Digital Logic Design

Second year - First Semester

Instruction: 3 Periods & 1 Tut /week

Univ. Exam : 3 Hours

Sessional Marks: 30

Univ-Exam-Marks:70

1. Binary Systems, Boolean Algebra and Logic Gates.

Digital Systems. Binary Numbers. Number Base Conversions. Octal and HexadecimalNumbers. Complements. Signed Binary Numbers. Binary Codes. Binary Storage andRegisters. Binary Logic

Basic Definitions. Axiomatic Definition of Boolean Algebra. Basic Theorems andProperties of Boolean Algebra. Boolean Functions. Canonical and Standard Forms.Other Logic Operations. Digital Logic Gates. Integrated Circuits.

2. Combinational Logic Design, Gate-Level Minimization.

The Map Method. Four-Variable Map. Five-Variable Map. Product of SumsSimplification. Don't-Care Conditions. NAND and NOR Implementation. Other Two-Level Implementations. Exclusive-OR Function. Hardware Description Language(HDL).

Combinational Logic

Combinational Circuits. Analysis Procedure. Design Procedure. Binary Adder-Subtractor. Decimal Adder. Binary Multiplier. Magnitude Comparator. Decoders.Encoders. Multiplexers. HDL For Combinational Circuits.

3. Sequential Logic Design, Synchronous Sequential Logic

Sequential Circuits. Latches. Flip-Flops. Analysis of Clocked Sequential Circuits.HDL For Sequential Circuits. State Reduction and Assignment. Design Procedure.

Registers ad Counters.

Registers. Shift Registers. Ripple Counters. Synchronous Counters. Other Counters.HDL for Registers and Counters

Fundamentals of Asynchronous Sequential Logic

Introduction. Analysis Procedure. Circuits With Latches. Design Procedure. Hazards

4. Memory and Programmable Logic

Introduction. Random-Access Memory. Memory Decoding. Error Detection andCorrection. Read-Only Memory. Programmable Logic Array. Programmable ArrayLogic. Sequential Programmable Devices.

Text Book :

Digital Design, 3rd Edition, M. Morris Mano, Pearson Education, Inc.,2002

Reference Books:

1. Digital Logic Design Principles, Norman Balabanian and Bradley Carlson,John Wiley & Sons(Asia) Pte. Ltd., 2002

2. Fundamentals of Digital Circuits, A. Ananda Kumar, PHI, 2002

3. Digital Circuits and Design, 2nd Edition,S Salivahanan and S Arivazhagan,Vikas Publishing House Pvt. Ltd., 2003

4. Fundamentals of Digital Logic with VHDL Design, Stephen Brown andZvonko Vranesic, Tata McGraw-Hill Edition, 2002

Data Structures

Introduction to Data Structures: Information and Meaning – Representation of Multi- Dimensional Arrays _ Review of C Programming.

The Stack: Primitive operations – As an Abstract Data Type – Implementing the Stack operations in C.

Infix, Postfix and Prefix: Definitions, Evaluation and Conversions using C.

Recursion: Recursive Definition and Processes, Recursion in C and Recursive Implementation of Applications. Simulation of Recursion – Efficiency of Recursion.

Queues and Lists: The Queue as Abstract Data Type – Sequential Representation _Types of Queues – Operations – Implementation in C.

Linked List: Operations – Implementation of Stacks, Queues and priority Queues in C.

Circular Lists: Insertion, Deletion and Concatenation Operations _ Stacks and Queues as Circular Lists _ Doubly Linked Lists _Applications.

Trees: Binary Trees Operations and Applications.

Binary Tree Representation: Node Representation – Implicit array Representation – Choice of Representation – Binary Tree Traversal – Threaded Binary Trees and their Traversal – Trees and their Applications

Sorting: General Background: Efficiency – The big 0 Notation – Efficiency of Sorting. Bubble Sort and Quick Sort and their Efficiency – Selection Sorting – Binary Tree Sort – Heap Sort – Insertion Sorts – Shell Sort – Address calculation Sort – Merge and Radix Sorts.

Searching: Basic Searching Techniques: Dictionary as an Abstract Data Type – Algorithmic Notation – Sequential Searching and its Efficiency – Binary Search – Interpolation Search.

Tree Searching: Insertion into a Binary Search Tree – Deleting from a Binary Search Tree – Efficiency of Binary Search Tree operation

Graphs and Their Application: Graphs: Application of Graphs – Representation of Graphs in C – Transitive closure – Warshall’s Algorithm – Shortest Path Algorithm.

Linked Representation of Graphs: Dijikstra’s Algorithm – Organizing the set of Graph Nodes – Application to Scheduling and its implication.

Graph Traversal and Spanning Forests – Undirected Graph and their Traversals, Applications and Efficiency – Minimal Spanning Trees –Prim’s and Kruskal’s Algorithms.

Textbooks:

1. Data Structures Using C and C++ Yddish Langsam, Moshe J. Augenstein and Aaron M. Tanenbaum, Prentice Hall Of India (2nd Edition) (Chapters 1 to 8)

2. Data Structures, Algorithms and Applications with C++, Sahani Mc-Graw Hill.

Note: All Implementation are Using C Language only

Discrete Mathematical Structures - I

Instruction: 3 Periods & 1 Tut /week

Univ. Exam : 3 Hours

Sessional Marks: 30

Univ-Exam-Marks:70

Introduction: Sets-Operations on sets-relations-functions-Proof methods and problem solving strategies-Fundamentals of Logic- Logical inferences-Methods of proof of an implication-First Order logic and Other Proof methods-Rules of inference for quantified Propositions-Mathematical Induction

Elementary Combinatorics: Basics of Counting- Combinations and Permutations-Their Enumeration with and without repetition-Binomial coefficients-Binomial and Multinomial Theorems-The Principle of Inclusion-Exclusion.

