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


 Justina Montgomery
 1 years ago
 Views:
Transcription
1 CSE4: Components and Design Techniques for Digital Systems Introduction Prof. Tajana Simunic Rosing
2 Welcome to CSE 4! Instructor: Tajana Simunic Rosing please put CSE4 in the subject line Office Hours: T 3:34:3pm, Th 2:45:45pm; CSE 28 Instructor s Assistant: Sheila Manalo Phone: (858) Discussion session: F 4:4:5am, CENTR 9 TAs: (office hrs and s to be updated at course website shortly) Lu, Jingwei Th am, Sunday 78pm Mast, Ryan Andrew Wed 45pm, B25 Nath, Rajib Kumar Tu am2pm Supanekar, Ketan Pranav ; Mon 78pm Class Website: Grades: 2
3 Course Description Prerequisites: CSE 2 or Math 5A, and CSE 3. CSE 4L must be taken concurrently Objective: Introduce digital components and system design concepts Grading Homeworks (~7): % HW picked up at beginning of the class, ZERO pts if late Three exams: # 25%; #2 3%; #3 35% No makeup exams; exceptions only for: documented illness (signed doctor s statement), death in the family Third exam will occur at the final time, but will be the same length as the other midterms, so you will have hr 2min to complete it Regrade requests: turn in a written request at the end of the class where your work (HW or exam) is returned 3
4 Textbook and Recommended Readings Required textbook: Digital Design & Computer Architecture, 2 nd Edition by David & Sarah Harris Recommended textbook: Digital Design by F. Vahid, & Contemporary Logic Design by R. Katz & G. Borriello Lecture slides are derived from the slides designed for all three books 4
5 Why Study Digital Design? Look under the hood of computers Become a better programmer when aware of hardware resource issues Everyday devices becoming digital Enables: Better devices: Better sound recorders, cameras, cars, cell phones, medical devices,... New devices: Video games, PDAs,... Known as embedded systems Thousands of new devices every year Designers needed: Potential career Portable music players Satellites Cell phones DVD players Video recorders Musical instruments Cameras TVs???
6 When Microprocessors Aren t Good Enough Execution time With microprocessors so easy to work with, cheap, and available, why design a digital circuit? Microprocessor may be too slow Or too big, power hungry, or costly ( a ) Image Sensor Memory Image Sensor Microprocessor (Read, Compress, and Store) Read circuit Compress circuit Sample digital camera task execution times (in seconds) on a microprocessor versus a digital circuit: ( b ) Memory Store circuit Task Microprocessor Custom Digital Circuit Read 5. Image Sensor Read circuit Compress circuit Compress 8.5 Store.8 ( c ) Memory Microprocessor (Store) 6
7 The big picture We start with Boolean algebra Y = A and B We end with a hardware design of a simple CPU PC READ ADDRESS INSTRUCTION MEMORY INSTRUCTION [3] 4 INSTRUCTION[326] INSTRUCTION[252] INSTRUCTION[26] INST[5] RESULT ADDER I[25] << 2 JMP ADDRESS [25] REGISTERS ER WRITE 2 MUX READ REGIST ER WRI DATA MUX INSTRUCTION[5] READ REGIST ER READ REGIST TE DAT A PC+4 [328] JMP ADDRESS [3] Sign Extend INSTRUCTION[5] << 2 RESULT ADDER ZERO ALU RESULT ALU CONTROL MUX BRANCH REG_DST JUMP CON TROL REG_WRITE MEM_READ,MEM_WRITE ALU_SRC ALU_OP READ DATA 2 ADDRESS DATA MEMORY WRITE DATA MUX READ DATA MUX MEM_TO_REG What s next? CSE4 more complex CPU architecture 7
8 Outline Number representations Analog vs. Digital Digital representations: Binary, Hexadecimal, Octal Binary addition, subtraction, multiplication, division Boolean algebra Properties How Boolean algebra can be used to design logic circuits Switches, MOS transistors, Logic gates What is a switch How a transistor operates Building logic gates out of transistors Building larger functions from logic gates Textbook chapter 8
9 CSE4: Components and Design Techniques for Digital Systems Number representations & Binary arithmetic Tajana Simunic Rosing 9
10 value value What Does Digital Mean? Analog signal Infinite possible values Ex: voltage on a wire created by microphone Digital signal Finite possible values Ex: button pressed on a keypad analog signal 2 digital signal Possible values:.,., 2.9,... infinite possibilities time time Possible values:,, 2, 3, or 4. That s it.
