I
`
`II
`
`|
`
`H
`
`I]
`
`I
`
`II_,I»I
`
`I
`
`II
`
`II
`
`DIGITAL DESIGN
`
`
`
`Skyworks Ex. 2005
`
`Kinetic V. Skyworks
`Case IPR2014—00529
`
`Page 1
`
`Skyworks Ex. 2005
` Kinetic v. Skyworks
` Case IPR2014-00529
`
`

`

`Page 2
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`Page 2
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`

`

`DIGITAL DESK-l!
`
`THIRD EDITION
`
`M. Morris Mano
`CALIFORNIA STATE UNIVERSITK LOS ANGELES
`
`Prentice
`Hall
`
`____,__————.____
`
`Prentice HaII
`
`Upper Saddle River, N] 0?453
`
`Page 3
`
`Page 3
`
`

`

`Library of Congress Cataloging-in-Publication Data
`CIP Data on file,
`
`Vice President and Editorial Director. ECS: Marcia J. Hurlon
`Publisher: Tom Robbin:
`'
`
`Acquisitions Editor: Eric Frank
`Editorial Assistant: Jessica Romeo
`
`Vice President and Director of Production and Manufacturing, ESM: David W. Riccurdi
`Executive Managing Editor: Vince O'Brien
`Managing Editor: David A. George
`Production Editor: Lakshmi Balasubramanian
`
`Director of Creative Services: Paul Belfanti
`Creative Director: Carole AHJOII
`Art Director and Cover Designer: Jonathan Boy/rm
`An Editor: Adam Vehhau:
`Manufacturing Manager: Trudy Piscioni
`Manufacturing Buyer: Lisa McD0well
`Marketing Manager: Holly Stark
`Marketing Assistant: Karen Moon
`
`Prentice
`Hall
`
`
`
`© 2002, 1991, 1984 by Prentice-Hall, Inc.
`Pearson Education
`Upper Saddle River, New Jersey 07458
`
`All rights reserved. No part of this book may be reproduced, in any form or by any means,
`without permission in writing from the publisher.
`
`Verilogger Pro and SynapLiCAD are trademarks of SynaptiCAD, lnc,, Blacksburg. VA 240624608.
`
`Printed in the United States of America
`
`10987654321
`
`ISBN 0-13-062121—8
`
`Prentice—Hall International (UK) Limited, London
`Prentice-Hall of Australia Pty. Limited, Sydney
`Prentice-Hall of Canada, Inc, Toronto
`Prentice-Hall Hispanoamericana, S. A., Mexico City
`Prentice—Hal] of India Private Limited, New Delhi
`Prentice—Hall of Japan, lnc., Tokyo
`Pearson Asia Pte. Ltd, Singapore
`Editora Prentice—Hall do Brasil, Ltda” Rio tie laneiro
`
`Page 4
`
`Page 4
`
`

`

`To My Wife, Cthren, and. Grandchildren
`
`Page 5
`
`Page 5
`
`

`

`Page 6
`
`Page 6
`
`

`

`
`
`CONTENTS
`
`P R E F A C E
`
`ix
`
`1
`BINARY SYSTEMS
`i
`
`
`1+1
`1-2
`1-3
`
`14
`1 5
`1-6
`1-?
`‘l-B
`L9
`
`Digital Systems
`Binary Numbers
`Number Base Conversions
`
`Octal and Hexadecimal Numbers
`Complements
`Signed BinaryP Numbers
`Binary Codes
`Binary Storage and Registers
`Binary Logic
`
`i
`3
`5
`
`7
`9
`l3
`l6
`24
`2?
`
`2
`BOOLEAN ALGEBRA AND LOGIC GATES
`33
`
`
`2:1
`2-2
`2-3
`
`2'4
`2:5
`243
`2-?
`2-8
`
`Basic Definitions
`Axiomatic Definition of Boolean Algebra
`Basic Theorems and ProperLies
`of Boolean Algebra
`Boolean Functions
`Canonical and Standard Forms
`Other Logic Operations
`Digital Logic GaLes
`IntegraLed Circuits
`
`33
`34
`
`3.7
`40
`44
`51
`54
`59
`
`Page 7
`
`Page 7
`
`

