# Digital Design Using Digilent FPGA Boards -- Verilog / Active-HDL Edition

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1 Digital Design Using Digilent FPGA Boards -- Verilog / Active-HDL Edition Table of Contents 1. Introduction to Digital Logic Background Digital Logic Verilog 8 2. Basic Logic Gates Truth Tables and Logic Equations 9 The Three Basic Gates 9 Four New Gates Positive and Negative Logic: De Morgan s Theorem Sum of Products Design Product of Sums Design 15 Verilog Examples 18 Example 1 2-Input Gates 18 Example 2 Multiple-Input Gates 21 Problems Boolean Algebra and Logic Equations Boolean Theorems 28 One-Variable Theorems 29 Two- and Three-Variable Theorems Karnaugh Maps 34 Two-Variable K-Maps 34 Three-Variable K-Maps 36 Four-Variable K-Maps Computer Mimimization Techniques 40 Tabular Representations 40 Prime Implicants 41 Essential Prime Implicants 43 Verilog Examples 45 Example 3 Majority Circuit 45 Example 4 2-Bit Comparator 47 Problems Implementing Digital Circuits Implementing Gates Transistor-Transistor Logic (TTL) Programmable Logic Devices (PLDs and CPLDs) 56 A 2-Input, 1-Output PLD 56

2 The GAL 16V8 58 CPLDs Field Programmable Gate Arrays (FPGAs) 60 Verilog Examples 62 Example 5 Map Report 62 Problems Combinational Logic Multiplexers 64 2-to-1 Multiplexer 64 4-to-1 Multiplexer 65 Quad 2-to-1 Multiplexer 66 Verilog Examples 67 Example 6 2-to-1 Multiplexer: if Statement 67 Example 7 4-to-1 Multiplexer: Module Instantiation 70 Example 8 4-to-1 Multiplexer: case Statement 74 Example 9 A Quad 2-to-1 Multiplexer 75 Example 10 Generic Multiplexer: Parameters 77 Example 11 Glitches Segment Displays 82 Verilog Examples 83 Example 12 7-Segment Decoder: Logic Equations 83 Example 13 7-Segment Decoder: case Statement 85 Example 14 Multiplexing 7-Segment Displays 87 Example 15 7-Segment Displays: x7seg and x7segb Comparators 94 Cascading Comparators 94 TTL Comparators 95 Verilog Examples 96 Example 16 4-Bit Comparator Using a Verilog Task 96 Example 17 N-Bit Comparator Using Relational Operators Decoders and Encoders 100 Decoders 100 TTL Decoders 101 Encoders 101 Priority Encoders 102 TTL Encoders 102 Verilog Examples 103 Example 18 3-to-8 Decoder: Logic Equations 103 Example 19 3-to-8 Decoder: for Loops 104 Example 20 8-to-3 Encoder: Logic Equations 105 Example 21 8-to-3 Encoder: for Loops 107 Example 22 8-to-3 Priority Encoder Code Converters 109 Binary-to-BCD Converters 109 Shift and Add 3 Algorithm 110

3 Gray Code Converters 111 Verilog Examples 112 Example 23 4-Bit Binary-to-BCD Converter: Logic Equations 112 Example 24 8-Bit Binary-to-BCD Converter: for Loops 113 Example 25 4-Bit Binary to Gray Code Converter 115 Example 26 4-Bit Gray Code to Binary Converter 116 Problems Arithmetic Circuits Adders 120 Half Adder 120 Full Adder 120 Carry and Overflow 123 TTL Adder 125 Verilog Examples 125 Example 27 4-Bit Adder: Logic Equations 125 Example 28 4-Bit Adder: Behavioral Statements 128 Example 29 N-Bit Adder: Behavioral Statements Subtractors 129 Half Subtractor 129 Full Subtractor 130 An Adder/Subtractor Circuit 131 Verilog Examples 133 Example 30 4-Bit Adder/Subtractor: Logic Equations 133 Example 31 N-Bit Subtractor: Behavioral Statements Shifters 135 Verilog Examples 136 Example 32 4-Bit Shifter Multiplication 137 Binary Multiplication 137 Signed Multiplication 139 Verilog Examples 140 Example 33 Multiplying by a Constant 140 Example 34 A 4-Bit Multiplier Division 143 Binary Division 143 Verilog Examples 144 Example 35 An 8-Bit Divider using a Task Arithmetic Logic Unit (ALU) 146 Verilog Examples 147 Example 36 4-Bit ALU 147 Problems Sequential Logic Latches and Flip-Flops 151 SR Latch 151

