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1Lecture 1, Slide 1EECS40, Fall 2003 Prof. KingLecture #1OUTLINE• Course overview• Introduction: integrated circuits• Analog vs. digital signalsLecture 1, Slide 2EECS40, Fall 2003 Prof. KingEECS 40:• One of five EECS core courses (with 20, 61A, 61B, and 61C) introduces “hardware” side of EECS prerequisite for EE105, EE130, EE141, EE150• Prerequisites: Math 1B, Physics 7BCourse content: • Electric circuits• Integrated-circuit devices and technology• CMOS digital integrated circuitsCourse Overview2Lecture 1, Slide 3EECS40, Fall 2003 Prof. KingIC Technology Advancement“Moore’s Law”: # of transistors/chip doubles every 1.5-2 years– achieved through miniaturizationTechnology ScalingInvestmentBetter Performance/CostMarket GrowthLecture 1, Slide 4EECS40, Fall 2003 Prof. KingGeneration:Intel386™ DXProcessorIntel486™ DXProcessorPentium®ProcessorPentium®II Processor1.5µ 1.0µ 0.8µ 0.6µ 0.35µ 0.25µBenefit of Transistor Scalingsmaller chip area Æ lower costmore functionality on a chip Æ better system performance3Lecture 1, Slide 5EECS40, Fall 2003 Prof. KingÆ Analog-to-digital & digital-to-analog conversion is essential (and nothing new)think of a piano keyboard• Most (but not all) observables are analogthink of analog vs. digital watchesbut the most convenient way to represent & transmit information electronically is to use digital signalsthink of telephonyAnalog vs. Digital SignalsLecture 1, Slide 6EECS40, Fall 2003 Prof. KingAnalog Signals• may have direct relationship to information presented• in simple cases, are waveforms of information vs. time• in more complex cases, may have information modulated on a carrier, e.g. AM or FM radioAmplitude Modulated Signal-1-0.8-0.6-0.4-0.200.20.40.60.810 5 10 15 20 25 30 35 40 45 50Time in microsecondsSignal in microvolts4Lecture 1, Slide 7EECS40, Fall 2003 Prof. KingVoltage with normal piano key stroke Voltage with soft pedal applied50 microvolt 220 Hz signal-60-40-2002040600123456789101112t in millisecondsV in microvolts50 microvolt 440 Hz signal-60-40-2002040600123456789101112t in millisecondsV in microvolts25 microvolt 440 Hz signal-60-40-2002040600123456789101112t in millisecondsV in microvoltsAnalog Signal Example: Microphone Voltage Analog signal representing piano key A, below middle C (220 Hz)Lecture 1, Slide 8EECS40, Fall 2003 Prof. KingDigital Signal RepresentationsBinary numbers can be used to represent any quantity.We generally have to agree on some sort of “code”, and the dynamic range of the signal in order to know the form and the number of binary digits (“bits”) required. Example 1: Voltage signal with maximum value 2 Volts• Binary two (10) could represent a 2 Volt signal.• To encode the signal to an accuracy of 1 part in 64 (1.5% precision), 6 binary digits (“bits”) are neededExample 2: Sine wave signal of known frequency and maximum amplitude 50 µV; 1 µV “resolution” needed.5Lecture 1, Slide 9EECS40, Fall 2003 Prof. KingPossible digital representation for the sine wave signal:Analog representation: Digital representation:Amplitude in µVBinary number1 0000012 0000103 0000114 0001005 0001018 00100016 01000032 10000050 11001063 111111Example 2 (continued)Lecture 1, Slide 10EECS40, Fall 2003 Prof. KingWhy Digital?(For example, why CDROM audio vs. vinyl recordings?)• Digital signals can be transmitted, received, amplified, and re-transmitted with no degradation.• Digital information is easily and inexpensively stored (in RAM, ROM, etc.), with arbitrary accuracy.• Complex logical functions are easily expressed as binary functions (e.g. in control applications).• Digital signals are easy to manipulate (as we shall see).6Lecture 1, Slide 11EECS40, Fall 2003 Prof. KingDigital signals offer an easy way to perform logical functions, using Boolean algebra.• Variables have two possible values: “true” or “false”– usually represented by 1 and 0, respectively.All modern control systems use this approach.Example: Hot tub controller with the following algorithmTurn on the heater if the temperature is less than desired (T < Tset) and the motor is on and the key switch to activate the hot tub is closed. Suppose there is also a “test switch” which can be used to activate the heater.Digital Representations of Logical FunctionsLecture 1, Slide 12EECS40, Fall 2003 Prof. King• Series-connected switches:A = thermostatic switchB = relay, closed if motor is onC = key switch• Test switch T used to bypass switches A, B, and CSimple Schematic Diagram of Possible Circuit110VHeaterCBATHot Tub Controller Example7Lecture 1, Slide 13EECS40, Fall 2003 Prof. KingABCTH00000001000100001100100001010011000111010001100111010110111110011101111101111111“Truth Table” for Hot Tub ControllerLecture 1, Slide 14EECS40, Fall 2003 Prof. KingBasic logical functions:AND: “dot” Example: X = A·BOR: “+ sign” Example: Y = A+BNOT: “bar over symbol” Example: Z = A¾ Any logical expression can be constructed using these basic logical functionsAdditional logical functions:Inverted AND = NAND:Inverted OR = NOR:Exclusive OR:Notation for Logical Expressions)1 and when 0ly (o AB =BAn)0BA when1ly n(o BA ==+BA BA i.e., differ)BA,when1(only BA⋅+⊕exceptThe most frequently used logical functions are implemented as electronic building blocks called “gates” in integrated circuits8Lecture 1, Slide 15EECS40, Fall 2003 Prof. KingFirst define logical values:• closed switch = “true”, i.e. boolean 1 • open switch = “false”, i.e. boolean 0Logical Statement:Heater is on (H = 1) if A and B and C are 1, or if T is 1.Logical Expression:H=1 if (A and B and C are 1) or (T is 1)Boolean Expression:H = (A · B · C ) + THot Tub Controller Example (cont’d)Lecture 1, Slide 16EECS40, Fall 2003 Prof. KingAttributes of digital electronic systems:1. Ability to represent real quantities by coding information in digital form2. Ability to control a system by manipulation and evaluation of binary variables using Boolean


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