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Discrete Mathematical Structures

Course Title:Discrete Mathematical

Structures

Course Code: :IS0401

Total Contact Hours: 4 Duration of SEE: 3 Hours

Semester End Examination Max. Marks:100 Continuous Internal Evaluation Max. Marks: 50

Lesson Plan Author: Pradeep kumar H SDate: 28/07/2017

Checked By: Date:

Course Outcomes:

On Successful Completion of the Course, the students will be able to:

1. Explain the fundamental principles of counting, permutation and combination theory.

2. Describe the basics of logic theory and its proofs.

3. Perform operations on Sets, Subsets and solve problems on probability.

4. Describe the discrete structures like functions and relations and apply the knowledge on

functions and its properties.

5. Apply the knowledge on relations and its properties.

6. Solve problems involving recurrence relations and Generating Functions.

UNIT 1: 7 Hrs

Fundamental Principles of Counting:

The Rules of Sum and Product, Permutations, Combinations The Binomial Theorem.

Self Learning Exercise: Combinations with repetition.

UNIT 2: 9 Hrs

Fundamentals of Logic:

Basic Connectives and Truth Tables, Logical Equivalence: The Laws of Logic. Logical Implication: Rules of Inference, The Use of Quantifiers, Mathematical Induction.

Self Learning Exercise: Definitions, and the Proofs of Theorems.

UNIT 3: 9 Hrs

Set Theory:

Sets and Subsets. Set Operations and the Laws of Set Theory. Counting and Venn Diagrams. A First Word on Probability. The Axioms of Probability.

Self Learning Exercise: Conditional Probability: Independence.

UNIT 4: 9 Hrs

Functions:

Cartesian Products and Relations. Functions: Plain and One-to-One. Onto Functions: Stirling Numbers of the Second Kind, Special Functions, The Pigeonhole Principle.

Self Learning Exercise: Function Composition and Inverse Functions.

UNIT 5: 9 Hrs

Relations:

Properties of Relations. Computer Recognition: Zero-One Matrices and Directed Graphs. Partial Orders: Hasse Diagrams.

Self Learning Exercise: Equivalence Relations and Partitions

UNIT 6: 9 Hrs

Recurrence Relations:

First order linear recurrence relations, The Second order linear homogeneous recurrence relation with constant coefficients, Non Homogeneous recurrence relation.

Self Learning Exercise: Method of generating functions.

TEXT BOOK:

1. Discrete and Combinatorial Mathematics, Ralph.P.Grimaldi, Pearson Education. 5th Edition, 2004

REFERENCE BOOK:

1. Discreet Mathematical Structures with Applications to Computer Science J.P.Tremblay and Manohar , MCGraw-Hill International Edition.

2. A Treatise on Discrete Mathematical Structures, Jayant Ganguly, Sanguine- Pearson, 2010

3. Discrete Mathematics and its Applications, Kenneth H. Rosen: 7th Edition. McGraw Hill, 2010

E-BOOKS:

1. Discrete Mathematics: Schaums outline, Third Edition,Schaums Outline Series McGRAW-HILL

2. Applied Discrete Structures by Al Doerr, Ken Levasseur Publisher: Lulu.com 2013

MOOCs: 1. http://www.nptel.ac.in/courses/106106094/ 2. http://www.tutorialspoint.com/discrete_mathematics/

http://www.nptel.ac.in/courses/106106094/http://www.nptel.ac.in/courses/106106094/http://www.nptel.ac.in/courses/106106094/

LOGIC DESIGN (4:0:0)

Sub Code : IS0402 CIE : 50% Marks

Hrs/Week : 04 SEE : 50% Marks

SEE Hrs : 03 Hrs Max. Marks : 100

Course Outcomes:

On Successful Completion of the Course, the students will be able to:

1. Understand the operation of basic gates and interpret basic Boolean laws, different methods of logic simplification. (Understand)

2. Determine output of data processing circuits, timer IC modes and operational amplifiers. (Analyze)

3. Understand different types of number system and operation of arithmetic building block. (Understand)

4. Describe operation of different types of Flip- Flops. (Understand) 5. Understand working of shift register and operation of synchronous, asynchronous and decade

counter. (Understand) 6. Design of SequentialCircuits using moore and mealy model. (Create)

UNIT1: 9Hrs

DigitalLogic:

OverviewofBasicGatesNOT,OR,AND;UniversalLogic GatesNOR,NAND;AND-OR-InvertGATES;Positiveand Negative Logic; Introduction to HDL

CombinationalLogicCircuits:

BooleanLawsAndTheorems;SOPMethod; TruthTabletoK-Map;Pairs,Quadsand Octets;KarnaughSimplifications; Dont-careConditions;POSMethod;POSSimplification; SimplificationbyQuine-McCluskyMethod, HDL Implementation Models

SelfLearningExercise: Conversion between SOP and POS.

UNIT2: 9Hrs

Data-ProcessingCircuits:

Multiplexers; Demultiplexers; BCD-to-decimal Decoders; Encoders; Ex-or GATES; Parity Generators and Checkers; HDL Implementation of Data Processing Circuits, Clocks and Timing Circuits- Clock Waveforms; Schmitt Trigger, 555 Timer- Astable, Monostable.

