EECS 579: SOC Testing

Size: px
Start display at page:

Download "EECS 579: SOC Testing"

Transcription

1 EECS 579: SOC Testing Core-Based Systems-On-A-Chip (SOCs) Cores or IP circuits are predesigned and verified functional units of three main types Soft core: synthesizable RTL Firm core: gate-level netlist Hard core: fixed layout Key feature: reusability, implying lower design cost Core is the intellectual property of the vendor. Usually internal details are not available to users Test from core vendors must be applied to embedded cores John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 1 Core Examples Processors: ARM, MIPS, PowerPC Memories: RAMs, memory controllers Peripherals: Bus interface units (PCI, USB, etc.), DMA controllers Multimedia: compression/decompression circuits (MPEG, JPEG, etc.) Digital signal processors John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 2

2 Core Examples VBAFE PCM RAM ROM Oak DSP processor ADC FIFO PLL Timer Viterbi Reg. file JTAG ICE DMA Exchange breaker controller buffer MMU UART RTC Mode conf. reg. IT & Timer Boot CSGEN ARM7 processor Cache Timer Trans PID processor Discrambler Cache controller MIPS processor Parallel port DRAM controller A/V buffer Teletext Serial port GSM wireless communication chip MPEG2 audio/video decoder chip John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 3 SOC Testing Partition into blocks according to test methodology: processors, memories, peripherals, etc. Introduce test access mechanisms such as boundary scan (IEEE ) or analog test bus (IEEE ) Place test-wrappers (collars) around embedded cores. For each I/O terminal a test wrapper provides: Normal mode: terminal driven by core and/or host External test mode Wrapper controls/observes terminal for interconnect test Internal test mode Wrapper observes/controls state terminal for core test John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 4

3 Test Wrapper Wrapper elements Functional core inputs Scan chain Core Scan chain Functional core outputs To/from external Test pins Scan chain To/from Test Access Port Wrapper test controller John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 5 DFT Architecture for SOC Test source Functional inputs User defined test access mechanism (TAM) Test Module 1 wrapper Fcn outputs Fcn. inputs Test Instruction register control Module N wrapper Test sink Functional outputs Serial instruction data Test access port (TAP) SOC inputs TDI TCK TMS TRST TDO SOC outputs John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 6

4 Motivation Realization-Independent ATPG To efficiently test SOC-style core-based designs Generate tests with a high degree of independence of implementation and technology details Protect IP by generating tests from the circuit s functional spec. Reduce the need for boundary scan and speed up test application Approach 1: Cell Fault (CF) Tests Uses exhaustive input pattern and responses sets Covers all implementations but is practical only for tiny cells Approach 2: Universal Test Sets John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 7 Universal Test Sets The universal test set (UTS) U z of z consists of all minimal true T F expanded vectors U z and all maximal false expanded vectors U z of z (Expanded vectors include all literals appearing in a function s minimal expression.) Minimal true vectors {t i } of a function z are such that z(t k ) = 1 for all t k t i, but z(t k ) = 0 for all t k < t i. Maximal false vectors are defined similarly. If z is a unate, its UTS is quite small. (A function z is unate if all its variables appear in minimal two-level expressions only in complemented or uncomplemented form.) If z is not unate (binate), its UTS increases in size up to 2 n tests John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 8

5 Universal Test Sets The UTS detects all MSL faults in a circuit R meeting the following restriction: every path between two points in R has the same inversion parity; these realizations are called unate-gate networks. This result is easy to prove for unate functions since an SSL or MSL fault changes a unate-gate network to another unate-gate network The UTS for unate z can be constructed by substituting 1 for every variable in each prime implicant of z, and substituting 0 for every variable not present, while substituting 0 for every variable in each prime implicate and 1 for every variable not present. UTS detects all multiple stuck-line (MSL) faults in a gate-level implementation of z that meets modest constraints, e.g. unate-gate networks John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 9 Universal Test Sets Example 1 Consider z 1 = ab + ac + bcd, which is unate in a,d but binate in b,c Input vectors abcd Expanded vectors abbccd Output z 1 Universal tests Max. false Max. false Max. false Min. true Min. true Min. true Min. true Max. false a b c d Universal test set: 0: : : : : : : : 1110 z 1 John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 10

6 Universal Tests Example 2: Carry Function Carry functions are positive unate In carry-lookahead form, the 4-bit carry function is as follows in (minimal) SOP and POS form: c 4 = p 0 p 1 p 2 p 3 c in + g 0 p 1 p 2 p 3 + g 1 p 2 p 3 + g 2 p 3 + g 3 = (g 3 + g 2 + g 1 + g 0 + c in )(g 3 + g 2 + g 1 + g 0 + p 0 ) (g 3 + g 2 + g 1 + p 1 )(g 3 + g 2 + p 2 )(g 3 + p 3 ) The corresponding 10 tests are: U T (p 3,g 3,p 2,g 2,p 1,g 1,p 0,g 0,c in ) = { , , , , } U F (p 3,g 3,p 2,g 2,p 1,g 1,p 0,g 0,c in ) = { , , , , } The UTS for c 4 is {U F,U T } John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 11 UTSs vs. CF Tests Universal Tests Number of tests Building blocks Inputs Outputs Universal Cell fault Carry generator Carry generator ,1072 Leading zero detector Leading zero detector ,536 Priority encoder Priority encoder ,072 Booth partial product Decoder with enable John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 12

7 Realization-Independent Block Tests Key Ideas Apply universal tests to small functional (RTL) blocks of large circuits Implement the blocks as balanced-inversion parity (BIP) circuits: paths from all unate variables have the same inversion parity Many blocks in datapath circuits are (nearly) unate and have small universal test sets Need to resolve controllability/observability problems of embedded blocks Reference [Kim & Hayes, IEEE Trans. CAD 2001] John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 13 Circuit Constraints Balanced inversion-parity (BIP) Paths from unate variables have same inversion parity Covers almost all practical implementations Unate-gate network a a BIP realization b c d z 2 b c d z 2 John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 14

