

More information

Digital Logic (2) Boolean Algebra

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

More information

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

Outline. EECS150 - Digital Design Lecture 4 - Boolean Algebra I (Representations of Combinational Logic Circuits) Combinational Logic (CL) Defined EECS150 - Digital Design Lecture 4 - Boolean Algebra I (Representations of Combinational Logic Circuits) January 30, 2003 John Wawrzynek Outline Review of three representations for combinational logic:

More information

CMPE12 - Notes chapter 2. Digital Logic. (Textbook Chapters and 2.1)"

CMPE12 - Notes chapter 2. Digital Logic. (Textbook Chapters and 2.1) CMPE12 - Notes chapter 2 Digital Logic (Textbook Chapters 3.1-3.5 and 2.1)" Truth table" The most basic representation of a logic function." Brute force representation listing the output for all possible

More information

UC Berkeley College of Engineering, EECS Department CS61C: Representations of Combinational Logic Circuits

UC Berkeley College of Engineering, EECS Department CS61C: Representations of Combinational Logic Circuits 2 Wawrzynek, Garcia 2004 c UCB UC Berkeley College of Engineering, EECS Department CS61C: Representations of Combinational Logic Circuits 1 Introduction Original document by J. Wawrzynek (2003-11-15) Revised

More information

vidyarthiplus.com vidyarthiplus.com vidyarthiplus.com ANNA UNIVERSITY- COMBATORE B.E./ B.TECH. DEGREE EXAMINATION - JUNE 2009. ELECTRICAL & ELECTONICS ENGG. - FOURTH SEMESTER DIGITAL LOGIC CIRCUITS PART-A

More information

Lecture A: Logic Design and Gates

Lecture A: Logic Design and Gates Lecture A: Logic Design and Gates Syllabus My office hours 9.15-10.35am T,Th or gchoi@ece.tamu.edu 333G WERC Text: Brown and Vranesic Fundamentals of Digital Logic,» Buy it.. Or borrow it» Other book:

More information

Sequential vs. Combinational

Sequential vs. Combinational Sequential Circuits Sequential vs. Combinational Combinational Logic: Output depends only on current input TV channel selector (-9) inputs system outputs Sequential Logic: Output depends not only on current

More information

Design of Sequential Circuits

Design of Sequential Circuits Design of Sequential Circuits Seven Steps: Construct a state diagram (showing contents of flip flop and inputs with next state) Assign letter variables to each flip flop and each input and output variable

More information

Adders, subtractors comparators, multipliers and other ALU elements

Adders, subtractors comparators, multipliers and other ALU elements CSE4: Components and Design Techniques for Digital Systems Adders, subtractors comparators, multipliers and other ALU elements Instructor: Mohsen Imani UC San Diego Slides from: Prof.Tajana Simunic Rosing

More information

CS 226: Digital Logic Design

CS 226: Digital Logic Design CS 226: Digital Logic Design 0 1 1 I S 0 1 0 S Department of Computer Science and Engineering, Indian Institute of Technology Bombay. 1 of 29 Objectives In this lecture we will introduce: 1. Logic functions

More information

Chapter 2 Combinational Logic Circuits

Chapter 2 Combinational Logic Circuits Logic and Computer Design Fundamentals Chapter 2 Combinational Logic Circuits Part 1 Gate Circuits and Boolean Equations Chapter 2 - Part 1 2 Chapter 2 - Part 1 3 Chapter 2 - Part 1 4 Chapter 2 - Part

More information

CHAPTER1: Digital Logic Circuits Combination Circuits

CHAPTER1: Digital Logic Circuits Combination Circuits CS224: Computer Organization S.KHABET CHAPTER1: Digital Logic Circuits Combination Circuits 1 PRIMITIVE LOGIC GATES Each of our basic operations can be implemented in hardware using a primitive logic gate.