`

`vi
`
`Contents
`
`
`
` 3 GATE-LEVEL MlNlMlZATlON 64
`
`
`
`3—1
`3-2
`3-3
`3-4
`3-5
`3—6
`3—7
`3-8
`3—9
`
`The Map Method
`Four-Variable Map
`Five-Variable Map
`Product of Sums Simplification
`Don’t-Care Conditions
`NAND and NOR Implementation
`Other Two-Level Implementations
`Exclusive—OR Function
`Hardware Description Language (HDL)
`
`4
`
`COMBINATIONAL LOGIC
`
`4-1
`4—2
`4-3
`4—4
`4—5
`4—6
`4—7
`4—8
`
`4—9
`4-70
`4-17
`
`Combinational Circuits
`Analysis Procedure
`Design Procedure
`Binary Adder-Subtractor
`Decimal Adder
`Binary Multiplier
`Magnitude Comparator
`Decoders
`
`Encoders
`Multiplexers
`HDL For Combinational Circuits
`
`64
`70
`74
`76
`80
`82
`89
`94
`99
`
`777
`7 72
`775
`7 79
`729
`737
`733
`734
`
`739
`747
`747
`
`777
`
`5
`
`SYNCHRONOUS SEQUENTIAL LOGIC
`
`767
`
`5-1
`5-2
`5-3
`5-4
`5-5
`5-6
`5—7
`
`Sequential Circuits
`Latches
`Flip-Flops
`Analysis of Clocked Sequential Circuits
`HDL For Sequential Circuits
`State Reduction and Assignment
`Design Procedure
`
`6
`
`REGISTERS AND COUNTERS
`
`6-1
`6-2
`6—3
`6-4
`6—5
`6-6
`
`Registers
`Shift Registers
`Ripple Counters
`Synchronous Counters
`Other Counters
`HDL for Registers and Counters
`
`767
`769
`772
`780
`790
`798
`203
`
`2 7 7
`279
`227
`232
`239
`244
`
`277
`
`Page 8
`
`Page 8
`
`

`

`7
`MEMORY AND PROGRAMMABLE LOGIC
`2.55
`
`
`Contents
`
`on
`
`3-1
`?—2
`?-3
`L4
`?-5
`?—6
`It?
`?-B
`
`Introduction
`Randomdnccess Memory
`Memory Decoding
`£rror Detection and Correction
`Read-Only Memoryr
`Programmable Logic. Array
`Programmable Array Logic
`Sequential Programmable Devices
`
`8
`
`REGISTER TRANSFER LEVEL
`
`3—1
`3-2
`3-3
`8-4
`8-5
`8-6
`3—?
`843
`3-9
`
`Register Transfer Level (RTL) Notation
`Register Transfer Level in HDL
`Algorithmic State Machines {ASM}
`Design Example
`HDL Description of Design Example
`Binary Multiplier
`Control Logic
`HDL Descrilflxrion of Binary Multiplier
`Design Wit Multiplexers
`
`255
`256
`262
`:6?
`220
`2?6
`280
`283
`
`29?
`293
`299
`304
`310
`3??
`3'21
`326
`32-9
`
`29?
`
`9
`ASYNCHRONOUS SEQUENTIAL LOGIC
`342
`
`
`9-1
`9-2
`9-3
`9-4
`9-5
`9-6
`9-?
`9-3
`
`Introduction
`Analysis Procedure
`Circuits With Latches
`Design Procedure
`Reduction of State and Flow Tables
`I'laceFree State Assignment
`Hazards
`Design Example
`
`342
`344
`352
`360
`35?
`334
`3 79
`384
`
`IO DIGITAL INTEGRATED CIRCUITS
`393
`
`
`10-1
`10-2
`10-3
`10-4
`“LS
`1045
`10-?
`10—8
`
`Introduction
`Special Characteristics
`Bipolar-Transistor Cl’iaracteristics
`HTL and DTL Circuits
`Transistor-Transistor Logic ("i—TL)
`Emitter-Coopied logic (LCL)
`MetaLCixide Semiconductor (MOS)
`Console:nentaryr MOS (CMOS)
`
`3 98
`400
`404
`403
`410
`430
`42I
`423
`
`Page 9
`
`Page 9
`
`

`

`viii
`
`Contents
`
`10-9
`10—10
`
`CMOS Transmission Gate Circuits
`Switch—Lever Modeling With HDL
`
`427
`430
`
`11
`LABORATORY EXPERIMENTS
`437
`
`
`11-0
`11—1
`11-2
`11-3
`11-4
`
`Introduction to Experiments
`Binary and Decimal Numbers
`Digital Logic Gates
`Simplification of Boolean Functions
`Combinational Circuits
`
`11-5
`Code Converters
`11-6
`Design with Multiplexers
`11-7
`Adders and Subtractors
`11—8
`Flip-flops
`11-9
`Sequential Circuits
`11-10
`Counters
`11-11
`Shift Registers
`11—12
`Serial Addition
`11-13 Memory Unit
`11-14
`Lamp Handball
`11-15
`Clock-Pulse Generator
`
`11-16
`
`Parallel Adder and Accumulator
`
`Binary Multiplier
`11-17
`11-18 Asynchronous Sequential Circuits
`11-19
`Verilog HDL Simulation Experiments
`
`12
`
`STANDARD GRAPHIC SYMBOLS
`
`12-1
`12—2
`12-3
`12-4
`12-5
`12-6
`12-7
`12-8
`
`Rectangular-Shape Symbols
`Qualifying Symbols
`Dependency Notation
`Symbols For Combinational Elements
`Symbols For Flip-Flops
`Symbols For Registers
`Symbols For Counters
`Symbol For RAM
`
`ANSWERS TO SELECTED PROBLEMS
`
`l N D E X
`
`437
`442
`445
`446
`448
`
`450
`452
`453
`456
`458
`460
`467
`465
`465
`467
`477
`
`473
`
`475
`478
`478
`
`482
`485
`487
`489
`49?
`493
`496
`498
`
`
`
`482
`
`501
`
`51 1
`
`Page 10
`
`Page 10
`
`