11 How Do We Encode Data into Binary? analog phenomena electric signal A2D digital data digital data sensors and other inputs Digital System D2A electric signal actuators and other outputs digital data digital data Some inputs are inherently binary Button: not pressed (), pressed () Some inputs are inherently digital Just need encoding into binary e.g., multibutton input: encode red=, blue=,... Other inputs are analog Need analogtodigital conversion air temperature sensor 33 degrees r ed r ed r ed button blue blue blue g r een g r een g r een black black black Binary digit = BIT Has 2 values: &
12 Volts Volts lengthy transmission (e.g, cell phone) Volts lengthy transmission (e.g, cell phone) A/D conversion & digitization benefits Analog signal (e.g., audio) may lose quality Voltage levels not saved/copied/transmitted perfectly Digitized version enables nearperfect save/cpy/trn. Sample voltage at particular rate, save sample using bit encoding Voltage levels still not kept perfectly But we can distinguish s from s Let bit encoding be: V: 2 V: 3 V: Digitized signal not perfect recreation, but higher sampling rate and more bits per encoding brings closer original signal time a2d digitized signal time d2a 3 2 received signal time How fix  higher, lower,? time Can fix  easily distinguish s and s, restore time 2
13 Encoding Text: ASCII, Unicode ASCII: 7 (or 8) bit encoding of each letter, number, or symbol Unicode: Increasingly popular 6bit bit encoding Encodes characters from various world languages S ymbol R S T L N E. <tab> En c oding S ymbol r s t l n e 9! <spa c e> En c oding What does this ASCII bit sequence represent? 3
14 Encoding Numbers Each position represents a quantity; symbol in position means how many of that quantity Base ten (decimal) Ten symbols:,, 2,..., 8, and 9 More than 9  next position So each position power of Nothing special about base  used because we have fingers Base two (binary) Two symbols: and More than  next position So each position power of
15 Bases Sixteen & Eight h e x bina r y 8 A F A F h e x 8 9 A B C D E F bina r y Base sixteen nice because each position represents four base two positions Used as compact means to write binary numbers Basic digits: 9, AF Known as hexadecimal, or just hex Base eight Used in some digital designs Each position represents three base two positions Basic digits: 7 Write in hex Write in octal 5
16 Sign and magnitude One bit dedicate to sign (positive or negative) sign: = positive (or zero), = negative Rest represent the absolute value or magnitude three low order bits: () thru 7 () Range for n bits +/ 2n (two representations for ) Cumbersome addition/subtraction must compare magnitudes to determine the sign of the result
17 2s complement If N is a positive number, then the negative of N (its 2s complement or N* ) is bitwise complement plus 7* is 7 : > + = (7) 7* is 7: > + = ( 7)
18 2s complement addition and subtraction
19 Detecting Overflow: Method Assuming 4bit two s complement numbers, one can detect overflow by detecting when the two numbers sign bits are the same but are different from the result s sign bit If the two numbers sign bits are different, overflow is impossible Adding a positive and negative can t exceed the largest magnitude positive or negative Simple circuit overflow = a3 b3 s3 + a3b3s3 sign bits overflow ( a ) overflow ( b ) no overflow ( c ) If the numbers sign bits have the same value, which differs from the result s sign bit, overflow has occurred. 9
20 Detecting Overflow: Method 2 Even simpler method: Detect difference between carryin to sign bit and carryout from sign bit Yields a simpler circuit: overflow = c3 xor c4 = c3 c4 + c3 c overflow ( a ) overflow ( b ) no overflow ( c ) If the carry into the sign bit column differs from the carry out of that column, overflow has occurred. 2
21 Multiplication of positive binary numbers Generalized representation of multiplication by hand 2
22 Division of positive binary numbers Repeated subtraction Set quotient to Repeat while dividend >= divisor Subtract divisor from dividend Add to quotient When dividend < divisor: Reminder = dividend Quotient is correct Example: Dividend: ; Divisor: Dividend Quotient
23 Summary of number representation Conversion between basis Decimal Binary Octal Hex Addition & subtraction in binary Overflow detection Multiplication Partial products For demo see: Division Repeated subtraction For demo see: 23
24 CSE4: Components and Design Techniques for Digital Systems Boolean algebra Tajana Simunic Rosing 24
