Digital Logic Design v 4 7a - engrcs.com

1 Digital Logic Design Version printed on February 2016 First published on August 2006 Digital Logic Design Page 2 Background and Acknowledgements This material has been developed for the first course in Digital Logic Design . The content is derived from the author s educational, technical and management experiences, in-addition to teaching experience. Many other sources, including the following specific sources, have also informed by the content and format of the following material: Katz, R. Contemporary Logic Design . (2005) Pearson. Wakerly, I. Digital Design . (2006) Prentice Hall.

2 Sandige, R. Digital Design Essentials. (2002) Prentice Hall. Nilsson, J. Electrical Circuits. (2004) Pearson. I would like to give special thanks to my students and colleagues for their valued contributions in making this material a more effective learning tool. I invite the reader to forward any corrections, additional topics, examples and problems to me for future Thanks, Izad Khormaee 2014 Izad Khormaee, All Rights Reserved. Digital Logic Design Page 3 Contents Chapter 1. Number Systems, Number Representations, and Codes .. 6 Key concepts and Overview.

3 6 Digital vs. Analog .. 7 Digital Design Overview (from Transistor to Super Computer) .. 9 Design Methodologies .. 11 Number Systems (Decimal, Binary, Octal, Hexadecimal) .. 12 Base Conversions .. 14 Signed Binary Number Conventions .. 17 Binary Arithmetic .. 20 Binary Codes .. 22 DC Electrical Circuit Fundamentals .. 24 Additional Resources .. 28 Problems .. 29 Chapter 2. Boolean Algebra, Functions, and Minimization .. 30 Key concepts and Overview .. 30 Logic Gates .. 31 Huntington s First Set of Postulates .. 34 Principle of Duality .. 35 Boolean Functions.

4 36 Boolean Algebra Theorems .. 38 Canonical or Standard Form of Functions .. 41 Methods of Function Minimization (reducing the number of literals in an expression) .. 46 Karnaugh-map or K-map .. 48 Special Case: Don t Care Terms .. 52 XOR Properties and Applications .. 53 Additional Resources .. 54 Problems .. 55 Chapter 3. Analyzing and Synthesizing Combinational Logic Circuits .. 56 Key concepts and Overview .. 56 Standard Logic and Schematic Layout (Review) .. 57 Designing Logic Circuits .. 62 Combinational Logic Analysis and Design .. 66 Compressing Truth Tables and K-maps.

5 67 Glitches and Their Causes .. 71 Types of Functions and Delays .. 74 Beyond Standard Logic : Applications .. 76 Programmable Logic Devices (PLDs) .. 85 Additional Resources .. 94 Problems .. 95 Chapter 4. Introduction to Feedback Circuits and Sequential Logic Analysis .. 96 Key concepts and Overview .. 96 SR Flip-Flops .. 97 Asynchronous Sequential Logic Issues .. 99 Finite State machine .. 101 Additional Flip Flops .. 107 Sequential Circuit Analysis .. 112 Debouncing Mechanical Switches .. 118 Digital Logic Design Page 4 Additional Resources .. 120 Problems.

6 121 Chapter 5. Sequential Circuit Design & Techniques .. 122 Key concepts and Overview .. 122 Synchronous Finite State Machine Design (Classical Design ) .. 123 State Assignment Encoding, Shift Register Counters, and Adding an Enable Input .. 133 Inspection Design Methods for Finite State Machines .. 137 FSM Design Examples .. 143 Additional Resources .. 151 Problems .. 152 Chapter 6. Finite State Machine Optimization & Testing .. 153 Key concepts and Overview .. 153 State Minimization and FSM Design Process .. 154 State Minimization Using an Implication Chart (or Table).

7 155 Design for Testability (DFT) .. 160 Additional Resources .. 163 Problems .. 164 Chapter 7 Verilog . Verilog Hardware Description Language (Verilog) .. 165 Key concepts and Overview .. 165 History .. 166 Introduction to Verilog 167 Syntax .. 169 Assignments .. 172 Operators .. 178 Operators .. 178 Types and Variable Declarations .. 180 Flow Control Statements .. 182 Code Modularization .. 184 185 Additional Resources .. 187 Problems .. 188 Chapter 8 VHDL . VHDL Hardware Description Language (VHDL) .. 189 Key concepts and Overview.

8 189 History .. 190 Steps in VHDL Design .. 191 Entity and Architecture .. 193 Declarations .. 195 Operators .. 202 Behavioral Design .. 204 Dataflow Design 206 Additional Resources .. 210 Problems .. 211 Chapter 9. Commercial Digital Integrated Circuits and Interface Design .. 213 Key concepts and Overview .. 213 Output Types .. 214 Logic Families .. 218 Multiplexer (MUX)/DeMultiplexer (DMUX) Design .. 219 Adder & Subtractor Design .. 223 Multiplier Design .. 227 Digital Logic Design Page 5 Arithmetic Logic Unit (ALU) Design .. 228 Additional Resources.

9 229 Problems .. 230 Appendix A. Additional Resources .. 231 Digital Logic Design Page 6 Chapter 1. Number Systems, Number Representations, and Codes Key concepts and Overview Digital vs. Analog Digital Design Overview (from Transistor to Super Computer) Design Methodologies Number systems (Binary, Octal, Decimal, Hexadecimal) Base Conversions Signed Binary Number Conventions Binary Arithmetic Binary Code DC Electrical Circuit Fundamentals Additional Resources Problems Digital Logic Design Page 7 Digital vs. Analog Natural forces and signals are all analog (or continuous) which means we hear, see and change items in a continuous manner.

10 On the other hand, our Digital technology (also called non-continuous or 2-value discrete) more effectively allows us to process and communicate more effectively. This leads us to Design systems that fit the following block diagram architecture: Why convert analog data to Digital data? We have the information we need (on-off, timing) Above a certain level is on, high, 1-state or true. Below a certain level is off, low, 0-state or False. Note: We have introduced a discontinuity when a signal goes from 1 to 0 or 0 to 1. This means we cannot say what the exact value is at the time of transition.