8 Realization-Independent Block Tests n For the entire adder n (2N +1) l Universal tests = 2 For a block-structured adde l Universal tests N = + 24 A B A B Adder p i = a i + b i, g i = a i b i c in p i = a i + b i g i = a i b i c i = g i 1 + p i 1 c i 1 s i = p i g i c i c in c i = g i 1 + p i 1 c i 1 s i = p i g i c i n S Block-structures lead to small universal test S John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 15 Realization-Independent Block Tests a 0 b 0 a 1 b 1 a 2 b 2 a 3 b 3 PGB Ripplecarry adder C in p 0 g 0 p 1 g 1 p 2 g 2 p 3 g 3 p 0 g 0 c 1 p 1 g 1 c 2 p 2 g 2 c 3 p 3 g 3 CB SB C out a 0 b 0 s 0 s 1 a 1 b 1 a 2 b 2 a 3 b 3 s 2 s 3 PGB Carrylookahead adder C in p 0 g 0 p 1 g 1 p 2 g 2 p 3 g 3 CB C out p 0, g 0 c 1 p 1, g 1 c 2 p 2, g 2 c 3 p 3, g 3 SB s 0 s 1 s 2 s 3 Fig 1: John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 16

9 Realization-Independent Block Tests Apply all universal tests to every block Observe all responses from every block, if possible All universal tests {t i } All faulty responses {r i } a b c d Block 1 x 1 = a + b x 2 = abc x 1 x 2 Block 2 y 1 = (x 2 + x 1 )(d + x 2 ) y 2 = x 1 + x 2 y 1 y 2 Block 3 z 1 = d(y 1 + y 2 ) z 2 = y 1 + y 2 + d z 1 z 2 John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 17 Realization-Independent Block Tests RIB (realization-independent block) tests Detect all faults even when non-applicable tests occur Fast RIB test computation Replace the non-applicable tests in the universal test set New tests are always at Hamming distance 1 from the non-applicable tests Add only a minimal number of new tests RIB fault model Any fault <t i, r j > causing r j when RIB test t i is applied John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 18

10 RIBTEC Program Input: behavioral Verilog code Generate initial universal tests Compute t RIBTEC by high-level PODEM (<t i, r j >) Failure Compute RIB tests for non-applicable vector t i No Drop other faults by FSIM All RIB faults detected? Yes Success Output: RIBTEC test vectors John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 19 RIBTEC Program Procedure RIBTEC(C) /* C = circuit and B = block */ 1:for each B repeat U(0) := UTgen (B);/* Initial UTS generation */ 2:S P := all pairs {(t i, r j )} for all t i s in all U(0) and all faulty responses r j s; 3:while (S P is nonempty) begin 4: Select pair (t i, r j ) for block B from S P ; 5: pt := HL-PODEM( (t i, r j ) );/* Compute pt via high-level PODEM */ 6: if (no pt exists) then /* t i is an NCV or NOV */ 7: T R := RIB-Tgen (t i, U(k)); k := k + 1; 8: S P := S P {new pairs (t h, r y ) derived from T R }; 9: if (t i = NCV) then S P := S P {(t i, r j ) for all j}; 10: else S P := S P (t i, r j ); 11: else 12: T RIBTEC := T RIBTEC {pt};/* T RIBTEC = the final test set */ 13: FaultSimulate (pt, S P );/* Find other covered pairs {(t i, r j )} in S P */ 14: S F := S F {all covered (t i, r j )};/* S F = the detectable RIB fault set */ 15:end; 16:Reverse-Order-FaultSimulate (T RIBTEC );/* Perform test compaction */ 17:return T RIBTEC and S F ; John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 20

11 Experimental Results RIBTEC Program Benchmark circuit Atalanta tests for high-speed realization Detectable RIB faults RIBTEC tests for high-level design NCVs and NOVs RIB fault coverage Number of tests CPU time (sec.) Atalanta tests for low-area realization RIB fault coverage Number of tests RIB fault coverage Number of tests 16-bit CLA % % % bit CLA % % % bit CSA % % % bit CSA % % % bit ALU % % % bit ALU % % % bit comparator % % % bit comparator % % % 213 c880 8-bit ALU/controller % % % 160 c bit adder/ comparator % % % 124 John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 21 Summary High degree of realization independence is possible with fairly small test sets Modular (partitioned) structure is useful in conjunction with special properties like unateness Approach provides a high-level ATPG tool (RIBTEC) and a functional, realization-independent fault model Seems promising for testing IP-based designs John P. Hayes University of Michigan EECS 579 Fall 2001 Lecture 24: Page 22

Hardware testing and design for testability. EE 3610 Digital Systems

Hardware testing and design for testability. EE 3610 Digital Systems EE 3610: Digital Systems 1 Hardware testing and design for testability Introduction A Digital System requires testing before and after it is manufactured 2 Level 1: behavioral modeling and test benches

More information

Design for Testability

Design for Testability Design for Testability Outline Ad Hoc Design for Testability Techniques Method of test points Multiplexing and demultiplexing of test points Time sharing of I/O for normal working and testing modes Partitioning

More information

IHS 3: Test of Digital Systems R.Ubar, A. Jutman, H-D. Wuttke

IHS 3: Test of Digital Systems R.Ubar, A. Jutman, H-D. Wuttke IHS 3: Test of Digital Systems R.Ubar, A. Jutman, H-D. Wuttke Integrierte Hard- und Softwaresysteme RT-Level Design data path and control path on RT-level RT level simulation Functional units (F1,..,F4)