4 Clocked SR Latch 153 D Latch 153 Edge-Triggered D Flip-Flop 154 Verilog Examples 156 Example 37 Edge-Triggered D Flip-Flop 156 Example 38 Edge-Triggered D Flip-Flop with Set and Clear 157 Example 39 D Flip-Flops in Verilog 158 Example 40 D Flip-Flop with Asynchronous Set and Clear 159 Example 41 Divide-by-2 Counter Registers 161 Verilog Examples 163 Example 42 1-Bit Register 163 Example 43 4-Bit Register 164 Example 44 N-Bit Register Shift Registers Bit Ring Counter 167 Verilog Examples 167 Example 45 Shift Registers 167 Example 46 Ring Counter 168 Example 47 Debounce Pushbuttons 169 Example 48 Clock Pulse Counters 173 Arbitrary Waveform 174 Verilog Examples 175 Example 49 3-Bit Counter 175 Example 50 Modulo-5 Counter 177 Example 51 N-Bit Counter 178 Example 52 Clock Divider: Modulo-10K Counter 180 Example 53 Arbitrary Waveform Pulse-Width Modulation (PWM) 185 Controlling the Speed of a DC Motor using PWM 186 Controlling the Position of a Servo using PWM 187 Verilog Examples 188 Example 54 Pulse-Width Modulation (PWM) 188 Example 55 PWM Signal for Controlling Servos BASYS/Nexys-2 Board Examples 191 Verilog Examples 191 Example 56 Loading Switch Data into a Register 191 Example 57 Shifting Data into a Shift Register 193 Example 58 Scrolling the 7-Segment Display 195 Example 59 Fibonacci Sequence 200 Problems State Machines Mealy and Moore State Machines A Moore Machine Sequence Detector 207

5 8.3 Mealy Machine Sequence Detector 209 Verilog Examples 210 Example 60 Sequence Detector 210 Example 61 Door Lock Code 215 Example 62 Traffic Lights 219 Problems Datapaths and Control Units Verilog while Statement 225 Example 63 GCD Algorithm Part Datapaths and Control Units 227 Example 64 GCD Algorithm Part Example 65 An Integer Square Root Algorithm Integrating the Datapath and Control Unit 247 Example 66 GCD Algorithm Part Example 67 Integer Square Root Part Memory 257 Example 68 A Verilog ROM 257 Example 69 Distributed RAM/ROM 262 Example 70 Block RAM/ROM VGA Controller 271 Example 71 VGA-Stripes 275 Example 72 VGA-PROM 281 Example 73 Sprites in Block ROM 286 Example 74 Screen Saver PS/2 Port 297 Example 75 Keyboard 300 Example 76 Mouse 307 Appendix A Aldec Active-HDL Tutorial 316 Part 1: Project Setup 316 Part 2: Design Entry 320 Part 3: Simulation 323 Part 4: Creating a Top-level Design 327 Part 5: Synthesis and Implementation 329 Part 6: Program FPGA Board 333 Appendix B Number Systems 334 B.1 Counting in Binary and Hexadecimal 334 B.2 Positional Notation 338 B.3 Fractional Numbers 339 B.4 Number System Conversions 339

6 B.5 Negative Numbers 343 Appendix C Making a Turnkey System 347 Appendix D Digilent FPGA Boards Comparison Chart 349 Appendix E Installing the Xilinx ISE/WebPACK, Aldec Active-HDL, and Digilent Adept2 Software 350 Appendix F Verilog Quick Reference Guide 352

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