`

`
`
`PREFACE
`
`Digital design is. concerned wtth tlte. deatgn tti digilui cleettunte ctmuite. Utgitrti eircutts ure
`empleyed In the tiestgn 11nd cnttetrut'tien tti systems such 'd-tt digital eemeutets. dnte cent—
`tnnrtierttien. rligttnl reenrrling. ttnti men}! ether ulrpiictttiune tlntl reunite digital hardware.
`Tltig. iJUIJk In'eeente the hnsic tenls t'er tlte deeign ul'dieitul eheults nntl pmvider. the funde-
`nientnt concepts used in the design 111‘ digital Syfiiiflmi
`It
`is fitttltthit: [er use 11:: e textbeek in
`en ttttreductery eettrtte itt
`.111 eleett'ieni engineering. entrtltttter engineering: m" computer
`ficiullct; curriculum.
`
`Merry n1" the hammer; in this third editittn remeitt lite ttutne rut tittitte of the itret'tetts editiutte
`wicrttl let
`tenrrnngement iii" the rnrtteriu] ur elturtgtet 'tu cutttltneut dtte tn changes in the tech
`nelegy. Centhituttienei circuits are ClWflIL‘Li in em: eletptet instentl nf tree. as in the previeus edia
`tree. The mittenttui L‘tt‘L‘tlil chapter empltusiree dceign wttlt H I'Iiii-littpe itetteed c-f .Ht’ und 3!?
`Hui-three. The materiel en nterner'ir end pregretntttnhle legit: ttrr. entuht'ned in em: ehnpter.
`Clutptet 3 line heet‘t revised tn include register-trundle level t'l-iTLJ destgu prtreedurett.
`'l'lte ntnin t'evittien in the third editiuu is the illt‘itthlfll'l nt‘ eeettens en 1it'eriltrglitrrt.it.~r'.trt: DI:-
`ect'ttrttntt Lengttnge t i ITJL t. ”The [ID]. ntuterittl IH ittetrt ted ttt eepnrete settintttt ran it can he cur-
`ererl er skipped mt desired. The preeentutien is. at :1 attlt-ui'tle Ie'trel l'nr beginning Siudeute than are
`Jettt'tttrtg digital circuits and ii hardware dcseriptlen lenguttge nt the same time.
`
`- Miguel circuits. are intt'tJ-dttced itt Chapters.
`HiJL in SEetittn 3 9.
`
`1 ilttuttglt
`
`.4 with en intreductitttt tu Vet'ileg
`
`- Further diseuxeiun el' Hill. neeurs tn Sectien 4» i] l'ullewintt the study e-f centbinetien-
`ul circttiLe.
`
`- Settuenltul t-trettitr. ere entered in Chapters 5 tutti ft with ltt'tl'rfl‘iptilttiillg H DL ettztrttpiee
`ll1 Seettene Fifi- :tnd fi-h.
`
`- The NHL deecriutiuu ul' tttetttut y 11'. presented in Sectittn T-E
`
`In
`
`Page 11
`
`Page 11
`
`

