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Lessons In Electric Circuits Volume IV Digital,By Tony R Kuphaldt. Fourth Edition last update November 01 2007,2000 2015 Tony R Kuphaldt. This book is published under the terms and conditions of the Design Science License These. terms and conditions allow for free copying distribution and or modification of this document. by the general public The full Design Science License text is included in the last chapter. As an open and collaboratively developed text this book is distributed in the hope that. it will be useful but WITHOUT ANY WARRANTY without even the implied warranty of. MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE See the Design Science. License for more details, Available in its entirety as part of the Open Book Project collection at. openbookproject net electricCircuits,PRINTING HISTORY. First Edition Printed in June of 2000 Plain ASCII illustrations for universal computer. readability, Second Edition Printed in September of 2000 Illustrations reworked in standard graphic.

eps and jpeg format Source files translated to Texinfo format for easy online and printed. publication, Third Edition Printed in February 2001 Source files translated to SubML format. SubML is a simple markup language designed to easily convert to other markups like. LATEX HTML or DocBook using nothing but search and replace substitutions. Fourth Edition Printed in March 2002 Additions and improvements to 3rd edition. 1 NUMERATION SYSTEMS 1,1 1 Numbers and symbols 1,1 2 Systems of numeration 6. 1 3 Decimal versus binary numeration 8,1 4 Octal and hexadecimal numeration 10. 1 5 Octal and hexadecimal to decimal conversion 12. 1 6 Conversion from decimal numeration 13,2 BINARY ARITHMETIC 19. 2 1 Numbers versus numeration 19,2 2 Binary addition 20.

2 3 Negative binary numbers 20,2 4 Subtraction 23,2 5 Overflow 25. 2 6 Bit groupings 27,3 LOGIC GATES 29,3 1 Digital signals and gates 30. 3 2 The NOT gate 33,3 3 The buffer gate 45,3 4 Multiple input gates 48. 3 5 TTL NAND and AND gates 60,3 6 TTL NOR and OR gates 65. 3 7 CMOS gate circuitry 68,3 8 Special output gates 81.

3 9 Gate universality 85,3 10 Logic signal voltage levels 90. 3 11 DIP gate packaging 100,3 12 Contributors 102,4 SWITCHES 103. 4 1 Switch types 103,4 2 Switch contact design 108. 4 3 Contact normal state and make break sequence 111. iv CONTENTS,4 4 Contact bounce 116,5 ELECTROMECHANICAL RELAYS 119. 5 1 Relay construction 119,5 2 Contactors 122,5 3 Time delay relays 126.

5 4 Protective relays 132,5 5 Solid state relays 133. 6 LADDER LOGIC 135,6 1 Ladder diagrams 135,6 2 Digital logic functions 139. 6 3 Permissive and interlock circuits 144,6 4 Motor control circuits 147. 6 5 Fail safe design 150,6 6 Programmable logic controllers 154. 6 7 Contributors 171,7 BOOLEAN ALGEBRA 173,7 1 Introduction 173.

7 2 Boolean arithmetic 175,7 3 Boolean algebraic identities 178. 7 4 Boolean algebraic properties 181,7 5 Boolean rules for simplification 184. 7 6 Circuit simplification examples 187,7 7 The Exclusive OR function 192. 7 8 DeMorgan s Theorems 193, 7 9 Converting truth tables into Boolean expressions 200. 8 KARNAUGH MAPPING 219,8 1 Introduction 219,8 2 Venn diagrams and sets 220.

8 3 Boolean Relationships on Venn Diagrams 223, 8 4 Making a Venn diagram look like a Karnaugh map 228. 8 5 Karnaugh maps truth tables and Boolean expressions 231. 8 6 Logic simplification with Karnaugh maps 238,8 7 Larger 4 variable Karnaugh maps 245. 8 8 Minterm vs maxterm solution 249,8 9 sum and product notation 261. 8 10 Don t care cells in the Karnaugh map 262,8 11 Larger 5 6 variable Karnaugh maps 265. 9 COMBINATIONAL LOGIC FUNCTIONS 273,9 1 Introduction 273.