SelfLearningExercise:TTL Clock

UNIT3: 8Hrs

NumberSystemsandCodes:

Binary Number System; Binary-to-decimal Conversion; Hexadecimal Numbers; The ASCII Code; The Excess-3 Code; The Gray Code

ArithmeticCircuit:

Binary Addition; Binary Subtraction; 2S Complement Representation; 2S ComplementArithmetic;ArithmeticBuildingBlocks;TheAdder-subtracter,ArithmeticLogicUnit; Binary Multiplication and Division.

SelfLearningExercise:Unsigned Binary Numbers; Sign-magnitude Numbers;

UNIT4: 9Hrs

Flip-Flops:

RSFlip-flops;GatedFlip-flops;Edge-triggeredRSFlip-flops; Edge-triggeredDFlip-flops;Edge-triggeredJKFlip-flops Master-slave Flip-flops; Various RepresentationsofFlip-flops;ConversionofFlip-flops: A Synthesis Example

SelfLearningExercise: Flip-flop Timing; AnalysisofSequentialCircuits;

UNIT5: 8Hrs

RegistersandCounters:

TypesofRegisters;SerialInSerialOut;SerialInParallel Out; Parallel InSerial Out Parallel InParallel Out; Asynchronous Counters-Ripple counter mod 16, 3 bit up-down counter; Synchronous-mod 8 binary counter, parallel up-down Counters;Decade Counters- mod 5 counter.

SelfLearningExercise:Applications of Shift Registers; DecodingGates;

UNIT6: 9Hrs

DesignofSequentialCircuits:

ModelSelection;StateTransitionDiagram;StateSynthesisTable;DesignEquationsandCircuitDiagram;Implementation UsingReadOnlyMemory;AlgorithmicStateMachine;State ReductionTechnique

SelfLearningExercise:DesignofAsynchronousSequential Circuit.

TEXTBOOK:

1. Digital Principles and Applications, D P Leach, Albert Paul Malvino, G Saha, Tata McGraw-Hill, 7th Edition, 2011.

REFERENCEBOOK:

1. Logic and Computer Design Fundamentals, M. Morris Mano, Charles R.Kime, Pearson Edu.TMH, 2nd Edition 2013.

2. Fundamentals of Logic Design, Charle H Roth, Jr.,Thomson, 5th Edition, 2010.

3. FundamentalsofDigitalLogicwithVerilogDesign,Stephen Brown, VonkoVranesic, TMH, 2nd

Edition, 2010.

E-BOOKS:

1. http://nsdl.oercommons.org/courses/digital-logic 2. http://www.collegeopentextbooks.org/textbook listings/text- books -by-subject/computer

science

3. http://nsdl.oercommons.org/courses/lab-2-introduction-to-vhdl/view 4. http://ocw.mit.edu/courses/electrical-engineering-and-computer-science

MOOCs: http://oscar.iitb.ac.in/ComputerScience

DATA STRUCTURES (4:0:0)

Sub code : IS0403 CIE : 50% Marks

Hrs/week : 04 SEE : 50% Marks

SEE Hrs : 03 Hours Max. Marks: 100

Course Outcomes:

On Successful Completion of the Course, the students will be able to:

1. Apply the concept of pointers. 2. Explain the basic concepts of stacks. 3. Analyze and solve the problems using types of Queues. 4. Discuss linked list operations and its implementation. 5. Design and implement the circular list. 6. Construct the non linear data structure trees.

UNIT 1: 9 Hrs

Pointer: Understanding pointers, Pointer variables, Accessing address of a variable, Initialization of pointer variables, Accessing variables through pointers, Chain of pointers, Pointer expressions, Pointer Arithmetic and arrays, Array of pointers, Pointers as function argument, Function returning pointers, Pointers to function.malloc, free

Self Learning Exercise:Dynamic memory allocation calloc, realloc,Similarity between pointers and subscripted variables.

UNIT 2: 9 Hrs

Abstract Data Types: Introduction. Stack: Definition and examples, Representing stacks in C, An example: Infix, Postfix, Prefix. Recursion: Recursive definition and processes. Recursion in C, Writing recursive programs

Self Learning Exercise:Application ofstacks

UNIT 3: 8 Hrs

Queue: The Queue and its representation and implementation, Circular Queue implementation.

Self Learning Exercise:Priority Queue

UNIT 4: 9 Hrs

Linked Lists1: Inserting and Removing nodes from a list, Implementation of stacks, getnode and freenode operations, Linked implementation of queues, Linked list as a data structure, Example of list operations, Header nodes, List in C. Allocating and freeing dynamic variables. Linked lists using dynamic variables.

Self Learning Exercise:Comparison of lists and arrays with respect to insertion, deletion and storage.

UNIT 5: 9 Hrs

Linked Lists2: Queues as lists in C, Examples of list operations in C, Circular lists, Stack as a circular lists, Que