More information

Design for Testability

Design for Testability Design for Testability Outline Ad Hoc Design for Testability Techniques Method of test points Multiplexing and demultiplexing of test points Time sharing of I/O for normal working and testing modes Partitioning

More information

Introduction to VLSI Testing

Introduction to VLSI Testing Introduction to 李昆忠 Kuen-Jong Lee Dept. of Electrical Engineering National Cheng-Kung University Tainan, Taiwan Class Problems to Think How are you going to test A 32 bit adder A 32 bit counter A 32Mb

More information

Combinational Logic. Mantıksal Tasarım BBM231. section instructor: Ufuk Çelikcan

Combinational Logic. Mantıksal Tasarım BBM231. section instructor: Ufuk Çelikcan Combinational Logic Mantıksal Tasarım BBM23 section instructor: Ufuk Çelikcan Classification. Combinational no memory outputs depends on only the present inputs expressed by Boolean functions 2. Sequential

More information

EECS 579: Logic and Fault Simulation. Simulation

EECS 579: Logic and Fault Simulation. Simulation EECS 579: Logic and Fault Simulation Simulation: Use of computer software models to verify correctness Fault Simulation: Use of simulation for fault analysis and ATPG Circuit description Input data for

More information

Chapter 7. VLSI System Components

Chapter 7. VLSI System Components VLSI Design Chapter 7 VLSI System Components Jin-Fu Li Chapter 7 VLSI System Components Introduction Datapath Operators Memory Elements Control Structures 2 System-Level Hierarchy System (Top) Complex

More information

Total Time = 90 Minutes, Total Marks = 50. Total /50 /10 /18

Total Time = 90 Minutes, Total Marks = 50. Total /50 /10 /18 University of Waterloo Department of Electrical & Computer Engineering E&CE 223 Digital Circuits and Systems Midterm Examination Instructor: M. Sachdev October 23rd, 2007 Total Time = 90 Minutes, Total

More information

Chapter 5. Digital Design and Computer Architecture, 2 nd Edition. David Money Harris and Sarah L. Harris. Chapter 5 <1>

Chapter 5. Digital Design and Computer Architecture, 2 nd Edition. David Money Harris and Sarah L. Harris. Chapter 5 <1> Chapter 5 Digital Design and Computer Architecture, 2 nd Edition David Money Harris and Sarah L. Harris Chapter 5 Chapter 5 :: Topics Introduction Arithmetic Circuits umber Systems Sequential Building

More information

Logic BIST. Sungho Kang Yonsei University

Logic BIST. Sungho Kang Yonsei University Logic BIST Sungho Kang Yonsei University Outline Introduction Basics Issues Weighted Random Pattern Generation BIST Architectures Deterministic BIST Conclusion 2 Built In Self Test Test/ Normal Input Pattern

More information

EECS150 - Digital Design Lecture 11 - Shifters & Counters. Register Summary

EECS150 - Digital Design Lecture 11 - Shifters & Counters. Register Summary EECS50 - Digital Design Lecture - Shifters & Counters February 24, 2003 John Wawrzynek Spring 2005 EECS50 - Lec-counters Page Register Summary All registers (this semester) based on Flip-flops: q 3 q 2

More information

S No. Questions Bloom s Taxonomy Level UNIT-I

S No. Questions Bloom s Taxonomy Level UNIT-I GROUP-A (SHORT ANSWER QUESTIONS) S No. Questions Bloom s UNIT-I 1 Define oxidation & Classify different types of oxidation Remember 1 2 Explain about Ion implantation Understand 1 3 Describe lithography

More information

Digital Integrated Circuits A Design Perspective. Arithmetic Circuits. Jan M. Rabaey Anantha Chandrakasan Borivoje Nikolic.

Digital Integrated Circuits A Design Perspective. Arithmetic Circuits. Jan M. Rabaey Anantha Chandrakasan Borivoje Nikolic. Digital Integrated Circuits A Design Perspective Jan M. Rabaey Anantha Chandrakasan Borivoje Nikolic Arithmetic Circuits January, 2003 1 A Generic Digital Processor MEMORY INPUT-OUTPUT CONTROL DATAPATH

More information

Fault Modeling. 李昆忠 Kuen-Jong Lee. Dept. of Electrical Engineering National Cheng-Kung University Tainan, Taiwan. VLSI Testing Class

Fault Modeling. 李昆忠 Kuen-Jong Lee. Dept. of Electrical Engineering National Cheng-Kung University Tainan, Taiwan. VLSI Testing Class Fault Modeling 李昆忠 Kuen-Jong Lee Dept. of Electrical Engineering National Cheng-Kung University Tainan, Taiwan Class Fault Modeling Some Definitions Why Modeling Faults Various Fault Models Fault Detection

More information

DIGITAL TECHNICS. Dr. Bálint Pődör. Óbuda University, Microelectronics and Technology Institute

DIGITAL TECHNICS. Dr. Bálint Pődör. Óbuda University, Microelectronics and Technology Institute DIGITAL TECHNICS Dr. Bálint Pődör Óbuda University, Microelectronics and Technology Institute 4. LECTURE: COMBINATIONAL LOGIC DESIGN: ARITHMETICS (THROUGH EXAMPLES) 2016/2017 COMBINATIONAL LOGIC DESIGN:

More information

211: Computer Architecture Summer 2016

211: Computer Architecture Summer 2016 211: Computer Architecture Summer 2016 Liu Liu Topic: Storage Project3 Digital Logic - Storage: Recap - Review: cache hit rate - Project3 - Digital Logic: - truth table => SOP - simplification: Boolean

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

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

CMPEN 411 VLSI Digital Circuits Spring Lecture 19: Adder Design

CMPEN 411 VLSI Digital Circuits Spring Lecture 19: Adder Design CMPEN 411 VLSI Digital Circuits Spring 2011 Lecture 19: Adder Design [Adapted from Rabaey s Digital Integrated Circuits, Second Edition, 2003 J. Rabaey, A. Chandrakasan, B. Nikolic] Sp11 CMPEN 411 L19