25 B = {, } Variables represent or only Operators return or only Basic operators Boolean algebra is logical AND: a AND b returns only when both a= and b= + is logical OR: a OR b returns if either (or both) a= or b= is logical NOT: NOT a returns the opposite of a ( if a=, if a=) AND OR NOT a NOT BUF a a a b a b AND a+b a b OR a BUF Derived operators: NAND a b NAND NOR a b NOR XOR a b XOR XNOR a b XOR
26 Representations of Boolean Functions 2.6 English : F outputs when a is and b is, or when a is and b is. ( a ) Equation : F(a,b) = a b + a b Equation 2: F(a,b) = a ( b ) English 2: F outputs when a is, regardless of b s value a a b F b F ( c ) Circuit Truth table a F ( d ) Circuit 2 T he function F 26
27 Examples: Converting to Boolean Functions a Convert the following English statements to a function Q. answer is if a is and b is. Answer: F = Q2. answer is if either of a or b is. Answer: F = Q3. answer is if both a and b are not. Answer: F= Q4. answer is if a is and b is. Answer: F = 27
28 Example: Convert equation to logic gates More than one way to map expressions to gates e.g., Z = A B (C + D) = (A (B (C + D))) 28
29 Boolean Duality Derived by replacing by +, + by, by, and by & leaving variables unchanged Generalized duality: X + Y +... X Y... f (X,X 2,...,X n,,,+, ) f(x,x 2,...,X n,,,,+) Any theorem that can be proven is also proven for its dual! Note: this is NOT demorgan s Law 29
30 Boolean Axioms & Theorems
31 Boolean theorems of multiple variables
32 Proving theorems Using the axioms of Boolean algebra (or a truth table): e.g., prove the theorem: X Y + X Y = X distributivity X Y + X Y = X (Y + Y ) complementarity X (Y + Y ) = X () identity X () = X e.g., prove the theorem: X + X Y = X identity X + X Y = X + X Y distributivity X + X Y = X ( + Y) identity X ( + Y) = X () identity X () = X 32
33 Proving theorems example Prove the following using the laws of Boolean algebra: (X Y) + (Y Z) + (X Z) = X Y + X Z (X Y) + (Y Z) + (X Z) identity (X Y) + () (Y Z) + (X Z) complementarity (X Y) + (X + X) (Y Z) + (X Z) distributivity (X Y) + (X Y Z) + (X Y Z) + (X Z) commutativity (X Y) + (X Y Z) + (X Y Z) + (X Z) factoring (X Y) ( + Z) + (X Z) ( + Y) null (X Y) () + (X Z) () identity (X Y) + (X Z) 33
34 Proving theorems (perfect induction) Using perfect induction (complete truth table): e.g., de Morgan s: (X + Y) = X Y NOR is equivalent to AND with inputs complemented X Y X Y (X + Y) X Y (X Y) = X + Y NAND is equivalent to OR with inputs complemented X Y X Y (X Y) X + Y 34
35 Completeness of NAND Any logic function can be implemented using just NAND gates. Why? Boolean algebra: need AND, OR and NOT 35
36 F = X Y + Z Implement using only NAND 36
37 Completeness of NOR Any logic function can be implemented using just NOR gates. Boolean algebra needs AND, OR and NOT 37
38 Implement using only NOR F = X Y + Z 38
39 Combinational circuit building blocks: Transistors, gates and timing Tajana Simunic Rosing 4
40 Switches Electronic switches are the basis of binary digital circuits Electrical terminology Voltage: Difference in electric potential between two points Analogous to water pressure 4.5 A 9V A Current: Flow of charged particles 2 ohms Analogous to water flow Resistance: Tendency of wire to resist current flow V 9 V Analogous to water pipe diameter 4.5 A V = I * R (Ohm s Law) 4
41 CMOS circuit The CMOS Switches Consists of N and PMOS transistors Both N and PMOS are similar to basic switches Rp ~ 2 Rn => PMOS in series is much slower than NMOS nmos gate conducts does not conduct pmos gate Silicon  not quite a conductor or insulator: Semiconductor does not conduct conducts 42
42 Transistor Circuit Design nmos: pass s well, so connect source to GND pmos: pass s well, so connect source to V DD inputs pmos pullup network output nmos pulldown network
43 CMOS Gates: NOT Gate NOT V DD A Y = A A Y Y A P Y N GND A P N Y
44 CMOS Gates: NAND Gate A B NAND Y = AB Y A B Y P2 P Y A B N N2 A B P P2 N N2 Y
45 Three input NOR gate CMOS gate structure: Threeinput NOR inputs pmos pullup network output nmos pulldown network
46 Other CMOS Gates Building a twoinput AND gate
47 Transmission Gates nmos pass s poorly pmos pass s poorly Transmission gate is a better switch passes both and well When EN =, the switch is ON: EN = and A is connected to B When EN =, the switch is OFF: A is not connected to B A EN EN B
48 How to make CMOS gates 49
49 CMOS Example 5
50 A CMOS design example Implement F and F using CMOS: F=A*(B+C) 5
51 Resistivity CMOS delay: resistance Function of: resistivity r, thickness t : defined by technology Width W, length L: defined by designer Approximate ON transistor with a resistor R = r L/W L is usually minimum; change only W 52 Source: Prof. Subhashish Mitra
52 CMOS delay: capacitance & timing estimates Capacitor Stores charge Q = C V (capacitance C; voltage V) Current: dq/dt = C dv/dt Timing estimate D t = C dv/ i = C dv / (V/R trans ) = R trans C dv/v Delay: time to go from 5% to 5% of waveform Source: Prof. Subhashish Mitra 53