9 2 A Half Adder 274,9 3 A Full Adder 275,CONTENTS v. 9 4 Decoder 282,9 5 Encoder 286,9 6 Demultiplexers 290. 9 7 Multiplexers 293,9 8 Using multiple combinational circuits 295. 10 MULTIVIBRATORS 299,10 1 Digital logic with feedback 299. 10 2 The S R latch 303,10 3 The gated S R latch 307.

10 4 The D latch 308,10 5 Edge triggered latches Flip Flops 310. 10 6 The J K flip flop 315,10 7 Asynchronous flip flop inputs 317. 10 8 Monostable multivibrators 319,11 SEQUENTIAL CIRCUITS 323. 11 1 Binary count sequence 323,11 2 Asynchronous counters 325. 11 3 Synchronous counters 332,11 4 Counter modulus 338.

11 5 Finite State Machines 338,Bibliography 347,12 SHIFT REGISTERS 349. 12 1 Introduction 349,12 2 Serial in serial out shift register 352. 12 3 Parallel in serial out shift register 361,12 4 Serial in parallel out shift register 372. 12 5 Parallel in parallel out universal shift register 381. 12 6 Ring counters 392,12 7 references 405,13 DIGITAL ANALOG CONVERSION 407. 13 1 Introduction 407,13 2 The R 2n R DAC 409,13 3 The R 2R DAC 412.

13 4 Flash ADC 414,13 5 Digital ramp ADC 417,13 6 Successive approximation ADC 419. 13 7 Tracking ADC 421,13 8 Slope integrating ADC 422. 13 9 Delta Sigma ADC 425,13 10Practical considerations of ADC circuits 427. vi CONTENTS,14 DIGITAL COMMUNICATION 433,14 1 Introduction 433. 14 2 Networks and busses 437,14 3 Data flow 441,14 4 Electrical signal types 442.

14 5 Optical data communication 446,14 6 Network topology 448. 14 7 Network protocols 450,14 8 Practical considerations 453. 15 DIGITAL STORAGE MEMORY 455,15 1 Why digital 455. 15 2 Digital memory terms and concepts 456,15 3 Modern nonmechanical memory 458. 15 4 Historical nonmechanical memory technologies 460. 15 5 Read only memory 466,15 6 Memory with moving parts Drives 467.

16 PRINCIPLES OF DIGITAL COMPUTING 471,16 1 A binary adder 471. 16 2 Look up tables 472,16 3 Finite state machines 477. 16 4 Microprocessors 481,16 5 Microprocessor programming 484. A 1 ABOUT THIS BOOK 487,A 2 CONTRIBUTOR LIST 493,A 3 DESIGN SCIENCE LICENSE 497. NUMERATION SYSTEMS,1 1 Numbers and symbols 1,1 2 Systems of numeration 6.

1 3 Decimal versus binary numeration 8,1 4 Octal and hexadecimal numeration 10. 1 5 Octal and hexadecimal to decimal conversion 12. 1 6 Conversion from decimal numeration 13, There are three types of people those who can count and those who can t. 1 1 Numbers and symbols, The expression of numerical quantities is something we tend to take for granted This is both. a good and a bad thing in the study of electronics It is good in that we re accustomed to. the use and manipulation of numbers for the many calculations used in analyzing electronic. circuits On the other hand the particular system of notation we ve been taught from grade. school onward is not the system used internally in modern electronic computing devices and. learning any different system of notation requires some re examination of deeply ingrained. assumptions, First we have to distinguish the difference between numbers and the symbols we use to. represent numbers A number is a mathematical quantity usually correlated in electronics to. a physical quantity such as voltage current or resistance There are many different types of. numbers Here are just a few types for example,WHOLE NUMBERS.

