Berkeley ELENG 40 - Lecture 35 (16 pages)

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Lecture 35



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Lecture 35

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16
School:
University of California, Berkeley
Course:
Eleng 40 - Introduction to Microelectronic Circuits
Introduction to Microelectronic Circuits Documents
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EE40 Lecture 35 Prof Chang Hasnain 12 5 07 Reading Ch 7 Supplementary Reader EE40 Fall 2006 Slide 1 Prof Chang Hasnain Week 15 OUTLINE Need for Input Controlled Pull Up CMOS Inverter Analysis CMOS Voltage Transfer Characteristic Combinatorial logic circuits Logic Binary representations Combinatorial logic circuits Reading Chap 7 7 5 Supplementary Notes Chapter 4 EE40 Fall 2006 Slide 2 Prof Chang Hasnain 1 Digital Circuits Introduction Analog signal amplitude is continuous with time Digital signal amplitude is represented by a restricted set of discrete numbers Binary only two values are allowed to represent the signal High or low i e logic 1 or 0 Digital word Each binary digit is called a bit A series of bits form a word Byte is a word consisting of 8 bits Advantages of digital signal Digital signal is more resilient to noise can more easily differentiate high 1 and low 0 Transmission Parallel transmission over a bus containing n wires Faster but short distance internal to a computer or chip Serial transmission transmit bits sequentially Longer distance EE40 Fall 2006 Slide 3 Prof Chang Hasnain 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 A D digital to analog D A conversion is essential and nothing new think of a piano keyboard EE40 Fall 2006 Slide 4 Prof Chang Hasnain 2 Analog Signal Example Microphone Voltage Voltage with normal piano key stroke Voltage with soft pedal applied 25 microvolt 440 Hz signal 60 40 20 0 20 0 1 2 3 4 5 6 7 8 9 10 11 12 40 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 EE40 Fall 2006 Slide 5 Prof Chang Hasnain 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 EE40 Fall 2006 Slide 6 Prof Chang Hasnain 3 Decimal Numbers Base 10 Digits 0 1 2 3 4 5 6 7 8 9 Example 3271 3x103 2x102 7x101 1x100 This is a four digit number The left hand most number 3 in this example is often referred as the most significant number and the right most the least significant number 1 in this example EE40 Fall 2006 Slide 7 Prof Chang Hasnain Numbers positional notation Number Base B B symbols per digit Base 10 Decimal Base 2 Binary 0 1 2 3 4 5 6 7 8 9 0 1 Number representation d31d30 d1d0 is a 32 digit number value d31 B31 d30 B30 d1 B1 d0 B0 Binary 0 1 In binary digits called bits 11010 1 24 1 23 0 22 1 21 0 20 16 8 2 26 Here 5 digit binary turns into a 2 digit decimal EE40 Fall 2006 Slide 8 Prof Chang Hasnain 4 Hexadecimal Numbers Base 16 Hexadecimal 0 1 2 3 4 5 6 7 8 9 A B C D E F Normal digits 6 more from the alphabet Conversion Binary Hex 1 hex digit represents 16 decimal values 4 binary digits represent 16 decimal values 1 hex digit replaces 4 binary digits EE40 Fall 2006 Slide 9 Prof Chang Hasnain 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 V and minimum of 0 V 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 EE40 Fall 2006 Slide 10 Prof Chang Hasnain 5 Resolution The size of the smallest element that can be separated from neighboring elements The term is used to describe imaging systems the frequency separation achieved by spectrometers and so on EE40 Fall 2006 Slide 11 Prof Chang Hasnain Decimal Binary Conversion Decimal to Binary Repeated Division By 2 Consider the number 2671 Subtraction if you know your 2N values by heart Binary to Decimal conversion 1100012 1x25 1x24 0x23 0x22 0x21 1x20 3210 1610 110 4910 4x101 9x100 EE40 Fall 2006 Slide 12 Prof Chang Hasnain 6 Example 2 continued Possible digital representation for the sine wave signal 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 EE40 Fall 2006 Slide 13 Prof Chang Hasnain Binary Representation N bit can represent 2N values typically from 0 to 2N 1 3 bit word can represent 8 values e g 0 1 2 3 4 5 6 7 Conversion Integer to binary Fraction to binary 13 510 1101 12 and 0 39210 0 0110012 Octal and hexadecimal EE40 Fall 2006 Slide 14 Prof Chang Hasnain 7 Logic gates Combine several logic variable inputs to produce a logic variable output Memory Memoryless output at a given instant depends the input values of that instant Momory output depends on previous and present input values EE40 Fall 2006 Slide 15 Prof Chang Hasnain Boolean algebras Algebraic structures capture the essence of the logical operations AND OR and NOT corresponding set for theoretic operations intersection union and complement named after George Boole an English mathematician at University College Cork who first defined them as part of a system of logic in the mid 19th century Boolean algebra was an attempt to use algebraic techniques to deal with expressions in the propositional calculus Today Boolean algebras find many applications in electronic design They were first applied to switching by Claude Shannon in the 20th century EE40 Fall 2006 Slide 16 Prof Chang Hasnain 8 Boolean algebras The operators of Boolean algebra may be represented in various ways Often they are simply written as AND OR and NOT In describing circuits NAND NOT AND NOR NOT OR and XOR eXclusive OR may also be used Mathematicians often use for OR and for AND since in some ways …


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