`

`X
`
`Preface
`
`- The RTL symbols used in Verilog HDL are introduced in Sections 8-2.
`. Examples of HDL descriptiOns in the RTL and structural levels are provided in Sections
`8-5 and 8-8.
`
`. Section 10-10 covers switch-level modeling corresponding to CMOS circuits.
`
`- Section 11-19 supplements the hardware experiments of Chapter ll with HDL experi—
`ments. Now the circuits designed in the laboratory can be checked by means of hardware
`components and/or by HDL simulation.
`
`The CD-ROM in the back of the book contains the Verilog HDL source code files for the
`examples in the book and two simulators provided by SynaptiCAD. The first simulator is Ver-
`iLogger Pro, a traditional Verilog simulator that can be used to simulate the HDL examples in
`the book and to verify the solutions of HDL problems. The Second is a new type of simulation
`technology, called an Interactive Simulator. This simulator allows engineers to simulate and an-
`alyze design ideas before a complete simulatiori model or schematic is available. This tech-
`nology is particularly useful for students, because they can quickly enter Boolean and D flip-flop
`or latch input equations to check equivalency or to experiment with flip-flops and latch de-
`signs. Thtorials are available as HTML files in the CD—ROM Flash display and as MS Word
`files in the SynaptiCAD installed directory under Book Tutorials.
`Additional resources are available in a companion Website at http/Iwww. prenhallcom/mano.
`It includes all the Verilog HDL examples from the book for downloading, all of the figures
`and tables in the book in PDF format, tutorials on the use of the Verilog software in the
`CD-ROM, and more.
`
`The following is a brief description of the topics that are covered in each chapter with em-
`phasis on the revisions that were made for the third edition.
`Chapter 1 presents the various binary systems suitable for representing information in dig—
`ital systems. The binary number system is explained and binary codes are illustrated. Exam-
`ples are given for addition and subtraction of signed binary numbers and decimal numbers in
`BCD.
`
`Chapter 2 introduces the basic postulates of Boolean algebra and shows the correlation be-
`tween Boolean expressions and their corresponding 'logic diagrams. All possible logic opera-
`tions for two variables are investigated and from that, the most useful logic gates used in the
`design of digital systems are determined. The characteristics of integrated circuit gates are
`mentioned in this chapter but a more detailed analysis of the electronic circuits of the gates is
`done in Chapter 10.
`Chapter 3 covers the map method for simplifying Boolean expressions. The map method
`is also used to simplify digital circuits constructed with AND-OR, NAND, or NOR gates. All
`other possible two-level gate circuits are considered and their method of implementation is ex-
`plained. Verilog HDL is introduced together with simple gate-level modeling examples.
`Chapter 4 outlines the formal procedures for the analysis and design of cornbi national cir—
`cuits. Some basic components used in the design of digital systems, such as adders and code
`converters, are introduced as design examples. Frequently u5ed digital logic functions such as
`parallel adder and subtractor, decoders, encoders, and multiplexers are explained, and their use
`in the design of combinational circuits is illustrated. HDL examples are given in the gate-level,
`dataflow, and behavioral modeling to show the alternative ways available for describing com-
`
`Page 12
`
`Page 12
`
`

`

`Preiace
`
`rd
`
`htttulinnttl circuits in Verilttg HDL. Tlte precedent Ier writing a simple test Ltettelt lu ptttyide
`stittttrlns tn an HDL design is presented.
`Chapter 5 nutiiaes the feudal pretcdtttes fer the analysis and design ttl' eleeltcd syltcitra—
`anus sequential circuiLs. The gate structure at several types of maritime; is presented ingether
`with n thstutssiuu tl-l'l the tlil'l'ctence between level and edge triggering. Spceilic esumples nae
`used in shuts the dedicated til the state rattle and state diagram when analysing a sequential cir-
`cuit. It ttttnthet ul' design esaaiples are presented with emphasis Ill] scepter-ital circuits that use
`ill-type I‘ltprl'lups. itchayteral mudeling in Verilug IlDl. liar sequet‘tlial circuits is explained.
`l-IDL Fistutuiles are aired in illustrate Meaty and Maura medals at seijncatlul circuits.
`Chapter ti deals with yarinus sequential circuits cutnlmucnts such as meislc-rs. shill regis-
`ters. and cheaters. These digital cumiinncnts ice the heart: building hlaclts titan which man:
`ctrmplcs digital systems an: cunslructed- llDL dcsenptians nl' shift registers rant caunter are
`presented.
`Chapter '1 deals with reads-at access inentury {RAM} and prugrammuhle legic devices.
`Mammy dethrding and cle‘ currectinn schemes are discussed. Cumhittatiertal and sequential
`programmable devices are presented such its. RUM. PAL. tiPLD. and ill-Tia.
`Chapter it deals with the register u'ansl'cr level [RTIJ representation at digital systems.
`The ulguritlintie state machine thSMi chart ls intretluced. A at iflli'ler ul‘ examples demonstrate
`the use til' the ASM chart. RTL reprcscatttt inn. and HDL dcserictlen in the design at digital sys-
`tems. This chapter is the meat itnpurtant chapter in the heat: as it prepares the student fur nut-re
`advanced design prejeets.
`Chapter "1 presents l'nrrnal procedures tier the analysis and design tif asyuehreaees se-
`quential circuits. Medtads are nntltncd ta shun Iltlw an asynchruneus sequential circuit can he
`littplementetl as u cmnhinatinnal circuit with feedback. An alternate itnnlerneatatian is alse dc~
`scrihed that uses SR latches as the sturege elements in asyaclntinuus sequential circuits.
`Chapter Ill presents the mast curarnuu integrated circuit digital Ingic lint-lilies. ‘I.'he clcctmnic
`circuits at‘ the channel: gate in each family is analysed using electrical circuit them y. A haste
`attuwledge ef clcettcnic circuits is necessary in l'ully understattcl the material in this chaptec
`Hitanatles el’iilertlag dWilElirlth'tl dcscriptiuns demunstrute the ability In simulate. circuits cea—
`stttteled with MUS and CMDR n’atta‘isturs.
`
`Chapter It eutliacs experiments that can he nerl’nrmed in the luheratary with htudwate
`that is readily available cummeiclally. The nperaticn til the integrated circuits used in the es-
`netlutcnts is captained try referring tu diagntms al similar cnaipnneuts inmtducci'l ta prcyiuus
`chapters. [inch experiment is presented infttl‘l'l‘lttily and the student is expected ta [tirrdnce the
`circuit diagatm and t'amiulste a pits-came far checking the utterance ultlte circuit tn the lab»
`shinny. The last sectiuu supplements the experiments with currcsptattling llDL experiments.
`instead Inf. er in tulliiliuu tn. the hardware causttttetiua. the student can use the ‘dealer; HDL
`sul‘twstc prayidcd en the CD—ttt that it: simulate and check the design
`Chapter II pies-elite the amhdnnl graphic synthnls i'ur legic t'nnetltiuu rectttamentled hy nu
`ANSlllEEE standard. These graphic symhets have hecu develuped l‘cr SS] and MS] cecapn-
`uents su that'the user can recugnirc each l‘unctiuu hunt the unique graphic synthni assigned.
`“the chapter shares the standard graphic cymbals ed the integrated circuit-t used in mi; taham-
`nary earmriments. The yttrietut digital cutapenents that are represented thrtrugltrnn the hunk arc
`lilt‘tltltlt' tu cammercial integrated circtuts. ltaweyer. the rest dccs nut meatiurt s1tit~c|tie intcgnded
`
`Page 13
`
`Page 13
`
`

