📘 Unit 3 – Boolean Algebra (MCA)

 

1. Boolean Algebra Basics

• Boolean Algebra deals with variables that take two values only:

  • 0 (false/LOW)

  • 1 (true/HIGH)

• The main operations are:

  • AND (·) → Output is 1 if both inputs are 1.

  • OR (+) → Output is 1 if at least one input is 1.

  • NOT (') → Output is the complement of the input.

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2. Basic Boolean Laws

Here are some important laws of Boolean algebra:

• Identity Laws

  • A + 0 = A

  • A · 1 = A

• Null Laws

  • A + 1 = 1

  • A · 0 = 0

• Idempotent Laws

  • A + A = A

  • A · A = A

• Complement Laws

  • A + A' = 1

  • A · A' = 0

• Involution Law

  • (A')' = A

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3. DeMorgan’s Theorems

Two very important rules:

1. (A · B)' = A' + B'

2. (A + B)' = A' · B'

👉 These are very useful for simplification and circuit design.

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4. Duality Principle

Every Boolean expression remains valid if:

• + is replaced with ·

• 0 is replaced with 1
  (and vice versa).

Example:
(A + 0) = A
Dual → (A · 1) = A ✅

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5. Simplification Example

Simplify:
F = A · (B + B')

• B + B' = 1 (Complement Law)

• So F = A · 1 = A ✅

UNIT 1 - DBMS (MCA )

 

Lesson 1: The Problem with Files (and why we need a DBMS)

Imagine you own a small online store. Initially, you might manage your business using spreadsheets, just like a regular file system. You'd have:

• Customers.xlsx (with customer names, addresses)

• Products.xlsx (with product names, prices)

• Orders.xlsx (with who ordered what, and the customer's shipping address)

This works for a while, but as your store grows, you'll run into some major headaches. 🤯

Problem 1: Data Redundancy (Duplication)

Notice that the customer's shipping address is in Customers.xlsx AND in Orders.xlsx. You're storing the same piece of information in multiple places. This is data redundancy. It wastes space and leads to the next big problem.

Problem 2: Data Inconsistency

A customer, Rohan, moves to a new house. He emails you his new address. You update his address in your main Customers.xlsx file, but you forget to update it in the Orders.xlsx file for a recent order he placed.

Now you have a conflict! Which address is correct? The data is inconsistent. You might accidentally ship his order to the old address.

Problem 3: Difficult Data Access

One day, you want to ask a simple business question: "Show me the top 3 products bought by customers from Delhi."

With your spreadsheets, this is a nightmare. You'd have to:

1. Go to Customers.xlsx to find all customers from Delhi.

2. Copy their names.

3. Go to Orders.xlsx and manually filter through thousands of rows to find the orders placed by those specific customers.

4. Count the products to find the top 3.

This is slow, tedious, and prone to errors.

The Solution: The Database Management System (DBMS) ✨

A DBMS is a smart software system designed to solve all these problems. Think of it as a highly organized, intelligent, and secure digital filing cabinet.

Here's how a DBMS would handle your store:

Instead of separate files, you'd have one central database. Inside, the data is stored in structured tables that are linked together.

1. A Customers Table: Stores customer info (ID, Name, Address). Each customer is listed only once.

2. A Products Table: Stores product info.

3. An Orders Table: When an order is placed, this table doesn't copy the customer's whole address. It simply references the customer using their unique Customer ID.

Now, let's see how the problems are solved:

• No Redundancy: Rohan's address is stored in only one place: the Customers table.

• Guaranteed Consistency: When Rohan moves, you update his address in the Customers table. Since the Orders table just points to Rohan's ID, any new order automatically uses the correct, updated address. The data is always consistent.

• Easy Data Access: Answering "Show me the top 3 products bought by customers from Delhi" becomes a simple, one-line command in a language like SQL (which we'll cover in Unit 3). The DBMS does all the hard work of linking the tables and finding the answer in seconds.

In summary:

Feature	File System (e.g., Excel)	DBMS
Structure	Unstructured, separate files 👎	Centralized, structured tables 👍
Redundancy	High	Minimal
Consistency	Low	High
Security	Poor (file-level)	Excellent (user-level)
Access	Difficult, manual	Easy, powerful (using SQL)

This fundamental difference is why almost every modern application, from banking apps to social media, is built on a database.

📖 Paper 1 – Unit 1: Algorithm Development and C Language Programming (MCA)

Part 1: Structure and Properties of an Algorithm

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1. What is an Algorithm?

An algorithm is a step-by-step set of instructions to solve a specific problem.

Example:
If you want to make tea:

1. Boil water.

2. Add tea leaves.

3. Add sugar.

4. Add milk.

5. Stir and serve.

That’s an algorithm — but in cooking terms.

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Properties of a Good Algorithm

1. Definiteness → Every step must be clear and unambiguous.

2. Finiteness → Must end after a finite number of steps.

3. Input → Takes zero or more inputs.

4. Output → Produces at least one output.

5. Effectiveness → Steps are basic enough to be done by hand or by computer.

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Example in Computing:
Problem: Find the largest of two numbers A and B.

