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Digital Systems: Principles and Design by Pearson

Name: Digital Systems: Principles and Design by Pearson
Author: Raj Kamal
ISBN: 9781299445482

by Raj Kamal

May 2024

Intermediate to advanced

593 pages

21h 30m

English

Pearson India

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Cover (1/2)
Cover (2/2)
Contents (1/2)
Contents (2/2)
Preface
Acknowledgements
Chapter 1: Basic Digital Concepts
1.1 Concepts of ‘1’s, ‘0’s1.1.1 Positive Logic
1.1.2 Negative Logic
1.1.3 Popular Representations of the Digital Circuits1.2 Analog vs. Digital Circuits
Chapter 2: Boolean Algebra and Theorems, Minterms and Maxterms
2.1 The NOT, AND, OR Logic Operations2.1.1 The NOT Logic Operation
2.1.2 The AND Logic Operation

2.1.3 The OR Logic Operation
2.2 The NAND and NOR Logic Operations2.2.1 NAND Gate
2.2.2 NOR Gate
2.3 The XOR, NOT-XOR, NOT-NOT Logic Operations2.3.1 XOR Logic Operation2.3.2 NOT-XOR (XNOR) Logic Operation
2.3.3 NOT-NOT Logic Operation
2.4 Boolean Algebraic Rules (for Outputs from the Inputs)2.4.1 OR Rules2.4.2 AND Rules
2.4.3 NOT Rules (Rules of Complementation)
2.5 Boolean Algebraic Laws2.5.1 Commutative Laws2.5.2 Associative Laws2.5.3 Distributive Laws2.6 Demorgan Theorems
2.7 The Sum of the Products (SOPs) as per Boolean Expression and Minterms
2.7.1 SOPs for Two Variables (Two Inputs) Case
2.7.2 SOPs for Three Variables (Three Inputs) Case
2.7.3 SOPs for Four Variables (Four Inputs) Case
2.7.4 Conversion of a Boolean Expression or Truth Table Outputs into the Standard SOP Format
2.8 Product of the Sums and Maxterms for a Boolean Expression
2.8.1 POS for Two Variables (Two Inputs) Case
2.8.2 POS for Three Variables (Three Inputs) Case
2.8.3 POS for Four Variables (Four Inputs) Case
2.8.4 Conversion of a Boolean Expression into Standard POS Format (1/3)
2.8.4 Conversion of a Boolean Expression into Standard POS Format (2/3)
2.8.4 Conversion of a Boolean Expression into Standard POS Format (3/3)
Chapter 3: Karnaugh Map and Minimization Procedures
3.1 The Three-Variable Karnaugh Map and Tables3.1.1 Karnaugh Map from the Truth Table
3.1.2 Karnaugh Map from the Minterms in a SOP
3.1.3 Karnaugh Map from the Maxterms in a POS
3.2 Four Variable Karnaugh Map and Tables
3.2.1 Karnaugh Map from the Truth Table
3.2.2 Karnaugh Map from the Minterms in an SOP
3.2.3 Karnaugh Map from the Maxterms in a POS
3.3 Five and Six Variable Karnaugh Maps and Tables
3.4 An Important Feature in the Design of a Karnaugh Map
3.4.1 Only Single Variable Changes into Its Complement in a Pair of Adjacent Cells
3.4.2 Only Two Variables Change into Their Complements in Adjacent Cells in a Square or Column of Four Cells
3.4.3 Three Variables Change into Their Complements in Adjacent Cells in Box of Eight Adjacent Cells
3.4.4 First and Last Columns for First and Last Rows and Purpose of Deciding Adjacency in a Karnaugh Map
3.4.5 Use of Don’t Care (or Unspecified) Input Conditions for Purpose of Deciding Adjacencies in a Karnaugh Map
3.5 Simplification of Logic Circuit Relation by Minimization Using Adjacencies
3.5.1 Minimization of a Karnaugh Map Using Pairs of Adjacent Cells
3.5.2 Minimization of a Karnaugh Map Using Quads of Four Adjacent Cells
3.5.3 Minimization of a Karnaugh Map Using Octet of Eight Adjacent Cells