More information

EEC 216 Lecture #3: Power Estimation, Interconnect, & Architecture. Rajeevan Amirtharajah University of California, Davis

EEC 216 Lecture #3: Power Estimation, Interconnect, & Architecture. Rajeevan Amirtharajah University of California, Davis EEC 216 Lecture #3: Power Estimation, Interconnect, & Architecture Rajeevan Amirtharajah University of California, Davis Outline Announcements Review: PDP, EDP, Intersignal Correlations, Glitching, Top

More information

EECS150 - Digital Design Lecture 23 - FFs revisited, FIFOs, ECCs, LSFRs. Cross-coupled NOR gates

EECS150 - Digital Design Lecture 23 - FFs revisited, FIFOs, ECCs, LSFRs. Cross-coupled NOR gates EECS150 - Digital Design Lecture 23 - FFs revisited, FIFOs, ECCs, LSFRs April 16, 2009 John Wawrzynek Spring 2009 EECS150 - Lec24-blocks Page 1 Cross-coupled NOR gates remember, If both R=0 & S=0, then

More information

MODEL ANSWER SUMMER 17 EXAMINATION Subject Title: Principles of Digital Techniques

MODEL ANSWER SUMMER 17 EXAMINATION Subject Title: Principles of Digital Techniques MODEL ANSWER SUMMER 17 EXAMINATION Subject Title: Principles of Digital Techniques Subject Code: Important Instructions to examiners: 1) The answers should be examined by key words and not as word-to-word

More information

THE UNIVERSITY OF MICHIGAN. Faster Static Timing Analysis via Bus Compression

THE UNIVERSITY OF MICHIGAN. Faster Static Timing Analysis via Bus Compression Faster Static Timing Analysis via Bus Compression by David Van Campenhout and Trevor Mudge CSE-TR-285-96 THE UNIVERSITY OF MICHIGAN Computer Science and Engineering Division Department of Electrical Engineering

More information

Digital Integrated Circuits A Design Perspective. Arithmetic Circuits. Jan M. Rabaey Anantha Chandrakasan Borivoje Nikolic.

Digital Integrated Circuits A Design Perspective. Arithmetic Circuits. Jan M. Rabaey Anantha Chandrakasan Borivoje Nikolic. Digital Integrated Circuits A Design Perspective Jan M. Rabaey Anantha Chandrakasan Borivoje Nikolic Arithmetic Circuits January, 2003 1 A Generic Digital Processor MEM ORY INPUT-OUTPUT CONTROL DATAPATH

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

CPS 104 Computer Organization and Programming Lecture 11: Gates, Buses, Latches. Robert Wagner

CPS 104 Computer Organization and Programming Lecture 11: Gates, Buses, Latches. Robert Wagner CPS 4 Computer Organization and Programming Lecture : Gates, Buses, Latches. Robert Wagner CPS4 GBL. RW Fall 2 Overview of Today s Lecture: The MIPS ALU Shifter The Tristate driver Bus Interconnections

More information

Reg. No. Question Paper Code : B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER Second Semester. Computer Science and Engineering

Reg. No. Question Paper Code : B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER Second Semester. Computer Science and Engineering Sp 6 Reg. No. Question Paper Code : 27156 B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2015. Second Semester Computer Science and Engineering CS 6201 DIGITAL PRINCIPLES AND SYSTEM DESIGN (Common

More information

How to create designs with Dynamic/Adaptive Voltage Scaling. Roy H. Liu National Semiconductor Corporation

How to create designs with Dynamic/Adaptive Voltage Scaling. Roy H. Liu National Semiconductor Corporation How to create designs with Dynamic/Adaptive Voltage Scaling Roy H. Liu National Semiconductor orporation What you will learn from this session Design challenges with variable voltage level Design partitioning

More information

Combinational Logic. Lan-Da Van ( 范倫達 ), Ph. D. Department of Computer Science National Chiao Tung University Taiwan, R.O.C.

Combinational Logic. Lan-Da Van ( 范倫達 ), Ph. D. Department of Computer Science National Chiao Tung University Taiwan, R.O.C. Combinational Logic ( 范倫達 ), Ph. D. Department of Computer Science National Chiao Tung University Taiwan, R.O.C. Fall, 2017 ldvan@cs.nctu.edu.tw http://www.cs.nctu.edu.tw/~ldvan/ Combinational Circuits

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

CprE 281: Digital Logic

CprE 281: Digital Logic CprE 28: Digital Logic Instructor: Alexander Stoytchev http://www.ece.iastate.edu/~alexs/classes/ Simple Processor CprE 28: Digital Logic Iowa State University, Ames, IA Copyright Alexander Stoytchev Digital

More information

LOGIC CIRCUITS. Basic Experiment and Design of Electronics. Ho Kyung Kim, Ph.D.