53 Charge/discharge in CMOS Calculate on resistance Calculate capacitance of the gates circuit is driving Get RC delay & use it as an estimate of circuit delay V out = V dd (  e t/rpc ) Rp ~ 2Rn 54 Source: Prof. Subhashish Mitra
54 Timing analysis: Inverter N O T x F x F x F = x 55
55 Timing analysis in gates x y F OR F x y AND F= x or y x y F y x y x x y F=x & y F x y F x y F
56 Power consumption in CMOS Power = Energy consumed per unit time Dynamic power consumption Static power consumption Dynamic power consumption: Power to charge transistor gate capacitances Energy required to charge a capacitance, C, to V DD is CV DD 2 Circuit running at frequency f: transistors switch (from to or vice versa) at that frequency Capacitor is charged f/2 times per second (discharging from to is free) P dynamic = ½CV DD2 f Static power consumption Power consumed when no gates are switching Caused by the leakage supply current, I DD : P static = I DD V DD
57 Power estimate example Estimate the power consumption of a tablet PC V DD =.2 V C = 2 nf f = GHz I DD = 2 ma P = ½CV DD2 f + I DD V DD = ½(2 nf)(.2 V) 2 ( GHz) + (2 ma)(.2 V) = 4.4 W
58 What we covered thus far: Summary Number representations Boolean algebra Switches, Logic gates How to build logic gates from CMOS transistors Timing and power estimates What is next: Combinatorial logic: Minimization Implementations 59
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 information1. 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 informationChapter 4. Gates and Circuits. Chapter Goals. Chapter Goals. Computers and Electricity. Computers and Electricity. Gates
Chapter Goals Chapter 4 Gates and Circuits Identify the basic gates and describe the behavior of each Describe how gates are implemented using transistors Combine basic gates into circuits Describe the
More informationInternational Journal of Electronics and Computer Science Engineering 1482
International Journal of Electronics and Computer Science Engineering 1482 Available Online at www.ijecse.org ISSN 22771956 Behavioral Analysis of Different ALU Architectures G.V.V.S.R.Krishna Assistant
More informationBinary Adder. sum of 2 binary numbers can be larger than either number need a carryout to store the overflow
Binary Addition single bit addition Binary Adder sum of 2 binary numbers can be larger than either number need a carryout to store the overflow HalfAdder 2 inputs (x and y) and 2 outputs (sum and carry)
More informationUnderstanding Logic Design
Understanding Logic Design ppendix of your Textbook does not have the needed background information. This document supplements it. When you write add DD R0, R1, R2, you imagine something like this: R1
More informationl What have discussed up until now & why: l C Programming language l More lowlevel then Java. l Better idea about what s really going on.
CS211 Computer Architecture l Topics Digital Logic l Transistors (Design & Types) l Logic Gates l Combinational Circuits l KMaps Class Checkpoint l What have discussed up until now & why: l C Programming
More informationToday 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/cgibin/caldwell/tutor/departments/math/graph/intro
More informationCSE140: 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 informationContent Map For Career & Technology
Content Strand: Applied Academics CTET11 analysis of electronic A. Fractions and decimals B. Powers of 10 and engineering notation C. Formula based problem solutions D. Powers and roots E. Linear equations
More informationDigital 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 informationEE360: 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 informationUpon 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 informationLab 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 informationW03 Analysis of DC Circuits. Yrd. Doç. Dr. Aytaç Gören
W03 Analysis of DC Circuits Yrd. Doç. Dr. Aytaç Gören ELK 2018  Contents W01 Basic Concepts in Electronics W02 AC to DC Conversion W03 Analysis of DC Circuits (self and condenser) W04 Transistors and
More informationEE 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 informationThe 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 informationExperiment 5. Arithmetic Logic Unit (ALU)
Experiment 5 Arithmetic Logic Unit (ALU) Objectives: To implement and test the circuits which constitute the arithmetic logic circuit (ALU). Background Information: The basic blocks of a computer are central
More informationELG3331: Lab 3 Digital Logic Circuits