`

`xii
`
`Preface
`
`circuits except in Chapters 1 1 and 12. The practical application of digital design will be en-
`hanced by doing the suggested experiments in Chapter ll while studying the theory present—
`ed in the text.
`.
`
`Each chapter has a list of references and a set of problems. Answers to selected problems
`appear in at the end of the book to aid the student and to help the independent reader. A solu—
`tions manual is available for the instructor from the publisher.
`I would like to thank Charles Kime for introducing me to Verilog. My greatest thanks go to
`Jack Levine for guiding me and checking the sections, examples, and problem solutions to all
`Verilog I-IDL material. Thanks go to Tom Robbins for helping me decide to write the third edi-
`tion and my editor Eric Frank for his patience throughout the revision. Appreciation goes to Gay
`Covington and Donna Mitchell for providing the CD-ROM from SynaptiCad. Thanks also to
`those who reviewed the third edition: Thomas G. Johnson, California State University; Umit
`Uyar, City University ofNew York; Thomas L. Drake, Clemson. University; and Richard Molyet,
`University of Toledo. Finally, I am grateful to my Wife Sandra for encouraging me to pursue
`this project.
`
`M. MORRIS MANO
`
`Page 14
`
`Page 14
`
`

`

`
`
`Binary Systems
`
`'l-‘l DIGITAL SYSTEMS
`
`Digital systems have such a {treatment telv in everyday life that We refer tn the present Ieeh-
`uulegieal period as the digital age. Digital systems are used in camrnanieatiaa. husiness trans-
`aetiuns. traffic central. space guideline. medical hairline-tit. WEIlll'ltfl' meditating. the interest, and
`many atlier eaiumereiat, iailastn'ai. and scientific enterprises. We have digital Ielepliaaes. dig-
`ital televisian. digital versatile discs. digital cameras. and n1' ceiirse. digital eamputers. The
`must striking property nf the digital eninpaler is its generality. lt ean feilaw a sequence (ii iii-
`slrueliuns. called a Fragrant. thst nus-tales eti given data. The user can specify and change Ila-
`pragram a: the data according m the specific new. Because ui' this fiesihi lity. general-namese
`dig‘ital cemputers can perlflrrn a variety dl tn [nt'ntatien pracessing tasks that range ever a wide
`spectrum of applicatieits.
`Cine characteristic ul' digital systems is their ability to manipulate discrete elettieuts at in-
`lermatiun. i'tuy set that is t'estrietetl tn a finite titltiiher ul' elements euntains diserete internin-
`Iiea. Examples at discrete sets are. the It;I decimal digits. the 26; letters aidie alphabet. the 5?.
`playing cards. and the I54 squares at a ehesshaard. Early digital eatnpaters were used fer na-
`rnerit: chmputatiuns. in this case. the diset'ete elements used Were the digits. Frnrn tltis appli-
`eatien. Lhe tern: digitiii cent-[utter emerged. Discrete elements at infarniatinn are represented
`iii-a. digital system by physical quantitles ealieil signals. Electrical signals such as vtiltages and
`eurruuts ate the must cnmmnu. Hlectmnie devises ettlled transislurs predutnitiate in the dir-
`ettiti'y that implements these signals, The signals it: tttust pteseut~dtiy eleetrunit' digital sys-
`tems use just iwa discrete values and ans tlierci'ute said In he bitten: A. hinary digit. ealled a
`bit. has two values: it and I. Discrete elements at ial'arrnatiaa are represented with grasps ai'
`hits milled hittnrv suites. Far example. the I'leeiutal ti igils l] through 9 are represented in a dig—
`ital system with a cutie Inf fear hits. Hy using vai'ieus techniques. groans af‘ hits can he made
`
`Page 15
`
`Page 15
`
`