More information

Appendix A: Digital Logic. Principles of Computer Architecture. Principles of Computer Architecture by M. Murdocca and V. Heuring

Appendix A: Digital Logic. Principles of Computer Architecture. Principles of Computer Architecture by M. Murdocca and V. Heuring - Principles of Computer rchitecture Miles Murdocca and Vincent Heuring 999 M. Murdocca and V. Heuring -2 Chapter Contents. Introduction.2 Combinational Logic.3 Truth Tables.4 Logic Gates.5 Properties

More information

Fundamentals of Computer Systems

Fundamentals of Computer Systems Fundamentals of Computer Systems Review for the Final Stephen A. Edwards Columbia University Summer 25 The Final 2 hours 8 problems Closed book Simple calculators are OK, but unnecessary One double-sided

More information

Menu. 7-Segment LED. Misc. 7-Segment LED MSI Components >MUX >Adders Memory Devices >D-FF, RAM, ROM Computer/Microprocessor >GCPU

Menu. 7-Segment LED. Misc. 7-Segment LED MSI Components >MUX >Adders Memory Devices >D-FF, RAM, ROM Computer/Microprocessor >GCPU Menu 7-Segment LED MSI Components >MUX >Adders Memory Devices >D-FF, RAM, ROM Computer/Microprocessor >GCPU Look into my... 1 7-Segment LED a b c h GND c g b d f a e h Show 7-segment LED in LogicWorks,

More information

Combinational Logic. By : Ali Mustafa

Combinational Logic. By : Ali Mustafa Combinational Logic By : Ali Mustafa Contents Adder Subtractor Multiplier Comparator Decoder Encoder Multiplexer How to Analyze any combinational circuit like this? Analysis Procedure To obtain the output

More information

COSC 243. Introduction to Logic And Combinatorial Logic. Lecture 4 - Introduction to Logic and Combinatorial Logic. COSC 243 (Computer Architecture)

COSC 243. Introduction to Logic And Combinatorial Logic. Lecture 4 - Introduction to Logic and Combinatorial Logic. COSC 243 (Computer Architecture) COSC 243 Introduction to Logic And Combinatorial Logic 1 Overview This Lecture Introduction to Digital Logic Gates Boolean algebra Combinatorial Logic Source: Chapter 11 (10 th edition) Source: J.R. Gregg,

More information

Synchronous Sequential Circuit

Synchronous Sequential Circuit Synchronous Sequential Circuit The change of internal state occurs in response to the synchronized clock pulses. Data are read during the clock pulse (e.g. rising-edge triggered) It is supposed to wait

More information

COMBINATIONAL LOGIC FUNCTIONS

COMBINATIONAL LOGIC FUNCTIONS COMBINATIONAL LOGIC FUNCTIONS Digital logic circuits can be classified as either combinational or sequential circuits. A combinational circuit is one where the output at any time depends only on the present

More information

Contents. Chapter 3 Combinational Circuits Page 1 of 36

Contents. Chapter 3 Combinational Circuits Page 1 of 36 Chapter 3 Combinational Circuits Page of 36 Contents Combinational Circuits...2 3. Analysis of Combinational Circuits...3 3.. Using a Truth Table...3 3..2 Using a Boolean Function...6 3.2 Synthesis of

More information

University of Guelph School of Engineering ENG 2410 Digital Design Fall There are 7 questions, answer all questions.

University of Guelph School of Engineering ENG 2410 Digital Design Fall There are 7 questions, answer all questions. Final Examination Instructor: Shawki M. Areibi Co-examiner: Medhat Moussa. Location: UOG Date: Wednesday, December 5th, 2007 Time: 8:30-10:30 AM Duration: 2 hours. Type: R Closed Book. Instructions: University

More information

Chapter 5. Digital systems. 5.1 Boolean algebra Negation, conjunction and disjunction

Chapter 5. Digital systems. 5.1 Boolean algebra Negation, conjunction and disjunction Chapter 5 igital systems digital system is any machine that processes information encoded in the form of digits. Modern digital systems use binary digits, encoded as voltage levels. Two voltage levels,

More information