ELG3331: Lab 3 Digital Logic Circuits What does Digital Means? Digital describes any system based on discontinuous data or events. Typically digital is computer data or electronic sampling of an analog
More informationBinary Adders: Half Adders and Full Adders
Binary Adders: Half Adders and Full Adders In this set of slides, we present the two basic types of adders: 1. Half adders, and 2. Full adders. Each type of adder functions to add two binary bits. In order
More informationLecture 8: Binary Multiplication & Division
Lecture 8: Binary Multiplication & Division Today s topics: Addition/Subtraction Multiplication Division Reminder: get started early on assignment 3 1 2 s Complement Signed Numbers two = 0 ten 0001 two
More informationExclusive OR/Exclusive NOR (XOR/XNOR)
Exclusive OR/Exclusive NOR (XOR/XNOR) XOR and XNOR are useful logic functions. Both have two or more inputs. The truth table for two inputs is shown at right. a XOR b = 1 if and only if (iff) a b. a XNOR
More informationECE 410: VLSI Design Course Introduction
ECE 410: VLSI Design Course Introduction Professor Andrew Mason Michigan State University Spring 2008 ECE 410, Prof. A. Mason Lecture Notes Page i.1 Age of electronics microcontrollers, DSPs, and other
More informationFundamentals of Microelectronics
Fundamentals of Microelectronics CH1 Why Microelectronics? CH2 Basic Physics of Semiconductors CH3 Diode Circuits CH4 Physics of Bipolar Transistors CH5 Bipolar Amplifiers CH6 Physics of MOS Transistors
More informationGates, Circuits and Boolean Functions
Lecture 2 Gates, Circuits and Boolean Functions DOC 112: Hardware Lecture 2 Slide 1 In this lecture we will: Introduce an electronic representation of Boolean operators called digital gates. Define a schematic
More informationELEC 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 IDL00 Bit
More informationChapter 6 Digital Arithmetic: Operations & Circuits
Chapter 6 Digital Arithmetic: Operations & Circuits Chapter 6 Objectives Selected areas covered in this chapter: Binary addition, subtraction, multiplication, division. Differences between binary addition
More informationDEGREE: Bachelor in Biomedical Engineering YEAR: 2 TERM: 2 WEEKLY PLANNING
SESSION WEEK COURSE: Electronic Technology in Biomedicine DEGREE: Bachelor in Biomedical Engineering YEAR: 2 TERM: 2 WEEKLY PLANNING DESCRIPTION GROUPS (mark X) SPECIAL ROOM FOR SESSION (Computer class
More informationBinary Numbers. Binary Octal Hexadecimal
Binary Numbers Binary Octal Hexadecimal Binary Numbers COUNTING SYSTEMS UNLIMITED... Since you have been using the 10 different digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 all your life, you may wonder how
More informationSECTION 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 informationDigital Systems. Syllabus 8/18/2010 1
Digital Systems Syllabus 1 Course Description: This course covers the design and implementation of digital systems. Topics include: combinational and sequential digital circuits, minimization methods,
More informationChapter 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 informationLet 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 informationCpE358/CS381. Switching Theory and Logical Design. Class 4
Switching Theory and Logical Design Class 4 1122 Today Fundamental concepts of digital systems (Mano Chapter 1) Binary codes, number systems, and arithmetic (Ch 1) Boolean algebra (Ch 2) Simplification
More informationDecimal Numbers: Base 10 Integer Numbers & Arithmetic
Decimal Numbers: Base 10 Integer Numbers & Arithmetic Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Example: 3271 = (3x10 3 ) + (2x10 2 ) + (7x10 1 )+(1x10 0 ) Ward 1 Ward 2 Numbers: positional notation Number
More informationBOOLEAN 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 informationGates & Boolean Algebra. Boolean Operators. Combinational Logic. Introduction
Introduction Gates & Boolean lgebra Boolean algebra: named after mathematician George Boole (85 864). 2valued algebra. digital circuit can have one of 2 values. Signal between and volt =, between 4 and
More informationPROGRAMMABLE LOGIC CONTROLLERS Unit code: A/601/1625 QCF level: 4 Credit value: 15 TUTORIAL OUTCOME 2 Part 3
UNIT 22: PROGRAMMABLE LOGIC CONTROLLERS Unit code: A/601/1625 QCF level: 4 Credit value: 15 TUTORIAL OUTCOME 2 Part 3 This work covers part of outcome 2 of the Edexcel standard module. The material is
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
CHAPTER3 QUESTIONS MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. ) If one input of an AND gate is LOW while the other is a clock signal, the output
More informationwhat operations can it perform? how does it perform them? on what kind of data? where are instructions and data stored?