LOGIC CIRCUITS. Basic Experiment and Design of Electronics. Ho Kyung Kim, Ph.D. Basic Experiment and Design of Electronics LOGIC CIRCUITS Ho Kyung Kim, Ph.D. hokyung@pusan.ac.kr School of Mechanical Engineering Pusan National University Digital IC packages TTL (transistor-transistor

More information

KUMARAGURU COLLEGE OF TECHNOLOGY COIMBATORE

KUMARAGURU COLLEGE OF TECHNOLOGY COIMBATORE Estd-1984 KUMARAGURU COLLEGE OF TECHNOLOGY COIMBATORE 641 006 QUESTION BANK UNIT I PART A ISO 9001:2000 Certified 1. Convert (100001110.010) 2 to a decimal number. 2. Find the canonical SOP for the function

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

LOGIC CIRCUITS. Basic Experiment and Design of Electronics

LOGIC CIRCUITS. Basic Experiment and Design of Electronics Basic Experiment and Design of Electronics LOGIC CIRCUITS Ho Kyung Kim, Ph.D. hokyung@pusan.ac.kr School of Mechanical Engineering Pusan National University Outline Combinational logic circuits Output

More information

CSE140: Components and Design Techniques for Digital Systems. Logic minimization algorithm summary. Instructor: Mohsen Imani UC San Diego

CSE140: Components and Design Techniques for Digital Systems. Logic minimization algorithm summary. Instructor: Mohsen Imani UC San Diego CSE4: Components and Design Techniques for Digital Systems Logic minimization algorithm summary Instructor: Mohsen Imani UC San Diego Slides from: Prof.Tajana Simunic Rosing & Dr.Pietro Mercati Definition

More information

T st Cost Reduction LG Electronics Lee Y, ong LG Electronics 2009

T st Cost Reduction LG Electronics Lee Y, ong LG Electronics 2009 Test Cost Reduction LG Electronics Lee, Yong LG Electronics 2009 Contents Introduction Key factors for test cost reduction in DFT Test vector volume Low cost ATE Test time Reuse a large block Test cost

More information

EECS150 - Digital Design Lecture 19 - Combinational Logic Circuits : A Deep Dive

EECS150 - Digital Design Lecture 19 - Combinational Logic Circuits : A Deep Dive EECS150 - Digital Design Lecture 19 - Combinational Logic Circuits : A Deep Dive March 30, 2010 John Wawrzynek Spring 2010 EECS150 - Lec19-cl1 Page 1 Boolean Algebra I (Representations of Combinational

More information

Digital Systems Design Overview. ENGIN 341 Advanced Digital Design University of Massachuse?s Boston Department of Engineering Dr.

Digital Systems Design Overview. ENGIN 341 Advanced Digital Design University of Massachuse?s Boston Department of Engineering Dr. Digital Systems Design Overview ENGIN 341 Advanced Digital Design University of Massachuse?s Boston Department of Engineering Dr. Filip Cuckov Overview 1. IntroducGon to Programmable Logic Devices 2. Field

More information

ALU A functional unit

ALU A functional unit ALU A functional unit that performs arithmetic operations such as ADD, SUB, MPY logical operations such as AND, OR, XOR, NOT on given data types: 8-,16-,32-, or 64-bit values A n-1 A n-2... A 1 A 0 B n-1

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

School of EECS Seoul National University

School of EECS Seoul National University 4!4 07$ 8902808 3 School of EECS Seoul National University Introduction Low power design 3974/:.9 43 Increasing demand on performance and integrity of VLSI circuits Popularity of portable devices Low power

More information

EECS150 - Digital Design Lecture 23 - FSMs & Counters

EECS150 - Digital Design Lecture 23 - FSMs & Counters EECS150 - Digital Design Lecture 23 - FSMs & Counters April 8, 2010 John Wawrzynek Spring 2010 EECS150 - Lec22-counters Page 1 One-hot encoding of states. One FF per state. State Encoding Why one-hot encoding?

More information

CSE 140 Midterm 3 version A Tajana Simunic Rosing Spring 2015

CSE 140 Midterm 3 version A Tajana Simunic Rosing Spring 2015 CSE 140 Midterm 3 version A Tajana Simunic Rosing Spring 2015 Name of the person on your left : Name of the person on your right: 1. 20 points 2. 20 points 3. 20 points 4. 15 points 5. 15 points 6. 10

More information

Built-In Self-Test. Outline

Built-In Self-Test. Outline Built-In Self-Test Outline Motivation for BIST Testing SoC with BIST Test per Scan and Test per Clock HW and SW based BIST Exhaustive and pseudoexhaustive test generation Pseudorandom test generation with

More information

Test-Length Selection and TAM Optimization for Wafer-Level, Reduced Pin-Count Testing of Core-Based Digital SoCs

Test-Length Selection and TAM Optimization for Wafer-Level, Reduced Pin-Count Testing of Core-Based Digital SoCs Test-Length Selection and TAM Optimization for Wafer-Level, Reduced Pin-Count Testing of Core-Based Digital SoCs Sudarshan Bahukudumbi and Krishnendu Chakrabarty Department of Electrical and Computer Engineering

More information

Chapter 4. Combinational: Circuits with logic gates whose outputs depend on the present combination of the inputs. elements. Dr.

Chapter 4. Combinational: Circuits with logic gates whose outputs depend on the present combination of the inputs. elements. Dr. Chapter 4 Dr. Panos Nasiopoulos Combinational: Circuits with logic gates whose outputs depend on the present combination of the inputs. Sequential: In addition, they include storage elements Combinational

More information

SIR C.R.REDDY COLLEGE OF ENGINEERING ELURU DIGITAL INTEGRATED CIRCUITS (DIC) LABORATORY MANUAL III / IV B.E. (ECE) : I - SEMESTER

SIR C.R.REDDY COLLEGE OF ENGINEERING ELURU DIGITAL INTEGRATED CIRCUITS (DIC) LABORATORY MANUAL III / IV B.E. (ECE) : I - SEMESTER SIR C.R.REDDY COLLEGE OF ENGINEERING ELURU 534 007 DIGITAL INTEGRATED CIRCUITS (DIC) LABORATORY MANUAL III / IV B.E. (ECE) : I - SEMESTER DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING DIGITAL

More information

Chapter 4: Designing Combinational Systems Uchechukwu Ofoegbu

Chapter 4: Designing Combinational Systems Uchechukwu Ofoegbu Chapter 4: Designing Combinational Systems Uchechukwu Ofoegbu Temple University Gate Delay ((1.1).1) ((1.0).0) ((0.1).1) ((0.1).0) ((1.1) = 1 0 s = sum c out carry-out a, b = added bits C = carry in a