3.5.4 Minimization of a Karnaugh Map Using Offset Adjacencies and Diagonal Adjacencies
3.5.5 Minimization by Finding Prime Implicants
3.6 Drawing of Logic Circuit Using AND-OR Gates, OR-AND Gates, NAND’s Only, NOR’s Only
3.7 Representations of a Function (Cover) for a Computer-aided Minimization for Simplifying the Logic Circuits
3.7.1 Representation in Cube Format for Computer-aided Minimization
3.7.2 Representation in Four-Dimensional Hypercube Formats for a Computer-aided Minimization
3.7.3 Representation in Hypercube (Multi-dimensional cube) Formats for Computer-aided Minimization
3.8 Multi-Output Simplification
3.8.1 Prime Implicants for Multi-Outputs Case
3.9 Two Outputs Simplification–Computer-Based Prime Implicants Using Star Product and Sharp Operations
3.9.1 Combination of Two Cubes Differing in One Variable into One Cube—A Star Product Operation
3.9.2 Finding Essential Prime Implicants Using Two Cubes—A Sharp Operation
3.9.3 Computer-Based Minimization Method to Find Minimum Required Cover (SOP function implicants)
3.10 Computer-Based Minimization–Quine-McCluskey Method
3.10.1 Quine-McCluskey Method of Finding Prime Implicants
3.10.2 Finding Minimal Sum from the Prime Implicants for an Output
3.10.3 Finding Minimal Sum for the Multi-Output Case Using Quine-McCluskey Method (1/3)
3.10.3 Finding Minimal Sum for the Multi-Output Case Using Quine-McCluskey Method (2/3)
3.10.3 Finding Minimal Sum for the Multi-Output Case Using Quine-McCluskey Method (3/3)
Chapter 4: Binary Arithmetic and Decoding and Mux Logic Units
4.1 Binary Arithmetic Units4.1.1 Binary Addition of Two Bits
4.1.2 Addition of Two Arithmetic Numbers Each of 4 Bits
4.1.3 Subtraction of Two Arithmetic Numbers Each of 4 Bits
4.2 Decoder
4.2.1 Decoder (Line Decoder)
4.2.2 The 1 of 2 and 1 of 4 Line Decoders
4.2.3 The Four-line to 16-line Decoder4.2.4 Function Specific Decoders
4.3 Encoder
4.3.1 Encoder (Line Encoder)
4.3.2 Encoder (Priority Encoder)
4.3.3 BCD 10 of 1 Four-bit Encoder
4.3.4 Octal 8 of 1 Three-bit Encoder and Hexadecimal Encoder
4.4 Multiplexer
4.4.1 Multiplexer (Line Selector)
4.4.2 Multiplexer with Outputs Enabling Control (gate) Pin(s)
4.5 Demultiplexer
4.5.1 Demultiplexer Definition
Chapter 5: Code Converters, Comparators and Other Logic Processing Circuits
5.1 Code Converters5.1.1 Codes for Decimal Numbers
5.1.2 Unit Distance Code Converter
5.1.3 ASCII (American Standard Code for Information Interchange) for the Alphanumeric Characters
5.2 Equality and Magnitude Comparators Between Two Four-bit Numbers
5.3 Odd Parity and Even Parity Generators
5.4 The 4-bit AND, OR, XOR Between Two Words
5.4.1 AND
5.4.2 OR
5.4.3 XOR5.4.4 Test
Chapter 6: Sequential Logic, Latches and Flip-Flops
6.1 Flip Flop and Latch
6.2 Sr Latch (Set-Reset Latch) Using Cross Coupled NANDs
6.2.1 SR Latch at Various Input Conditions
6.2.2 Difficulties in Using an SR Latch
6.2.3 Timing Diagrams of an SR Latch
6.2.4 Level Clocked SR Latch
6.3 JK Flip-Flop
6.3.1 Explanation of the State Table for the Logic Circuit of an Edge-Triggered JK FF
6.4 T Flip-Flop
6.4.1 T Flip-Flop with Clear and Preset
6.5 D Flip-Flop and Latch
6.5.1 D Flip-Flop
6.5.2 D Flip-Flop with Clear and Preset
6.5.3 D Latch
6.6 Master-Slave RS Flip-Flop
6.7 Master-Slave (Pulse Triggered) JK Flip-Flop
6.7.1 MS JK Flip-Flop with Clear and Preset
