Lecture 1 OUTLINE Course overview Introduction integrated circuits Analog vs digital signals EECS40 Fall 2003 Lecture 1 Slide 1 Prof King Course Overview EECS 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 7B Course content Electric circuits Integrated circuit devices and technology CMOS digital integrated circuits EECS40 Fall 2003 Lecture 1 Slide 2 Prof King 1 IC Technology Advancement Moore s Law of transistors chip doubles every 1 5 2 years achieved through miniaturization Technology Scaling Investment Better Performance Cost Market Growth EECS40 Fall 2003 Lecture 1 Slide 3 Prof King Benefit of Transistor Scaling Generation 1 5 Intel386 DX Processor 1 0 0 8 0 6 0 35 0 25 smaller chip area lower cost Intel486 DX Processor Pentium Processor Pentium II Processor more functionality on a chip better system performance EECS40 Fall 2003 Lecture 1 Slide 4 Prof King 2 Analog vs Digital Signals Most but not all observables are analog think of analog vs digital watches but the most convenient way to represent transmit information electronically is to use digital signals think of telephony Analog to digital digital to analog conversion is essential and nothing new think of a piano keyboard EECS40 Fall 2003 Lecture 1 Slide 5 Prof King Analog 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 radio A m p litu d e M o d u la te d S ig n a l 1 0 8 Signal in microvolts 0 6 0 4 0 2 0 0 2 0 5 10 15 20 25 30 35 40 45 50 0 4 0 6 0 8 1 T im e in m ic ro s e c o n d s EECS40 Fall 2003 Lecture 1 Slide 6 Prof King 3 Analog Signal Example Microphone Voltage Voltage with normal piano key stroke Voltage with soft pedal applied 60 40 20 0 20 0 1 2 3 4 5 6 7 8 9 10 11 12 40 25 microvolt 440 Hz signal V in microvolts V in microvolts 50 microvolt 440 Hz signal 60 40 20 0 20 0 1 2 3 4 5 6 7 8 9 10 11 12 40 60 60 t in milliseconds t in milliseconds V in microvolts 50 microvolt 220 Hz signal 60 40 20 0 20 0 1 2 3 4 5 6 7 8 9 10 11 12 Analog signal representing piano key A below middle C 220 Hz 40 60 t in milliseconds EECS40 Fall 2003 Lecture 1 Slide 7 Prof King Digital Signal Representations Binary 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 needed Example 2 Sine wave signal of known frequency and maximum amplitude 50 V 1 V resolution needed EECS40 Fall 2003 Lecture 1 Slide 8 Prof King 4 Example 2 continued Possible digital representation for the sine wave signal EECS40 Fall 2003 Analog representation Amplitude in V 1 2 3 4 5 Digital representation Binary number 000001 000010 000011 000100 000101 8 001000 16 010000 32 100000 50 110010 63 111111 Lecture 1 Slide 9 Prof King Why 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 EECS40 Fall 2003 Lecture 1 Slide 10 Prof King 5 Digital Representations of Logical Functions Digital 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 algorithm Turn 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 EECS40 Fall 2003 Lecture 1 Slide 11 Prof King Hot Tub Controller Example Series connected switches A thermostatic switch B relay closed if motor is on C key switch Test switch T used to bypass switches A B and C Simple Schematic Diagram of Possible Circuit C 110V EECS40 Fall 2003 B T Lecture 1 Slide 12 A Heater Prof King 6 Truth Table for Hot Tub Controller A 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 EECS40 Fall 2003 C 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 T 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 H 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 Lecture 1 Slide 13 Prof King Notation for Logical Expressions Basic logical functions AND dot Example X A B OR NOT sign bar over symbol Example Y A B Example Z A Any logical expression can be constructed using these basic logical functions Additional logical functions Inverted AND NAND Inverted OR NOR Exclusive OR AB only 0 when A and B 1 A B only 1 when A B 0 A B only 1 when A B differ i e A B except A B The most frequently used logical functions are implemented as electronic building blocks called gates in integrated circuits EECS40 Fall 2003 Lecture 1 Slide 14 Prof King 7 Hot Tub Controller Example cont d First define logical values closed switch true i e boolean 1 open switch false i e boolean 0 Logical 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 T EECS40 Fall 2003 Lecture 1 Slide 15 Prof King Summary Attributes of digital electronic systems 1 Ability to represent real quantities by coding information in digital form 2 Ability to control a system by manipulation and evaluation of binary variables using Boolean algebra EECS40 Fall 2003 Lecture 1 Slide 16 Prof King 8
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