More information

Inadmissible Class of Boolean Functions under Stuck-at Faults

Inadmissible Class of Boolean Functions under Stuck-at Faults Inadmissible Class of Boolean Functions under Stuck-at Faults Debesh K. Das 1, Debabani Chowdhury 1, Bhargab B. Bhattacharya 2, Tsutomu Sasao 3 1 Computer Sc. & Engg. Dept., Jadavpur University, Kolkata

More information

CMP 338: Third Class

CMP 338: Third Class CMP 338: Third Class HW 2 solution Conversion between bases The TINY processor Abstraction and separation of concerns Circuit design big picture Moore s law and chip fabrication cost Performance What does

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

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

EECS150 - Digital Design Lecture 24 - Arithmetic Blocks, Part 2 + Shifters

EECS150 - Digital Design Lecture 24 - Arithmetic Blocks, Part 2 + Shifters EECS150 - Digital Design Lecture 24 - Arithmetic Blocks, Part 2 + Shifters April 15, 2010 John Wawrzynek 1 Multiplication a 3 a 2 a 1 a 0 Multiplicand b 3 b 2 b 1 b 0 Multiplier X a 3 b 0 a 2 b 0 a 1 b

More information

CSE140: Components and Design Techniques for Digital Systems. Decoders, adders, comparators, multipliers and other ALU elements. Tajana Simunic Rosing

CSE140: Components and Design Techniques for Digital Systems. Decoders, adders, comparators, multipliers and other ALU elements. Tajana Simunic Rosing CSE4: Components and Design Techniques for Digital Systems Decoders, adders, comparators, multipliers and other ALU elements Tajana Simunic Rosing Mux, Demux Encoder, Decoder 2 Transmission Gate: Mux/Tristate

More information

Methodology to combine Formal and Fault simulator to measure safety metrics

Methodology to combine Formal and Fault simulator to measure safety metrics Methodology to combine Formal and Fault simulator to measure safety metrics Jain Gaurav, Infineon Technologies AP Pte LTD, Singapore Kadambi Ranga, Infineon Technologies AP Pte LTD, Singapore Bandlamudi

More information

EECS150 - Digital Design Lecture 17 - Sequential Circuits 3 (Counters)

EECS150 - Digital Design Lecture 17 - Sequential Circuits 3 (Counters) EECS150 - Digital Design Lecture 17 - Sequential Circuits 3 (Counters) March 19&21, 2002 John Wawrzynek Spring 2002 EECS150 - Lec13-seq3 version 2 Page 1 Counters Special sequential circuits (FSMs) that

More information

Advanced Digital Design with the Verilog HDL, Second Edition Michael D. Ciletti Prentice Hall, Pearson Education, 2011

Advanced Digital Design with the Verilog HDL, Second Edition Michael D. Ciletti Prentice Hall, Pearson Education, 2011 Problem 2-1 Recall that a minterm is a cube in which every variable appears. A Boolean expression in SOP form is canonical if every cube in the expression has a unique representation in which all of the

More information

Department of Electrical and Computer Engineering University of Wisconsin Madison. Fall Final Examination

Department of Electrical and Computer Engineering University of Wisconsin Madison. Fall Final Examination Department of Electrical and Computer Engineering University of Wisconsin Madison ECE 553: Testing and Testable Design of Digital Systems Fall 2013-2014 Final Examination CLOSED BOOK Kewal K. Saluja Date:

More information

Logic and Boolean algebra

Logic and Boolean algebra Computer Mathematics Week 7 Logic and Boolean algebra College of Information Science and Engineering Ritsumeikan University last week coding theory channel coding information theory concept Hamming distance

More information

Chap 2. Combinational Logic Circuits

Chap 2. Combinational Logic Circuits Overview 2 Chap 2. Combinational Logic Circuits Spring 24 Part Gate Circuits and Boolean Equations Binary Logic and Gates Boolean Algebra Standard Forms Part 2 Circuit Optimization Two-Level Optimization

More information

SIMULATION-BASED APPROXIMATE GLOBAL FAULT COLLAPSING

SIMULATION-BASED APPROXIMATE GLOBAL FAULT COLLAPSING SIMULATION-BASED APPROXIMATE GLOBAL FAULT COLLAPSING Hussain Al-Asaad and Raymond Lee Computer Engineering Research Laboratory Department of Electrical & Computer Engineering University of California One

More information

Overview. 4. Built in Self-Test. 1. Introduction 2. Testability measuring 3. Design for testability. Technical University Tallinn, ESTONIA

Overview. 4. Built in Self-Test. 1. Introduction 2. Testability measuring 3. Design for testability. Technical University Tallinn, ESTONIA Overview. Introduction 2. Testability measuring 3. Design for testability 4. Built in Self-Test Built-In Self-Test Outline Motivation for BIST Testing SoC with BIST Test per Scan and Test per Clock HW

More information

DE58/DC58 LOGIC DESIGN DEC 2014

DE58/DC58 LOGIC DESIGN DEC 2014 Q.2 a. In a base-5 number system, 3 digit representations is used. Find out (i) Number of distinct quantities that can be represented.(ii) Representation of highest decimal number in base-5. Since, r=5

More information

EGFC: AN EXACT GLOBAL FAULT COLLAPSING TOOL FOR COMBINATIONAL CIRCUITS

EGFC: AN EXACT GLOBAL FAULT COLLAPSING TOOL FOR COMBINATIONAL CIRCUITS EGFC: AN EXACT GLOBAL FAULT COLLAPSING TOOL FOR COMBINATIONAL CIRCUITS Hussain Al-Asaad Department of Electrical & Computer Engineering University of California One Shields Avenue, Davis, CA 95616-5294

More information

Practice Final Exam Solutions

Practice Final Exam Solutions The University of Michigan Department of Electrical Engineering and Computer Science EECS 270 Fall 2003 Practice Final Exam Solutions Name: UM ID: For all questions, show all work that leads to your answer.