6.8 Clock Inputs
6.8.1 Level Clocking of a Clock Input6.8.2 Edge Triggering at a Clock Input
6.9 Pulse Clocking of the Latches in the Flip-Flops
6.10 Characteristic Equations for the Analysis
Chapter 7: Sequential Circuits Analysis, State Minimization, State Assignment and Circuit Implementation
7.1 General Sequential Circuit with a Memory Section and Combinational Circuits at the Input and Output Stages
7.2 Synchronous and Asynchronous Sequential Circuits7.2.1 Synchronous Sequential Circuit
7.2.2 Asynchronous Sequential Circuits
7.3 Clocked Sequential Circuit7.4 Classification of Sequential Circuit as Moore and Mealy State Machine Circuits7.4.1 Classification of a Sequential Circuit as Moore Model Circuit
7.4.2 Classification of a Sequential Circuit as Mealy Model Circuit
7.5 Analysis Procedure
7.5.1 Excitation Table
7.5.2 Transition Table
7.5.3 State Table
7.5.4 State Diagram
7.6 Conditions of States Equivalency
7.6.1 State Reduction and Minimization Procedure
7.6.2 Assignment of Variables to a State
7.7 Implementation Procedure (1/4)
7.7 Implementation Procedure (2/4)
7.7 Implementation Procedure (3/4)
7.7 Implementation Procedure (4/4)
Chapter 8: Sequential Circuits for Registers and Counters
8.1 Registers
8.1.1 Bi-stable Latches as the Register
8.1.2 Parallel-In Parallel-Out Buffer Register
8.1.3 Number of Bits in a Register
8.2 Shift Registers
8.2.1 Serial-In Serial-Out (SISO) Unidirectional Shift Register
8.2.2 Serial-In Parallel-Out (SIPO) Right Shift Register
8.2.3 Parallel-In Serial-Out (PISO) Right Shift Register
8.3 Counter
8.4 Ripple Counter
8.4.1 Cascaded Divide-By-2n Circuit as a Ripple Counter
8.4.2 Modulo-6, Modulo-7 and Modulo-10 Counters
8.4.3 Ring Counter
8.4.4 Johnson Counter (Even Sequences Switch Tail or Twisted Ring Counter)
8.4.5 Odd Sequencer Johnson Counter (Odd Sequencer Switch Tail or Twisted Ring Counter)
8.5 Synchronous Counter
8.5.1 Synchronous Counter Using Additional Logic Circuit
8.6 Asynchronous Clear, Preset and Load (JAM) in a Counter
8.7 Synchronous Clear, Preset and Load Facilities in a Counter
8.8 Timing Diagrams (1/4)
8.8 Timing Diagrams (2/4)
8.8 Timing Diagrams (3/4)
8.8 Timing Diagrams (4/4)
Chapter 9: Fundamental Mode Sequential Circuits
9.1 General Asynchronous Sequential Circuit
9.2 Unstable Circuit Operation
9.3 Stable Circuit Asynchronous Mode Operation
9.4 Fundamental Mode Asynchronous Circuit
9.4.1 Tabular Representation of Excitation-cum-Transitions of States and Outputs
9.5 Analysis Procedure
9.5.1 Excitation Table
9.5.2 Transition Table
9.5.3 State Table
9.5.4 State Diagram
9.5.5 Flow Table
9.5.6 Example of an Excitation-cum-Transition Table
9.5.7 Flow Table from Excitation-Transition Table
9.5.8 Flow Diagram
9.6 Races
9.6.1 Cycles of the Races
9.7 Race-Free Assignments (1/2)
9.7 Race-Free Assignments (2/2)
Chapter 10: Hazards and Pulse Mode Sequential Circuits
10.1 Hazards
10.1.1 Static-0 Hazard
10.1.2 Static-1 Hazard
10.2 Identifying Static Hazards
10.2.1 Identification from the Boolean Expressions
10.2.2 Identification from the Karnaugh Map (Only One-variable Input Case)
10.2.3 Identification from the Karnaugh Map (Three-Variable Input)
10.2.4 Detecting Absence of Static 1 Hazard from the POS Form of Boolean Expression
10.2.5 Detecting Absence of Static 0 Hazard from the SOP Form of Boolean Expression