Inside the CPU how does the CPU work? what operations can it perform? how does it perform them? on what kind of data? where are instructions and data stored? some short, boring programs to illustrate the
More informationLow Power VLSI Circuits and Systems Prof. Pro. Ajit Pal Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur
Low Power VLSI Circuits and Systems Prof. Pro. Ajit Pal Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Lecture No. # 14 Pass Transistor Logic Circuits  I Hello
More informationDiscrete 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 informationGates. J. Robert Jump Department of Electrical And Computer Engineering Rice University Houston, TX 77251
Gates J. Robert Jump Department of Electrical And Computer Engineering Rice University Houston, T 77251 1. The Evolution of Electronic Digital Devices...1 2. Logical Operations and the Behavior of Gates...2
More informationDigital Logic cct. Lec. (6)
THE NAND GATE The NAND gate is a popular logic element because it can be used as a universal gate: that is, NAND gates can be used in combination to perform the AND, OR, and inverter operations. The term
More informationCMOS, the Ideal Logic Family
CMOS, the Ideal Logic Family INTRODUCTION Let s talk about the characteristics of an ideal logic family. It should dissipate no power, have zero propagation delay, controlled rise and fall times, and have
More informationCS 16: Assembly Language Programming for the IBM PC and Compatibles
CS 16: Assembly Language Programming for the IBM PC and Compatibles First, a little about you Your name Have you ever worked with/used/played with assembly language? If so, talk about it Why are you taking
More informationLogic Gates & Operational Characteristics
Logic Gates & Operational Characteristics NOR Gate as a Universal Gate The NOR gate is also used as a Universal Gate as the NOR Gate can be used in a combination to perform the function of a AND, OR and
More informationJEFFERSON COLLEGE COURSE SYLLABUS ETC255 INTRODUCTION TO DIGITAL CIRCUITS. 4 Credit Hours. Prepared By: John McDaniel March 2012
JEFFERSON COLLEGE COURSE SYLLABUS ETC255 INTRODUCTION TO DIGITAL CIRCUITS 4 Credit Hours Prepared By: John McDaniel March 2012 Mary Beth Ottinger, Ph.D., Division Chair Dena McCaffrey, Ed.D., Interim Dean,
More informationBasics of Energy & Power Dissipation
Basics of Energy & Power Dissipation ecture notes S. Yalamanchili, S. Mukhopadhyay. A. Chowdhary Basic Concepts Dynamic power Static power Time, Energy, Power Tradeoffs Activity model for power estimation
More informationplc 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 informationFault Modeling. Why model faults? Some real defects in VLSI and PCB Common fault models Stuckat faults. Transistor faults Summary
Fault Modeling Why model faults? Some real defects in VLSI and PCB Common fault models Stuckat faults Single stuckat faults Fault equivalence Fault dominance and checkpoint theorem Classes of stuckat
More informationLecture N 1 PHYS 3330. Microcontrollers
Lecture N 1 PHYS 3330 Microcontrollers If you need more than a handful of logic gates to accomplish the task at hand, you likely should use a microcontroller instead of discrete logic gates 1. Microcontrollers
More informationCOURSE SYLLABUS. PREREQUISITES: Take CETT1303(41052); Minimum grade C, CR.
COURSE SYLLABUS COURSE NUMBER AND TITLE: CETT 1325 Digital Fundamentals COURSE (CATALOG) DESCRIPTION An entry level course in digital electronics covering number systems, binary mathematics, digital codes,
More informationDigital Integrated Circuits EECS 312
14 12 10 8 6 Fujitsu VP2000 IBM 3090S Pulsar 4 IBM 3090 IBM RY6 CDC Cyber 205 IBM 4381 IBM RY4 2 IBM 3081 Apache Fujitsu M380 IBM 370 Merced IBM 360 IBM 3033 Vacuum Pentium II(DSIP) 0 1950 1960 1970 1980
More informationReadonly 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 Readonly memory Implementing logic with ROM Programmable logic
More informationDigital 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 Email: siddika.ors@itu.edu.tr Grading 1st Midterm 
More informationEE 42/100 Lecture 24: Latches and Flip Flops. Rev B 4/21/2010 (2:04 PM) Prof. Ali M. Niknejad
A. M. Niknejad University of California, Berkeley EE 100 / 42 Lecture 24 p. 1/20 EE 42/100 Lecture 24: Latches and Flip Flops ELECTRONICS Rev B 4/21/2010 (2:04 PM) Prof. Ali M. Niknejad University of California,
More informationLecture 2. Binary and Hexadecimal Numbers
Lecture 2 Binary and Hexadecimal Numbers Purpose: Review binary and hexadecimal number representations Convert directly from one base to another base Review addition and subtraction in binary representations
More informationTwolevel logic using NAND gates
CSE140: Components and Design Techniques for Digital Systems Two and Multilevel logic implementation Tajana Simunic Rosing 1 Twolevel logic using NND gates Replace minterm ND gates with NND gates Place
More informationC H A P T E R 14. CMOS Digital Logic Circuits
C H A P T E R 14 CMOS Digital Logic Circuits Introduction CMOS is by far the most popular technology for the implementation of digital systems. The small size, ease of fabrication, and low power consumption
More informationChapter # 5: Arithmetic Circuits
Chapter # 5: rithmetic Circuits Contemporary Logic Design 5 Number ystems Representation of Negative Numbers Representation of positive numbers same in most systems Major differences are in how negative
More informationMODULE 13  INTERFACING THE ANALOG WORLD TO DIGITAL CIRCUITS
Introduction to Digital Electronic Design Module 13, Interfacing Analog to Digital Circuits 1 MODULE 13  INTERFACING THE ANALOG WORLD TO DIGITAL CIRCUITS OVERVIEW: Digital circuits require the input signal
More informationNEW 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 floatingpoint unit and for address generation in case of cache
More informationHere we introduced (1) basic circuit for logic and (2)recent nanodevices, and presented (3) some practical issues on nanodevices.