More information

Formal Verification of Systems-on-Chip

Formal Verification of Systems-on-Chip Formal Verification of Systems-on-Chip Wolfgang Kunz Department of Electrical & Computer Engineering University of Kaiserslautern, Germany Slide 1 Industrial Experiences Formal verification of Systems-on-Chip

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

Unit 3 Session - 9 Data-Processing Circuits

Unit 3 Session - 9 Data-Processing Circuits Objectives Unit 3 Session - 9 Data-Processing Design of multiplexer circuits Discuss multiplexer applications Realization of higher order multiplexers using lower orders (multiplexer trees) Introduction

More information

Multi-Level Logic Optimization. Technology Independent. Thanks to R. Rudell, S. Malik, R. Rutenbar. University of California, Berkeley, CA

Multi-Level Logic Optimization. Technology Independent. Thanks to R. Rudell, S. Malik, R. Rutenbar. University of California, Berkeley, CA Technology Independent Multi-Level Logic Optimization Prof. Kurt Keutzer Prof. Sanjit Seshia EECS University of California, Berkeley, CA Thanks to R. Rudell, S. Malik, R. Rutenbar 1 Logic Optimization

More information

KINGS COLLEGE OF ENGINEERING PUNALKULAM. DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING QUESTION BANK

KINGS COLLEGE OF ENGINEERING PUNALKULAM. DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING QUESTION BANK KINGS COLLEGE OF ENGINEERING PUNALKULAM. DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING QUESTION BANK SUBJECT CODE : EC1401 SEM / YEAR : VII/ IV SUBJECT NAME : VLSI DESIGN UNIT I CMOS TECHNOLOGY

More information

CMSC 313 Lecture 19 Combinational Logic Components Programmable Logic Arrays Karnaugh Maps

CMSC 313 Lecture 19 Combinational Logic Components Programmable Logic Arrays Karnaugh Maps CMSC 33 Lecture 9 Combinational Logic Components Programmable Logic rrays Karnaugh Maps UMC, CMSC33, Richard Chang Last Time & efore Returned midterm exam Half adders & full adders Ripple

More information

ELECTRONICS & COMMUNICATION ENGINEERING PROFESSIONAL ETHICS AND HUMAN VALUES

ELECTRONICS & COMMUNICATION ENGINEERING PROFESSIONAL ETHICS AND HUMAN VALUES EC 216(R-15) Total No. of Questions :09] [Total No. of Pages : 02 II/IV B.Tech. DEGREE EXAMINATIONS, DECEMBER- 2016 First Semester ELECTRONICS & COMMUNICATION ENGINEERING PROFESSIONAL ETHICS AND HUMAN

More information

Design of Combinational Logic

Design of Combinational Logic Pune Vidyarthi Griha s COLLEGE OF ENGINEERING, NASHIK 3. Design of Combinational Logic By Prof. Anand N. Gharu (Assistant Professor) PVGCOE Computer Dept.. 30 th June 2017 CONTENTS :- 1. Code Converter

More information

EECS 579: Test Generation 4. Test Generation System

EECS 579: Test Generation 4. Test Generation System EECS 579: Test Generation 4 Other Combinational ATPG Algorithms SOCRATES Structure-Oriented Cost-Reducing Automatic TESt pattern generation [Schultz et al. 988] An ATPG system not just a test generation

More information

WITH increasing complexity in systems design from increased

WITH increasing complexity in systems design from increased 150 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 51, NO. 1, FEBRUARY 2001 Data Compression in Space Under Generalized Mergeability Based on Concepts of Cover Table and Frequency Ordering

More information

For smaller NRE cost For faster time to market For smaller high-volume manufacturing cost For higher performance

For smaller NRE cost For faster time to market For smaller high-volume manufacturing cost For higher performance University of California at Berkeley College of Engineering Department of Electrical Engineering and Computer Sciences EECS5 J. Wawrzynek Spring 22 2/22/2. [2 pts] Short Answers. Midterm Exam I a) [2 pts]

More information

ECE 2300 Digital Logic & Computer Organization

ECE 2300 Digital Logic & Computer Organization ECE 23 Digital Logic & Computer Organization Spring 28 Combinational Building Blocks Lecture 5: Announcements Lab 2 prelab due tomorrow HW due Friday HW 2 to be posted on Thursday Lecture 4 to be replayed

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

CSE 140 Lecture 11 Standard Combinational Modules. CK Cheng and Diba Mirza CSE Dept. UC San Diego

CSE 140 Lecture 11 Standard Combinational Modules. CK Cheng and Diba Mirza CSE Dept. UC San Diego CSE 4 Lecture Standard Combinational Modules CK Cheng and Diba Mirza CSE Dept. UC San Diego Part III - Standard Combinational Modules (Harris: 2.8, 5) Signal Transport Decoder: Decode address Encoder:

More information

Chapter 2 (Lect 2) Canonical and Standard Forms. Standard Form. Other Logic Operators Logic Gates. Sum of Minterms Product of Maxterms

Chapter 2 (Lect 2) Canonical and Standard Forms. Standard Form. Other Logic Operators Logic Gates. Sum of Minterms Product of Maxterms Chapter 2 (Lect 2) Canonical and Standard Forms Sum of Minterms Product of Maxterms Standard Form Sum of products Product of sums Other Logic Operators Logic Gates Basic and Multiple Inputs Positive and

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

The University of Michigan Department of Electrical Engineering and Computer Science. EECS 270 Fall Practice Final Exam.