`

`Chapter 1
`
`Binary Systems
`
`to represent discrete symbols, which are then used to develop the system in a digital format.
`Thus, a digital system is_a system that manipulates discrete elements of information that is
`represented internally in binary form.
`Discrete quantities of information either emerge from the nature of the data being processed
`or may be quantized from a continuous process. For example, a payroll schedule is an inher—
`ently disorete process that contains employee names, social security numbers, weekly salaries,
`income taxes, and so on. An employee’s paycheck is processed using discrete data values such
`as letters of the alphabet (names), digits (salary), and Special symbols (such as 55). On the other
`hand, a research scientist may observe a continuous process, but record only specific quanti-
`ties in tabular form. The scientist is thus quantizing his continuous data, making each number
`in his table a discrete quantity. In many cases, the quantization of a process can be performed
`automatically by an analog—to-digital converter.
`The general—purpose digital computer is the best-known example of a digital system. The
`major parts of a computer are a memory unit, a central processing unit, and input-output units.
`The memory unit stores programs as well as input, output, and intermediate data. The central
`processing unit performs arithmetic and other data processing operations as specified by the pro-
`gram. The program and data prepared by a user are transferred into memory by means of an
`input device such as a keyboard. An output device, such as a printer, receives the results of the
`computations and the printed results are presented to the user. A digital computer can accom-
`modate many input and output devices. One very useful device is a communication unit that
`provides interaction with other users through the Internet. A digital computer is a powerful in-
`strument and can perform not only arithmetic computations, but also logical operations. In ad-
`dition, it can be programmed to make decisions based on internal and external conditions.
`There are fundamental reasons why commercial products are made with digital circuits.
`Like a digital computer, most digital devices are programmable. By changing the program in
`a programmable device, the same underlying hardware can be used for many different appli-
`cations. Dramatic cost reductions in digital devices have come about because of the advances
`in digital integrated circuit technology. As the number of transistors that can be put on a piece
`
`of silicon increases to produce complex functions, the cost per unit decreases and digital de-
`vices can be bought at an increasingly reduced price. Equipment built with digital integrated
`circuits can perform at a speed of hundreds of millions of Operations per second. Digital sys-
`tems can be made to operate with extreme reliability by using error-correcting codes. An ex-
`ample of' this is the digital versatile disk (DVD) in which digital information representing video,
`audio, and other data is recorded without a loss of a single item. Digital information on a DVD
`is recorded in such a way that by examining the code in each digital sample before it is played
`back, any error can be automatically identified and corrected.
`A digital system is an interconnection of digital modules. To understand the operation of each
`digital module, it is necessary to have a basic knowledge of digital circuits and their logical func-
`tion. The first seven chapters of this book present the basic tools of digital design such as logic
`gate structures, combinational and sequential circuits, and programmable logic devices. Chap-
`ter 8 introduces digital design at the register transfer level (RTL). Chapters 9 and 10 deal with
`asynchronous sequential circuits and the various integrated digital logic families. Chapters 11
`and 12 introduce commercial integrated circuits and show how they can be connected in the
`laboratOry to perform experiments with digital circuits.
`
`Page 16
`
`Page 16
`
`

`

`Section 1-2 Binary Numbers
`
`3
`
`Au itnpurtaut trend in digital design is the use at hardware description language t'HDLt.
`HI 3].. resembles a prugramming language and is suitable l'ur describing digital circuits in test—
`tuul term. It is used to simulate a digital system to verify its uperatiun befnre. hardware is built
`in. it is tthu used in conjunction with lngic synthesis reels tn auttnnate the design. “[1]. tier
`scriptiuas uf digital circuits an: presented throughput the bunk.
`As preyiuusly stated. digital systems manipulate discrete qunnlltiee ul' iiti'urtnatiun that are
`tuptttetenieti in binary term. Upctaads used but calculations may be expressed in the binary
`number system. tit-her disctete elements. including the decimal digits. an; represented in binary
`etsJes. Data preccssing is carried uttt by means at binary iugir elements using binary signals.
`Quantities are stated in binary sturagc clentcnls.'i'i1e purpose ul' this chapter is tu lntruduee tlte
`variuus binary cmtccpl‘i as a it'atuc ui' tefertntee Fur Further study in the succeeding chapters.
`
`
`
`1—2 BINi’tRY NUMBERS
`
`A decimal number such as 1392 represents a quantity equal in T tttuusituds plus 3 hundredt-h
`plus 9 lens. plus 2 units. The tltettsands. hundreds. etc. are pnwets ef iii impiied by the parti-
`tum ut‘ the cueffieiene. in he mute esact. 1391‘! should be written as
`
`is. tu-‘+ss- ttF+as til' +2 it
`
`in“
`
`Huwever. the enttventiun is in write euly lite euelficiettts and item their pusitiun deduce the
`Iieeeiiettt'y puwets ui' li'l. in general. a number with a decimal pntul is represented by a series
`nt enciiicicttts as fullness:
`
`H5fl¢£laflifllfln " I'J- IflLIILs
`
`'i'he u, ceci'iicicnts are any of the ill digits lfl. 1.2 ..... ii}. and the subscript value t gives the
`place 1trttlue and. hence. the pnwer nl‘ Ill by which the euefficient must be multiplied. This can
`he. ex pressed as
`
`lusts. + Ie‘in -|
`
`iu-‘ej + Inlay + tu'e1 + tailsu + lil'e . + urine: + Itr'a__.
`
`'l'l'te. decimal number system is said in be (if mate. er radix. Iii because it been ill digits and
`the cuelflctents are multiplied by nuwet's ul' Iii. The bunny system is a different number sys-
`tem. 'l'be euetficicuts ct” the binary anmbets system have enly twn pussible values: ii er l
`. Each
`cneti'icieut tiJ is multiplied by 23. Fur example. the decitnai equivalent at the l'ulltfl’y number
`5 ”Hill I
`is. Eli-.15. as sltuwa item the tnnltipltealinn ul'tbe cuei'i'teients by passes at it:
`
`Issl+lxsJ l us22+txr+us1i+ts2"+t ss"i=st~.-.'!5
`
`in general. a number expressed in a base“:- systettt has cuci’flciettts multiplied by puwets ui' r:
`
`ttfl' t'" + ttrl ‘ t""'l
`
`l
`
`I ”1' r: + til 't + tin. + at, ' t"I
`
`l at, '
`
`t"
`
`I: + ..- + (1%!" t-"‘"
`
`The euel'fieients a, range in value item it In t- - l. ‘l‘u distinguish between numbers uI differ-
`ent bases. We cuclesc the coefficients in parentheses and write a subscript equal In the base used
`texeertt settletimcs l'ur decimal numbers. where the entttent makes it ubyiuus that n is tlcet-
`malt. An example ui it basef- number is
`
`Page 17
`
`Page 17
`
`