Outline Here we introduced () basic circuit for logic and (2)recent nanodevices, and presented (3) some practical issues on nanodevices. Circuit Logic Gate A logic gate is an elemantary building block
More informationDigital Logic: Boolean Algebra and Gates
Digital Logic: Boolean Algebra and Gates Textbook Chapter 3 CMPE2 Summer 28 Basic Logic Gates CMPE2 Summer 28 Slides by ADB 2 Truth Table The most basic representation of a logic function Lists the output
More informationLecture 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 informationCapacitors and RC Circuits
Chapter 6 Capacitors and RC Circuits Up until now, we have analyzed circuits that do not change with time. In other words, these circuits have no dynamic elements. When the behavior of all elements is
More informationDigital Fundamentals
Digital Fundamentals Tenth Edition Floyd Chapter 1 2009 Pearson Education, Upper 2008 Pearson Saddle River, Education NJ 07458. All Rights Reserved Analog Quantities Most natural quantities that we see
More informationFORDHAM UNIVERSITY CISC 3593. Dept. of Computer and Info. Science Spring, 2011. Lab 2. The FullAdder
FORDHAM UNIVERSITY CISC 3593 Fordham College Lincoln Center Computer Organization Dept. of Computer and Info. Science Spring, 2011 Lab 2 The FullAdder 1 Introduction In this lab, the student will construct
More informationBinary Division. Decimal Division. Hardware for Binary Division. Simple 16bit Divider Circuit
Decimal Division Remember 4th grade long division? 43 // quotient 12 521 // divisor dividend 480 4136 5 // remainder Shift divisor left (multiply by 10) until MSB lines up with dividend s Repeat until
More informationPhysics 219 Fall, 2005 LabNotes 11 Combinational Logic. Table of Contents
Physics 219 Fall, 2005 LabNotes 11 Combinational Logic Table of Contents Friday, December 2... 2 Digital uilding locks... 2 Combinational Logic... 3 n example of combinational logic: car s warning buzzer...
More informationGRADE 11A: Physics 5. UNIT 11AP.5 6 hours. Electronic devices. Resources. About this unit. Previous learning. Expectations
GRADE 11A: Physics 5 Electronic devices UNIT 11AP.5 6 hours About this unit This unit is the fifth of seven units on physics for Grade 11 advanced. The unit is designed to guide your planning and teaching
More informationMachine Architecture and Number Systems. Major Computer Components. Schematic Diagram of a Computer. The CPU. The Bus. Main Memory.
1 Topics Machine Architecture and Number Systems Major Computer Components Bits, Bytes, and Words The Decimal Number System The Binary Number System Converting from Decimal to Binary Major Computer Components
More information6 3 4 9 = 6 10 + 3 10 + 4 10 + 9 10
Lesson The Binary Number System. Why Binary? The number system that you are familiar with, that you use every day, is the decimal number system, also commonly referred to as the base system. When you
More informationDigital Electronics Part I Combinational and Sequential Logic. Dr. I. J. Wassell
Digital Electronics Part I Combinational and Sequential Logic Dr. I. J. Wassell Introduction Aims To familiarise students with Combinational logic circuits Sequential logic circuits How digital logic gates
More informationModule 3 Digital Gates and Combinational Logic
Introduction to Digital Electronics, Module 3: Digital Gates and Combinational Logic 1 Module 3 Digital Gates and Combinational Logic INTRODUCTION: The principles behind digital electronics were developed
More informationCHAPTER 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 informationChapter 1: Digital Systems and Binary Numbers
Chapter 1: Digital Systems and Binary Numbers Digital age and information age Digital computers general purposes many scientific, industrial and commercial applications Digital systems telephone switching
More informationData Storage 3.1. Foundations of Computer Science Cengage Learning
3 Data Storage 3.1 Foundations of Computer Science Cengage Learning Objectives After studying this chapter, the student should be able to: List five different data types used in a computer. Describe how
More informationA 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. Accumulatorbased 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 informationLevent EREN levent.eren@ieu.edu.tr A306 Office Phone:4889882 INTRODUCTION TO DIGITAL LOGIC
Levent EREN levent.eren@ieu.edu.tr A306 Office Phone:4889882 1 Number Systems Representation Positive radix, positional number systems A number with radix r is represented by a string of digits: A n
More information2011, The McGrawHill Companies, Inc. Chapter 3
Chapter 3 3.1 Decimal System The radix or base of a number system determines the total number of different symbols or digits used by that system. The decimal system has a base of 10 with the digits 0 through
More informationChapter 10 Advanced CMOS Circuits
Transmission Gates Chapter 10 Advanced CMOS Circuits NMOS Transmission Gate The active pullup inverter circuit leads one to thinking about alternate uses of NMOS devices. Consider the circuit shown in