Recurrence Relations: Generating Functions of Sequences-Calculating their Coefficients-Recurrence relations-Solving recurrence relations-Method of characteristic Roots- Non-homogeneous Recurrence relations and their solutions

Relations and Digraphs: Relations and Directed Graphs-Special Properties of Binary relations- Equivalence Relations-Ordering Relations-Lattices and Enumeration- Operations on relations-Paths and Closures-Directed Graphs and Adjacency matrices- Applications of sorting, searching and topological sorting.

Graphs: Basic concepts-Isomorphism-subgraphs-Planar Graphs-Euler’s formula- Multigraphs and Euler circuits-Hamiltonian graphs-Chromatic numbers-Four color theorem.

Trees: Trees and their properties-Trees as graphs-spanning trees-Directed trees-Binary trees-Their traversals-Arithmetic and Boolean expressions as trees- height balanced trees.

Text Book:

"Discrete Mathematics for computer scientists & Mathematicians" by Joe L. Mott, Abraham Kandel & T. P. Baker, Prentice Hall of India Ltd, New Delhi

Reference Books:

1) "Discrete mathematics and its applications" by Keneth. H. Rosen, , Tata McGraw- Hill Publishing Company, New Delhi

2) "Discrete mathematics" by Richard Johnsonbaug, Pearson Education, New Delhi

Probability, Statistics & Queuing Theory

Instruction: 3 Periods & 1 Tut /week

Univ. Exam : 3 Hours

Sessional Marks: 30

Univ-Exam-Marks:70

Probability: Definitions of probability, Addition theorem, Conditional probability,Multiplication theorem, Bayes theorem of probability and Geometric probability.

Random variables and their properties, Discrete Random variable, Continuous Randomvariable, Probability Distribution joint probability distributions their properties,Transformation variables, Mathematical expectations, probability generating functions.

Probability Distributions / Discrete distributions: Binomial, Poisson Negative binominaldistributions and their properties. (Definition, mean, variance, moment generatingfunction., Additive properties, fitting of the distribution.)

Continuous distributions: Uniform, Normal, exponential distributions and their roperties.Curve fitting using Principle of Least Squares.

Multivariate Analysis: Correlation, correlation coefficient, Rank correlation, RegressionAnalysis, Multiple Regression, Attributes, coefficient of Association, X² – test forgoodness of fit, test for independence.

Sample, populations, statistic, parameter, Sampling distribution, standard error,unbiasedness, efficiency, Maximum likelihood estimator, notion & interval estimation.Testing of Hypothesis: Formulation of Null hypothesis, critical region, level ofsignificance, power of the test.

Small Sample Tests: Testing equality of .means, testing equality of variances, test ofcorrelation coefficient, test for Regression Coefficient.

Large Sample tests: Tests based on normal distribution

Queuing theory: Queue description, characteristics of a queuing model, study statesolutions of M/M/1: α Model, M/M/1 ; N Model.

Text Book:

Probability, Statistics and Random Processes by T.Veerarajan, Tata McGraw Hill

Reference Book:

Probability & Statistics with Reliability, Queuing and Computer Applications by Kishor S. Trivedi , Prentice Hall of India ,1999

Elements of Electrical Engineering

Instruction: 3 Periods & 1 Tut /week

Univ. Exam : 3 Hours

Sessional Marks: 30

Univ-Exam-Marks:70

Magnetic circuits: Definitions of magnetic circuit, Reluctance, Magneto-motive force), magnetic flux, Simple problems on magnetic circuits, Hysterisis loss.

Electromagnetic Induction : Faraday’s laws of Electromagnetic Induction, Induced E.M.F., Dynamically induced E.M.F., Statistically induced EMF, Self Inductance, Mutual Inductance.

D.C. Generators: D.C.Generator principle, construction of D.C. generator, E.M.F equation of D.C. generator, Types of D.C. generator, Efficiency, Characteristics of D.C. generator, Efficiency, Applications of D.C. generator

D.C. Motors: D.C. Motor principle, working of D.C.Motors. significance of back E.M.F., Torque equation of D.C. Motors, Types of D.C. Motors, Characteristics of D.C. Motors, Speed control methods of D.C. Motors, Applications of D.C. Motor. Testing of D.C. Machines : Losses and Efficiency, Direct load test and Swinburne’s test.

A.C. Circuits: Introduction to Steady State Analysis of A.C. Circuits, Single and Balanced 3 Phase Circuits.

Transformers: Transformer principle, EMF equation of transformer, Transformer on load, Equivalent circuit of Transformer, Voltage regulation of Transformer, Losses in a Transformer, Calculation of Efficiency and Regulation by Open circuit and Short circuit Tests.

Three phase Inductance Motor: Induction Motor working principle. Construction of 3 Phase induction Motor, Principle of operation. Types of 3 phase induction Motor., Torque Equation of Induction Motor., slip – Torque characteristics., Starting Torque, Torque under running condition., Maximum Torque Equation., Power stages of Induction Motor., Efficiency Calculation of Induction Motor by direct loading.

Alternator: Alternator working principle, EMF equation of Alternator, Voltage Regulation by Sync. Impedance method.

Synchronous Motor: Synchronous Motor principle of Operation, Construction., Methods of starting of synchronous motor

Text Book:

"Elements of Electrical Engineering and Electronics" by V.K.Mehta, S. Chand & Co

Reference Book:

"A First Course in Electrical Engineering" by Kothari.