1 2 3 4 5 6 7 8 9,2 CHAPTER 1 NUMERATION SYSTEMS,4 3 2 1 0 1 2 3 4. IRRATIONAL NUMBERS,approx 3 1415927 e approx 2 718281828. square root of any prime,REAL NUMBERS, All one dimensional numerical values negative and positive. including zero whole integer and irrational numbers. COMPLEX NUMBERS,3 j4 34 5 6 20o, Different types of numbers find different application in the physical world Whole numbers. work well for counting discrete objects such as the number of resistors in a circuit Integers. are needed when negative equivalents of whole numbers are required Irrational numbers are. numbers that cannot be exactly expressed as the ratio of two integers and the ratio of a perfect. circle s circumference to its diameter is a good physical example of this The non integer. quantities of voltage current and resistance that we re used to dealing with in DC circuits can. be expressed as real numbers in either fractional or decimal form For AC circuit analysis. however real numbers fail to capture the dual essence of magnitude and phase angle and so. we turn to the use of complex numbers in either rectangular or polar form. If we are to use numbers to understand processes in the physical world make scientific. predictions or balance our checkbooks we must have a way of symbolically denoting them. In other words we may know how much money we have in our checking account but to keep. record of it we need to have some system worked out to symbolize that quantity on paper or in. some other kind of form for record keeping and tracking There are two basic ways we can do. this analog and digital With analog representation the quantity is symbolized in a way that. is infinitely divisible With digital representation the quantity is symbolized in a way that is. discretely packaged, You re probably already familiar with an analog representation of money and didn t realize.

it for what it was Have you ever seen a fund raising poster made with a picture of a ther. mometer on it where the height of the red column indicated the amount of money collected for. the cause The more money collected the taller the column of red ink on the poster. 1 1 NUMBERS AND SYMBOLS 3,An analog representation. of a numerical quantity, This is an example of an analog representation of a number There is no real limit to how. finely divided the height of that column can be made to symbolize the amount of money in the. account Changing the height of that column is something that can be done without changing. the essential nature of what it is Length is a physical quantity that can be divided as small. as you would like with no practical limit The slide rule is a mechanical device that uses the. very same physical quantity length to represent numbers and to help perform arithmetical. operations with two or more numbers at a time It too is an analog device. On the other hand a digital representation of that same monetary figure written with. standard symbols sometimes called ciphers looks like this. Unlike the thermometer poster with its red column those symbolic characters above can. not be finely divided that particular combination of ciphers stand for one quantity and one. quantity only If more money is added to the account 40 12 different symbols must be. used to represent the new balance 35 995 50 or at least the same symbols arranged in dif. ferent patterns This is an example of digital representation The counterpart to the slide rule. analog is also a digital device the abacus with beads that are moved back and forth on rods. to symbolize numerical quantities,4 CHAPTER 1 NUMERATION SYSTEMS. Slide rule an analog device,Numerical quantities are represented by. the positioning of the slide,Abacus a digital device.

Numerical quantities are represented by,the discrete positions of the beads. Let s contrast these two methods of numerical representation. ANALOG DIGITAL, Intuitively understood Requires training to interpret. Infinitely divisible Discrete,Prone to errors of precision Absolute precision. Interpretation of numerical symbols is something we tend to take for granted because it. has been taught to us for many years However if you were to try to communicate a quantity. of something to a person ignorant of decimal numerals that person could still understand the. simple thermometer chart, The infinitely divisible vs discrete and precision comparisons are really flip sides of the. same coin The fact that digital representation is composed of individual discrete symbols. decimal digits and abacus beads necessarily means that it will be able to symbolize quantities. in precise steps On the other hand an analog representation such as a slide rule s length. is not composed of individual steps but rather a continuous range of motion The ability. for a slide rule to characterize a numerical quantity to infinite resolution is a trade off for. imprecision If a slide rule is bumped an error will be introduced into the representation of. 1 1 NUMBERS AND SYMBOLS 5, the number that was entered into it However an abacus must be bumped much harder.

before its beads are completely dislodged from their places sufficient to represent a different. Please don t misunderstand this difference in precision by thinking that digital represen. tation is necessarily more accurate than analog Just because a clock is digital doesn t mean. that it will always read time more accurately than an analog clock it just means that the. interpretation of its display is less ambiguous, Divisibility of analog versus digital representation can be further illuminated by talking. about the representation of irrational numbers Numbers such as are called irrational be. cause they cannot be exactly expressed as the fraction of integers or whole numbers Although. you might have learned in the past that the fraction 22 7 can be used for in calculations this. is just an approximation The actual number pi cannot be exactly expressed by any finite or. limited number of decimal places The digits of go on forever. 3 1415926535897932384, It is possible at least theoretically to set a slide rule or even a thermometer column so

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