Logic Design

By Jaden Mclean & Carmen Hurley

Chapter 1 Introduction .............................................................................................. 1 History ...................................................................................................... 2 Types ......................................................................................................... 3 Logical Form ............................................................................................ 8 Semantics .................................................................................................. 9 Inference ................................................................................................. 10 Logical Systems ...................................................................................... 11 Logic and Rationality ............................................................................. 11 Rival Conceptions ................................................................................... 12 Controversies .......................................................................................... 13 History of Logic ...................................................................................... 15 Boolean Algebra ..................................................................................... 35 Boolean Expressions ............................................................................... 36 Minimization of Boolean Equations ....................................................... 37 Logic Gates ............................................................................................. 38 Combinational and Sequential Circuits .................................................. 43 Edge Triggered Flip-Flops and Registers ............................................... 46 Tristate Logic .......................................................................................... 47 Specification Languages ......................................................................... 48 Summary ................................................................................................. 49 Chapter 2 Digital System ................................................................................... 51 Circuit Diagram ...................................................................................... 51 Linkages .................................................................................................. 53 Preface ix TABLE OF CONTENTS Organization of Drawings in Circuit ...................................................... 54 Basic Operation of Circuit ...................................................................... 56 Equivalent Circuits ................................................................................. 59 Current Division of Parallel Components............................................... 63 Digital Integrated Circuits ...................................................................... 69 History of Integrated Circuits ................................................................. 69 Digital Circuit Analysis and Design ....................................................... 71 Combinational Logic Circuits................................................................. 74 Molecular Electronic Digital Logic ........................................................ 77 Molecular Recitying Diodes Switch Design .......................................... 78 Digital Design in Digital Circuits Analysis ............................................ 81 Digital Signals ........................................................................................ 85 Concept of Information........................................................................... 87 Transmission Over Medium Distances ................................................... 89 Passive and Active Networks.................................................................. 91 Logic Signal Voltage Levels ................................................................... 93 TCP / IP Model ....................................................................................... 96 OSI Model Concepts............................................................................... 97 Examples of Signals ............................................................................. 100 Digital and Analog Signals ................................................................... 102 Chapter 3 Asynchronous Sequential Logic .................................................... 106 Asynchronous Circuit ........................................................................... 106 Asynchronous Decade Counters ........................................................... 112 Synchronous Circuit ............................................................................. 114 Synchronous Counters .......................................................................... 118 Sequential Circuits ................................................................................ 125 Circuit Analysis .................................................................................... 126 Latches Circuit elements ....................................................................... 129 Flip Flops .............................................................................................. 134 Shift Registers ....................................................................................... 142 Serial In-Serial Out Shift Registers ...................................................... 145 Serial In-Parallel Out Shift Registers ................................................... 149 State Reduction ..................................................................................... 155 States Assignment ................................................................................. 156 Chapter 4 Combinational Logic ...................................................................... 157 Combinational Logic ............................................................................ 157 Design Procedure .................................................................................. 157 Analysis Procedure ............................................................................... 158 Binary Adder-subtractor ....................................................................... 159 Binary Multiplier .................................................................................. 162 vi Magnitude Comparator ......................................................................... 162 Multiplexes ........................................................................................... 163 Decoders ............................................................................................... 166 Chapter 5 Binary Numbers System ................................................................ 171 Number Systems and Codes ................................................................. 173 Signed Binary Numbers ........................................................................ 176 Basic Rules of Binary System .............................................................. 180 Integers of Signed Binary System ........................................................ 181 Positive Binary Fractions...................................................................... 182 Negative Binary Numbers .................................................................... 183 Binary Arithmetic and Numbers versus numeration ............................ 185 Decimal numeration Number................................................................ 187 Binary Notation System........................................................................ 192 Subtraction of Large Bit Binary Numbers ............................................ 195 Binary Codes ........................................................................................ 201 Floating Point Representation .............................................................. 204 Error-Correcting Codes ........................................................................ 208 Digital Computing ................................................................................ 217 Chapter 6 Fundamental of Boolean Alebra .................................................... 221 Mathematicalule ................................................................................... 221 Boolean Algebraic Identities................................................................. 223 Boolean Arithmetic ............................................................................... 229 Boolean Functions ................................................................................ 231 Laws of Boolean Algebra ..................................................................... 231 Circuits Containing Inverters ................................................................ 236 Chapter 7 Circuit Theory and Logic Design .................................................. 239 Parts of a Circuit ................................................................................... 239 Automated Design Tools ...................................................................... 241 Chapter 8 Programmable Logic ...................................................................... 245 Programmable Logic Array .................................................................. 245 Programmable Array Logic .................................................................. 246 Generic Array Logic ............................................................................. 251 Complex Programmable Logic Device................................................. 251 Erasable Programmable Logic Device ................................................. 252 PsoC ...................................................................................................... 252 Reconfigurable Computing ................................................................... 256 Soft Microprocessor.............................................................................. 261 Circuit Underutilization ........................................................................ 262 vii . Application-specific Integrated Circuit ................................................ 262 Field-programmable Gate Array ........................................................... 267 Languages ............................................................................................. 276 Bibliography ..................................................................................... 289 Index ................................................................................................. 293