`

`4
`
`Chapter 1
`
`Binary Systems
`
`(4021.2),=4><53+0><52+2><5I+1><50+2>~<5—‘=(511.4),0
`
`The coefficient values for base 5 can be only 0, 1, 2, 3, and 4. The octal number system is a
`base-8 system that has eight digits: 0, 1, 2, 3, 4, 5, 6, 7, An example of an octal number is
`127.4. To determine its equivalent decimal value, we expand the number in a power series with
`a base of 8:
`
`(127.4)8 = l x 82 + 2 x 8‘ + 7 x 8° + 4 x s‘1 = (87.5),0
`
`Note that the digits 8 and 9 cannot appear in an octal number.
`It is customary to borrow the needed :- digits for the coefficients from the decimal system
`when the base of the number is less than 10. The letters of the alphabet are used to supplement
`the 10 decimal digits when the base of the number is greater than l0. For example, in the hexa-
`decimal (base 16) number system, the first ten digits are borrowed from the decimal system.
`The letters A, B, C, D, E, and F are used for digits 10, ll, l2, l3, l4, and 15, respectively. An
`example of a hexadecimal number is
`
`(365ml6 = 11 x 163 + 6 x 162 + 5 x 16‘ +15 >< [6° = (46,687)",
`
`As noted before, the digits in a binary number are called bits. When a bit is equal to 0, it does
`not contribute to the sum during the conversion. Therefore, the conversion from binary to dec-
`imal can be obtained by adding the numbers with powers of two corresponding to the bits that
`are equal to 1. For example,
`
`(110101).2 = 32 +16 + 4 +1=(53),0
`
`There are four 1’s in the binary number. The corresponding decimal number is the sum of the
`four powers of two numbers. The first 24 numbers obtained from 2 to the power of n are list-
`ed in Table 1-1. In computer work, 2'0 is referred to as K(kilo), 220 as M(mega), 230 as G(giga),
`and 240 as T(tera). Thus 4K = 2‘2 = 4096 and 16M = 224 = 16,777,216. Computer capaci-
`ty is usually given in bytes. A byte is equal to eight bits and can accommodate one keyboard
`character. A computer hard disk with 4 gigabytes of storage has a capacity of 4G = 232 bytes
`(approximately 10 billion bytes).
`Arithmetic operations with numbers in base r follow the same rules as for decimal numbers.
`When a base other than the familiar base 10 is used, one must be careful to use only the
`
`Table 1-1
`Powers of Two
`
`n
`
`0
`
`i
`2
`3
`
`4
`5
`6
`
`7
`
`2n
`
`l
`
`2
`4
`8
`
`l6
`32
`64
`
`128
`
`n
`
`8
`
`9
`10
`l
`1
`
`12
`13
`14
`
`15
`
`2n
`
`256
`
`512
`1,024
`2,048
`
`4,096
`8,192
`16,384
`
`32,768
`
`n
`
`[6
`
`17
`18
`19
`
`20
`21
`22
`
`23
`
`2n
`
`65,536
`
`131,072
`262,144
`524,288
`
`1,048,576
`2,097,152
`4,194,304
`
`8,388,608
`
`Page 18
`
`Page 18
`
`