10.3 Eliminating Static Hazards
10.4 Dynamic Hazards
10.5 Hazards Free Circuits
10.6 Essential Hazards
10.7 Pulse Mode Sequential Circuit (1/2)
10.7 Pulse Mode Sequential Circuit (2/2)
Chapter 11: Implementation of Combinational Logic by Standard ICs and Programmable ROM Memories
11.1 Standard ICs for Design Implementation
11.1.1 Adder/Subtractor IC and Magnitude Comparator
11.1.2 Decoder IC
11.1.3 Encoder IC
11.1.4 Multiplexer IC
11.2 Programming and Programmable Logic Memories11.2.1 ROM (Pre-Programmed Read Only Memory) and PROM (Programmable Read Only Memory)
Chapter 12: Implementation of Combinational Logic by Programmable Logic Devices
12.1 Basics Points to Remember When Using the PLDs (PROMs, PALs, PLAs)
12.2 PAL (Programmable Array Logic)
12.3 PLA (Programmable Logic Arrays) (1/4)
12.3 PLA (Programmable Logic Arrays) (2/4)
12.3 PLA (Programmable Logic Arrays) (3/4)
12.3 PLA (Programmable Logic Arrays) (4/4)
Chapter 13: Logic Gates
13.1 Revision of the Important Gates
13.2 Diode Circuit
13.3 Bipolar Junction Transistors and Mosfets13.3.1 N-P-N Transistor Common Emitter Circuit
13.3.2 MOSFET Circuits
13.4 RTL, DTL, TTL Logic Gates
13.4.1 Resistor–Transistor Logic (RTL)
13.4.2 Diode–Transistor Logic (DTL)
13.4.3 Transistor–Transistor Logic (TTL)
13.4.4 TTL Other than NAND Gate
13.5 Emitter Coupled Logic (ECL)13.5.1 ECL OR/NOR Gate
13.6 Integrated Injection Logic (I2L)
13.6.1 I2L Circuit Internal Connections
13.6.2 I2L Circuit Working13.6.3 I2L Circuit Switching Speed, Delay Times and Power Dissipation
13.7 High Threshold Logic (HTL)
13.7.1 HTL Connections for the Output at F
13.7.2 Logic Operation for the Output at F
13.8 NMOS13.8.1 NMOS Circuit Connections and Working
13.8.2 Calculation of Fan Out
13.8.3 Calculation of Propagation Delay13.8.4 Calculation of Power Dissipation
13.8.5 NMOS Circuit Voltage Levels
13.8.6 Unconnected Input(s) not Permitted13.9 CMOS13.9.1 Importance and Features of CMOS Logic Circuits
13.9.2 Operations as Inverter (NOT), NOR and NAND
13.9.3 Calculation of Fan out
13.9.4 Calculation of Propagation Delay13.9.5 Calculation of Power Dissipation
13.9.6 CMOS Circuit Voltage Levels
13.9.7 MOS Logic Circuits (CMOSs) and Their Relative Advantages with Respect to TTLs13.10 Meanings of Speed , Propagation Delay, Operating Frequency, Power Dissipated per Gate, Supply Voltage Levels, Operational Voltage Levels that Define Logic States 1 and 0
13.11 Speed , Propagation Delay, Operating Frequency, Power Dissipated per Gate, Supply Voltage Levels, Operational Voltage Levels that Define Logic States ‘1’ and ‘0’ for Various Families of Gates (1/3)
13.11 Speed , Propagation Delay, Operating Frequency, Power Dissipated per Gate, Supply Voltage Levels, Operational Voltage Levels that Define Logic States ‘1’ and ‘0’ for Various Families of Gates (2/3)
13.11 Speed , Propagation Delay, Operating Frequency, Power Dissipated per Gate, Supply Voltage Levels, Operational Voltage Levels that Define Logic States ‘1’ and ‘0’ for Various Families of Gates (3/3)
Chapter 14: CPLDs and FPGAs
14.1 CPLDS
14.2 Registered PAL
14.3 Array Logic Cell
14.4 Field Programmable Gate Arrays (FPGAS) (1/2)
14.4 Field Programmable Gate Arrays (FPGAS) (2/2)
Chapter 15: VHDL—RTL Design, Combinational Logic, Data Types, and Operators
15.1 VHDL
15.1.1 VHDL Standard IEEE 1076