More informationBinary. ! You are probably familiar with decimal
Arithmetic operations in assembly language Prof. Gustavo Alonso Computer Science Department ETH Zürich alonso@inf.ethz.ch http://www.inf.ethz.ch/department/is/iks/ Binary! You are probably familiar with
More informationSection 1.4 Place Value Systems of Numeration in Other Bases
Section.4 Place Value Systems of Numeration in Other Bases Other Bases The HinduArabic system that is used in most of the world today is a positional value system with a base of ten. The simplest reason
More informationCPEN 214  Digital Logic Design Binary Systems
CPEN 4  Digital Logic Design Binary Systems C. Gerousis Digital Design 3 rd Ed., Mano Prentice Hall Digital vs. Analog An analog system has continuous range of values A mercury thermometer Vinyl records
More information9 2339A The Three Basics of Electric Circuits: Voltage, Current, and Resistance
PROGRESS RECORD Study your lessons in the order listed below. Electronics Technology and Advanced Troubleshooting I & II Number of Lessons: 118 Completion Time: 36 months 1 2330A Current and Voltage 2
More informationUniversity of St. Thomas ENGR 230  Digital Design 4 Credit Course Monday, Wednesday, Friday from 1:35 p.m. to 2:40 p.m. Lecture: Room OWS LL54
Fall 2005 Instructor Texts University of St. Thomas ENGR 230  Digital Design 4 Credit Course Monday, Wednesday, Friday from 1:35 p.m. to 2:40 p.m. Lecture: Room OWS LL54 Lab: Section 1: OSS LL14 Tuesday
More informationBinary Representation. Number Systems. Base 10, Base 2, Base 16. Positional Notation. Conversion of Any Base to Decimal.
Binary Representation The basis of all digital data is binary representation. Binary  means two 1, 0 True, False Hot, Cold On, Off We must be able to handle more than just values for real world problems
More informationData Storage. Chapter 3. Objectives. 31 Data Types. Data Inside the Computer. After studying this chapter, students should be able to:
Chapter 3 Data Storage Objectives After studying this chapter, students should be able to: List five different data types used in a computer. Describe how integers are stored in a computer. Describe how
More informationSystem on Chip Design. Michael Nydegger
Short Questions, 26. February 2015 What is meant by the term nwell process? What does this mean for the ntype MOSFETs in your design? What is the meaning of the threshold voltage (practically)? What
More informationStudy Guide for the Electronics Technician PreEmployment Examination
Bay Area Rapid Transit District Study Guide for the Electronics Technician PreEmployment Examination INTRODUCTION The Bay Area Rapid Transit (BART) District makes extensive use of electronics technology
More informationELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, OAKLAND UNIVERSITY ECE470/570: MicroprocessorBased System Design Fall 2014.
REVIEW OF NUMBER SYSTEMS Notes Unit 2 BINARY NUMBER SYSTEM In the decimal system, a decimal digit can take values from to 9. For the binary system, the counterpart of the decimal digit is the binary digit,
More informationChapter 2 Logic Gates and Introduction to Computer Architecture
Chapter 2 Logic Gates and Introduction to Computer Architecture 2.1 Introduction The basic components of an Integrated Circuit (IC) is logic gates which made of transistors, in digital system there are
More informationIntroduction. Logic. Most Difficult Reading Topics. Basic Logic Gates Truth Tables Logical Functions. COMP370 Introduction to Computer Architecture
Introduction LOGIC GATES COMP370 Introduction to Computer Architecture Basic Logic Gates Truth Tables Logical Functions Truth Tables Logical Expression Graphical l Form Most Difficult Reading Topics Logic
More informationDecimal Number (base 10) Binary Number (base 2)
LECTURE 5. BINARY COUNTER Before starting with counters there is some vital information that needs to be understood. The most important is the fact that since the outputs of a digital chip can only be
More informationOct: 50 8 = 6 (r = 2) 6 8 = 0 (r = 6) Writing the remainders in reverse order we get: (50) 10 = (62) 8
ECE Department Summer LECTURE #5: Number Systems EEL : Digital Logic and Computer Systems Based on lecture notes by Dr. Eric M. Schwartz Decimal Number System: Our standard number system is base, also
More informationBase Conversion written by Cathy Saxton
Base Conversion written by Cathy Saxton 1. Base 10 In base 10, the digits, from right to left, specify the 1 s, 10 s, 100 s, 1000 s, etc. These are powers of 10 (10 x ): 10 0 = 1, 10 1 = 10, 10 2 = 100,
More informationNumber Systems, Base Conversions, and Computer Data Representation
, Base Conversions, and Computer Data Representation Decimal and Binary Numbers When we write decimal (base 10) numbers, we use a positional notation system. Each digit is multiplied by an appropriate
More informationBasic 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