The University of Michigan Department of Electrical Engineering and Computer Science. EECS 270 Fall Practice Final Exam. The University of Michigan Department of Electrical Engineering and Computer Science EECS 270 Fall 2003 Practice Final Exam Name: UM ID: For all questions, show all work that leads to your answer. Problem

More information

II/IV B.Tech. DEGREE EXAMINATIONS, NOV/DEC-2017

II/IV B.Tech. DEGREE EXAMINATIONS, NOV/DEC-2017 CSE/IT 213 (CR) Total No. of Questions :09] [Total No. of Pages : 03 II/IV B.Tech. DEGREE EXAMINATIONS, NOV/DEC-2017 First Semester CSE/IT BASIC ELECTRICAL AND ELECTRONICS ENGINEERING Time: Three Hours

More information

EECS150 - Digital Design Lecture 25 Shifters and Counters. Recap

EECS150 - Digital Design Lecture 25 Shifters and Counters. Recap EECS150 - Digital Design Lecture 25 Shifters and Counters Nov. 21, 2013 Prof. Ronald Fearing Electrical Engineering and Computer Sciences University of California, Berkeley (slides courtesy of Prof. John

More information

Combinational Logic. Lan-Da Van ( 范倫達 ), Ph. D. Department of Computer Science National Chiao Tung University Taiwan, R.O.C.

Combinational Logic. Lan-Da Van ( 范倫達 ), Ph. D. Department of Computer Science National Chiao Tung University Taiwan, R.O.C. Combinational Logic ( 范倫達 ), Ph. D. Department of Computer Science National Chiao Tung University Taiwan, R.O.C. Fall, 2010 ldvan@cs.nctu.edu.tw http://www.cs.nctu.edu.tw/~ldvan/ Combinational Circuits

More information

ECE 448 Lecture 6. Finite State Machines. State Diagrams, State Tables, Algorithmic State Machine (ASM) Charts, and VHDL Code. George Mason University

ECE 448 Lecture 6. Finite State Machines. State Diagrams, State Tables, Algorithmic State Machine (ASM) Charts, and VHDL Code. George Mason University ECE 448 Lecture 6 Finite State Machines State Diagrams, State Tables, Algorithmic State Machine (ASM) Charts, and VHDL Code George Mason University Required reading P. Chu, FPGA Prototyping by VHDL Examples

More information

Introduction to Digital Logic Missouri S&T University CPE 2210 PLDs

Introduction to Digital Logic Missouri S&T University CPE 2210 PLDs Introduction to Digital Logic Missouri S&T University CPE 2210 PLDs Egemen K. Çetinkaya Egemen K. Çetinkaya Department of Electrical & Computer Engineering Missouri University of Science and Technology

More information

And Inverter Graphs. and and nand. inverter or nor xor

And Inverter Graphs. and and nand. inverter or nor xor And Inverter Graphs and and nand inverter or nor xor And Inverter Graphs A B gate 1 u gate 4 X C w gate 3 v gate 2 gate 5 Y A u B X w Y C v And Inverter Graphs Can represent any Boolean function: v i+1

More information

Parity Checker Example. EECS150 - Digital Design Lecture 9 - Finite State Machines 1. Formal Design Process. Formal Design Process

Parity Checker Example. EECS150 - Digital Design Lecture 9 - Finite State Machines 1. Formal Design Process. Formal Design Process Parity Checker Example A string of bits has even parity if the number of 1 s in the string is even. Design a circuit that accepts a bit-serial stream of bits and outputs a 0 if the parity thus far is even

More information

CMP 334: Seventh Class

CMP 334: Seventh Class CMP 334: Seventh Class Performance HW 5 solution Averages and weighted averages (review) Amdahl's law Ripple-carry adder circuits Binary addition Half-adder circuits Full-adder circuits Subtraction, negative

More information

Logical Design of Digital Systems

Logical Design of Digital Systems Lecture 4 Table of Content 1. Combinational circuit design 2. Elementary combinatorial circuits for data transmission 3. Memory structures 4. Programmable logic devices 5. Algorithmic minimization approaches

More information

VLSI. Faculty. Srikanth

VLSI. Faculty. Srikanth J.B. Institute of Engineering & Technology Department of CSE COURSE FILE VLSI Faculty Srikanth J.B. Institute of Engineering & Technology Department of CSE SYLLABUS Subject Name: VLSI Subject Code: VLSI

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

UNIT 4 MINTERM AND MAXTERM EXPANSIONS

UNIT 4 MINTERM AND MAXTERM EXPANSIONS UNIT 4 MINTERM AND MAXTERM EXPANSIONS Spring 2 Minterm and Maxterm Expansions 2 Contents Conversion of English sentences to Boolean equations Combinational logic design using a truth table Minterm and

More information

CMSC 313 Lecture 25 Registers Memory Organization DRAM

CMSC 313 Lecture 25 Registers Memory Organization DRAM CMSC 33 Lecture 25 Registers Memory Organization DRAM UMBC, CMSC33, Richard Chang A-75 Four-Bit Register Appendix A: Digital Logic Makes use of tri-state buffers so that multiple registers

More information

EEC 216 Lecture #2: Metrics and Logic Level Power Estimation. Rajeevan Amirtharajah University of California, Davis

EEC 216 Lecture #2: Metrics and Logic Level Power Estimation. Rajeevan Amirtharajah University of California, Davis EEC 216 Lecture #2: Metrics and Logic Level Power Estimation Rajeevan Amirtharajah University of California, Davis Announcements PS1 available online tonight R. Amirtharajah, EEC216 Winter 2008 2 Outline

More information

Chapter 5 Arithmetic Circuits

Chapter 5 Arithmetic Circuits Chapter 5 Arithmetic Circuits SKEE2263 Digital Systems Mun im/ismahani/izam {munim@utm.my,e-izam@utm.my,ismahani@fke.utm.my} February 11, 2016 Table of Contents 1 Iterative Designs 2 Adders 3 High-Speed

More information