15.1.2 VHDL Standard IEEE 1164
15.1.3 VHDL Libraries
15.1.4 VHDL Identifiers, Keywords, and Comments
15.1.5 VHDL Data Objects
15.2 RTL Design
15.2.1 Data Flow Model
15.2.2 Port
15.2.3 Finite State Machine (FSM)
15.2.4 Entity in RTL Model
15.3 Behaviour Model for Process in an RTL Design
15.3.1 RTL Model Architecture
15.4 RTL Design for Combination Logic
15.5 Data Types
15.5.1 Subtypes
15.5.2 Array
15.5.3 Type Checking
15.6 Operators
Chapter 16: VHDL—Packages, Sub Programs, and Sequential Circuits
16.1 Package
16.1.1 Package Declarations
16.1.2 Package Body
16.2 Subprograms
16.2.1 Procedure
16.2.2 Function
16.2.3 Attribute
16.3 Design Library
16.4 Sequential Circuits
16.4.1 General Sequential Circuit—Entity, Components, Architecture, and Processes
16.4.2 Synchronous Sequential Circuit
16.4.3 Sequencing Clock Circuit—Entity, Architecture and Processes
16.4.4 Clock inputs for Flip-flop and Latch Synchronous Sequential Circuits
16.4.5 Multiple Clock Signals from Main Clock
Chapter 17: VHDL—Test Benches
17.1 Processes and Subprograms
17.1.1 Statements
17.1.2 Vectors
17.1.3 Conversions from a Data Type to another
17.1.4 Now and Wait
17.1.5 Files
17.1.6 Events and Sensitivity List
17.1.7 Assertion, Report, and Severity Functions
17.1.8 Instantiation During Structural Modeling
17.2 Testing of Combinational and Sequential Circuits
17.2.1 Testing of a Combinational Circuit
17.2.2 Testing of a Sequential Circuit
17.3 Test Benches (1/3)
17.3 Test Benches (2/3)
17.3 Test Benches (3/3)
Chapter 18: VHDL—Examples of Modeling of Adder, Counter, Flip-Flop, Finite State Machine, Multiplexer, and Demultiplexer
18.1 Adder18.1.1 Adder Circuit
18.1.2 Test Bench for the Adder
18.2 Counter
18.2.1 Counter Circuit
18.2.2 Test Bench for the Counter
18.3 Flip-Flop
18.3.1 D-Flip-Flop18.3.2 Test Bench for the D-Flip-Flop
18.3.3 JK-Flip-Flop
18.3.4 Test Bench for the JK-Flip-Flop
18.4 Finite State Machine
18.4.1 Finite State Machine Sequential Circuit
18.4.2 Test Bench for the Finite State Machine
18.5 Multiplexer
18.5.1 Multiplexer Circuit
18.5.2 Test Bench for the Multiplexer (2:1)
18.6 Demultiplexer
18.6.1 Demultiplexer Circuit
18.6.2 Test Bench for the Demultiplexer (2:1) (1/6)
18.6.2 Test Bench for the Demultiplexer (2:1) (2/6)
18.6.2 Test Bench for the Demultiplexer (2:1) (3/6)
18.6.2 Test Bench for the Demultiplexer (2:1) (4/6)
18.6.2 Test Bench for the Demultiplexer (2:1) (5/6)
18.6.2 Test Bench for the Demultiplexer (2:1) (6/6)
Solved Question Papers (1/2)
Solved Question Papers (2/2)
Index

Content preview from Digital Systems: Principles and Design by Pearson

Karnaugh Map and Minimization Procedures 3.21

3.7 REPRESENTATIONS OF A FUNCTION (COVER)

FOR A COMPUTER-AIDED MINIMIZATION FOR

SIMPLIFYING THE LOGIC CIRCUITS

When simplifying and ﬁnding the prime implicants manually and up to fewer vari-

ables (six), the Karnaugh maps are suitable. For complex circuits, the computer-

aided minimization is used.

3.7.1 Representation in Cube Format for Computer-aided

Minimization

A cube has three axes, X-axis, Y-axis and Z-axis. Figure 3.5 shows a cube. It has

8 vertices. The origin vertex coordinates are 000, to represent ABC

...

The other

3 vertices along the axes has coordinates are 100, 010, 001 (corresponding ...

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