Logically determined design: clockless system design with NULL convention logic

310 Pages·2005·6.202 MB·English

by  Karl Fant

LOGICALLY DETERMINED
DESIGN

LOGICALLY DETERMINED
DESIGN
CLOCKLESS SYSTEM DESIGN WITH
NULL CONVENTION LOGIC
TM
Karl M. Fant
Theseus Research, Inc.
A JOHN WILEY & SONS, INC., PUBLICATION
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LibraryofCongressCataloging-in-PublicationData:
Fant,KarlM.
Logicallydetermineddesign:clocklesssystemdesignwithNULLconventionlogicTM/KarlM.Fant.
p.cm.
“AWiley-Intersciencepublication.”
Includesbibliographicalreferencesandindex.
ISBN0-471-68478-3
1.Asynchronouscircuits–Designandconstruction.2.Logic,Symbolicandmathematical.
3.Logicdesign.4.Computerarchitecture.I.Title.
TK7868.A79F362005
621.381–dc22 2004050923
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
To Michelle, Lara, and Omi

&CONTENTS
Preface xv
Acknowledgments xvi
1. Trusting Logic 1
1.1 Mathematicianless Enlivenment ofLogic Expression 1
1.2 Emulatingthe Mathematician 2
1.3 Supplementing the Expressivity ofBoolean Logic 2
1.3.1 The Expressional Insufficiency ofBooleanLogic 2
1.3.2 Supplementing the Logical Expression 3
1.3.3 Coordinating CombinationalExpressions 3
1.3.4 The ComplexityBurden ofthe TimeInterval 4
1.3.5 Forms ofSupplementation Other Than the Time Interval 4
1.3.6 The ComplexityBurden ofAsynchronous Design 5
1.3.7 The Cost of Supplementation 5
1.4 DefiningaSufficiently Expressive Logic 5
1.4.1 LogicallyExpressing Data PresentationBoundaries 6
1.4.2 LogicallyRecognizing Data PresentationBoundaries 6
1.4.3 LogicallyCoordinating the Flow ofData 8
1.4.4 Mathematicianless Completeness ofExpression 9
1.5 The Logically Determined System 9
1.6 Trustingthe Logic: AMethodology ofLogical Confidence 10
1.7 Summary 10
1.8 Exercises 11
2. ASufficiently Expressive Logic 13
2.1 Searching for aNew Logic 13
2.1.1 Expressing DiscreteData PresentationBoundaries 13
2.1.2 LogicallyRecognizing Discrete Data Presentation
Boundaries 13
2.1.3 The Universalityof the NULL Function 14
2.1.4 Bounding the Behaviorofa Combinational Expression 14
2.1.5 Relationship of4NCL toBoolean Logic 16
vii
viii CONTENTS
2.2 Deriving a3 Value Logic 16
2.2.1 Expressing 3NCL State-holding Behavior 17
2.2.2 3NCL Summary 18
2.3 Deriving a2 Value Logic 18
2.3.1 The Data DifferentiationConvention 19
2.3.2 2NCL asa Threshold Logic 20
2.3.3 2NCL inRelationto Boolean Logic 21
2.3.4 Subvariable Expressivity 22
2.3.5 Completeness at the Variable Level 22
2.3.6 The 2NCL OrphanPath 22
2.3.7 2NCL Summary 26
2.4 Compromising Logical Completeness 27
2.4.1 Moving LogicallyDetermined Completeness
Boundaries Farther Apart 27
2.4.2 NoLogicallyDetermined Boundaries inData Path 28
2.4.3 NoLogicallyDetermined Boundaries at All 29
2.5 Summary 30
3. The Structure ofLogically Determined Systems 31
3.1 The Cycle 31
3.1.1 The RingOscillator 31
3.1.2 Oscillator Composition with SharedCompleteness Path 32
3.1.3 Cycles and 2NCL Data Paths 34
3.1.4 Data Path Abstraction 35
3.1.5 Composition inTermsof Cycles 35
3.1.6 Composition inTermsof Registration Stages 36
3.2 Basic PipelineStructures 36
3.2.1 Pipeline Fan-out 36
3.2.2 Pipeline Fan-in 37
3.2.3 The Pipeline Ring 37
3.2.4 Cycle Structure Example 38
3.3 Control Variablesand WavefrontSteering 39
3.3.1 Steering ControlVariables 39
3.3.2 Fan-outWavefrontSteering 39
3.3.3 Fan-in WavefrontSteering 44
3.3.4 WavefrontSteering Philosophy 47
3.3.5 Concurrent Pipelined FunctionPaths 50
3.4 The Logically Determined System 50
3.4.1 Managing WavefrontInteraction 51
3.4.2 ASimple Example System 51
3.5 Initialization 55
3.5.1 Initializingthe System 55
3.5.2 InitializingData Wavefronts 56