`

`Section 1-3 Number Base Conversions
`
`5
`
`rufilluwublu digits. Eaaatples nf additinn. subtractiuu, and tnulttplicalinn at live binary.l mun
`bent are as I'ntlnws:
`
`IDiltil
`augnlttl.‘
`
`addend: +lt'itlt II
`
`minnend:
`
`subtraltnatl:
`
`ltilltil
`
`'llltllll
`
`SUITE
`
`it‘llfllflfl
`
`difference:
`
`tititiltlt
`
`innitiplieand:
`
`ltil
`
`tnnlltplinr:
`
`plndncn
`
`Yfl
`
`It'ill
`
`ULIL'IU
`
`lit.“—
`
`it]! I
`
`|
`
`'l‘be suai nl' Iwn inner},r numbers is calculated by the same rules as in decimal. except that
`the digits at the sum in any significant pnsitinn can be tail;J U at l Any carry nbtained in a given
`significant pnsitinn is used by the pair n1" digits tine signiiicant [maltnm higher. The subtractinn
`is slightlyr inc-re entnplicatntl. The rules are still the same as In decimal. except that lite burniw
`in a given significant pnsitinn adds '2 in n minuend digit. tilt lintrnw in the decimal system adds
`lit in a ntlnaend digit.) Militiplientinn is very simple. The multiplier digits are aIWays | nr it.
`'l'herefnre. the partial prndttcts an:- equal either tn the intiitipiinnlitl nt' in it.
`
`1-3 NUMBER BASE CONVERSIONS
`
`Tite cntwersinn at" a number in base r' in decimal Is dune by Expanding the number in a petite!
`series and adding all the terms as shnwa pminnsly. We ntntt present a general prtnicdtttt: lit:
`the reverse apt-retina ui' cementing a decimal number in a number in base a It the demise ll]-
`eludes a rntlitt pnml. it is rteeessai'y tn separate the number intn an integer part anti a l'ractinn
`part. since each part must lie enlivened differently. The nnnt'ersina et' a decimal integer in a
`number in base l" is dune by dividing the number and all successitte quutienta by r and aneu-
`nntlatine Lhc remainders. This pmeedate is best Illustrated by example-
`
`W'—
`
`in binary. First. 41 is divided by '2 in give an integer quntient nf 1t] and a
`tJnIWert decimal 4|
`remainder of i. The quotient is again divided by 2 in give a new duntieni and remainder. ‘I'ltis
`prtnrnss is entitiniled until the integer quotient beennies ii. The mmfllelents {if the desired bina~
`r}; number are obtained t'rnrn the remninders' as t'ellnws:
`
`Integer
`Quatienl
`
`Remainder
`
`(Inefficient
`
`41f}: -
`
`1W2 =
`
`left :-
`
`se 2
`
`“if: =
`
`if: =
`
`2n
`
`1L]
`
`ii
`
`a
`
`l
`
`u
`
`Therefnre. the answer is {tl l
`
`+
`
`1
`
`4-
`
`+
`
`+
`
`t
`
`ii
`
`ii
`
`i
`
`l]
`
`a” = I
`
`an m {'1
`
`a; - ii
`
`a. = I
`
`114 f l}
`
`#5 = t
`i
`+
`j,“ = I'lt‘lfit'tqtllrflzt'l‘lfi'ttll-l = {lllltJ-lil )1
`
`Page 19
`
`Page 19
`
`

`

`6
`
`Chapter 1
`
`Binary Systems
`
`The arithmetic process can be manipulated more conveniently as follows:
`
`Integer
`
`Remainder
`
`41
`
`20
`
`10
`
`5
`
`2
`
`l
`
`0
`
`l
`
`O
`
`0
`
`l
`
`0
`
`l
`
`101001 = answer
`
`The conversion from decimal integers to any base-r system is similar to the example, except
`that division is done by r instead of 2.
`
`Convert decimal 153 to octal. The required base r is 8. First, [53 is divided by 8 to give an in-
`teger quotient of 19 and a remainder of 1. Then 19 is divided by 8 to give an integer quotient
`of 2 and a remainder of 3. Finally, 2 is divided by 8 to give a quotient of 0 and a remainder of
`2. This process can be conveniently manipulated as follows:
`
`153
`
`19
`
`2
`
`o
`
`l
`
`3
`
`2 L = (231)8
`
`The conversion of a decimal fraction to binaiy is accomplished by a method similar to that
`used for integers. However, multiplication is used instead of division, and integers are accu-
`mulated instead of remainders Again, the method is best explained by example.
`
`W C
`
`onvert (06875)“, to binary. First, 06875 is multiplied by 2 to give an integer and a fraction.
`The new fraction is multiplied by 2 to give a new integer and a new fraction. This process is
`continued until the fraction becomes 0 or until the number of digits have sufficient accuracy.
`The coefficients of the binaiy number are obtained from the integers as follows:
`