Algorithm:

1. Start.

2. Input A and B.

3. If A > B, print A.

4. Else, print B.

5. Stop.

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📍 Flowcharts

A flowchart is a graphical representation of an algorithm, using different shapes to represent different actions.

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Common Flowchart Symbols

Symbol	Meaning
⭕ Oval	Start / End
⬜ Rectangle	Process / Instruction
🔶 Diamond	Decision (Yes/No)
⬠ Parallelogram	Input / Output

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Example Flowchart:
Algorithm: Find the largest of two numbers.

   ⭕  Start
    ↓
  ⬠  Input A, B
    ↓
  🔶 Is A > B ?
   /  \
 Yes    No
 |      |
⬜ Print A  ⬜ Print B
 |      |
 ⭕ End

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Why Flowcharts Matter:

• Makes logic visual.

• Easier to debug before coding.

• Helps in team communication.

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✅ Practice Task:
Draw a flowchart for finding the largest of three numbers (A, B, C).
Hint: You’ll need two decision diamonds.

MCA SYLLABUS ALLAHABAD UNIVERSITY 2025

 PAPER 1: PROGRAMMING IN ‘C’ WITH DATA STRUCTURES (MCA540) 

Unit 1 : Algorithm development and C language Programming: Structure and properties of algorithm,   Flowchart, Introduction to C, Compilation & execution of C programs, , Data types & sizes, Declaration of variables, Modifiers, Identifiers & keywords, Symbolic constants, Operators: Unary operators, Arithmetic & Logical operators, Bit-wise operators, Assignment operators and expressions, Conditional expressions, Precedence & associativity, order of evaluation. Control statements: If-else, Switch, Break, Continue, Go-to statement; Loops: For, While, Do-while. 

Unit 2: Functions and Arrays: Functions: Built-in & User-defined, Function declaration, Definition &function call, Parameter passing: Call by value, Call by reference, Recursive functions. Linear arrays, Multi-dimensional arrays, passing arrays to functions, Arrays & Strings; Storage classes: Automatic, External, Register & Static. 

Unit 3: Pointers and Linked list: Pointers: Value at (*) and address of (&) operator, Pointer to pointer, Dynamic memory allocation, Calloc & Malloc functions, Array of pointers, Function of pointers, Macros, C pre-processor, Structures & Union: Definition and differences. Linked list and Operations (insertion, deletion and modification): Singly linked lists, Circular list, Doubly linked lists and its application, array and linked representation.  

Unit 4: Stacks and Queues and Trees: Stacks: Basic idea, array and linked representation. Prefix/ infix / postfix expressions and their inter-conversion for evaluation. Queues:  Basic idea, array and linked representation, Priority queues and simulation, Recursion. Trees: Definition, terminologies and properties, Binary tree representation traversals and applications, Binary Search trees, Threaded binary trees.

 Unit 5:Sort and Search Algorithms: Linear and Binary search. Internal and External Sorting algorithms, Heap sort, Merge sort, Quick-sort, Radix sort, Bucket sort. Hashing: Hash functions, collision resolution techniques (chaining, linear offset, others). 

Reference Books: 

1. The C Programming Language, B.W. Kernighan and D.M. Ritchie (PHI) 

2. Programming using the C language, R.C. Hutchinson and S.B. Just (McGraw Hill) 

3. Data Structures and Program Design- Robert Kruse. 

4. Data Structures- Horowitz and Sahni 

5. Data Structures through C- A. Tennenbaum 4 

PAPER 2: DATABASE MANAGEMENT SYSTEM (MCA541) 

Unit 1: Introduction and ER Modelling: An overview of database management system, Database System Vs File System, Data models schema and instances, data independence and data base languages. Data Definitions Language, Data Manipulation Language, Overall Database Structure. Data Modelling using the Entity Relationship Model: ER model concepts, notation for ER diagram, mapping constraints, keys, Concepts of Super Key, candidate key, primary key, Generalization, aggregation, reduction of an ER diagrams to tables, extended ER model, relationships of higher degree. 

Unit 2: Relational data Model and Language: Relational data model concepts, integrity constraints: entity integrity, referential integrity, Keys constraints, Domain constraints, relational algebra, relational calculus, tuple and domain calculus. 

Unit 3: Introduction to SQL: Characteristics of SQL, Advantages of SQL, SQL data types and literals, Types of SQL commands, SQL operators and their procedure, Tables, views and indexes, Queries and sub queries, Aggregate functions, Insert, update and delete operations, Joins, Unions, Intersection, Minus, Cursors in SQL. PL/SQL, Triggers and clusters. 

Unit 4: Data Base Design & Normalization: Functional dependencies, normal forms, first, second, third normal forms, BCNF, inclusion dependencies, normalization using functional dependency, Multivalued dependency and Join dependency. 

Unit 5: Transaction Processing & System Architecture: Introduction: Transaction Processing, Transaction System Concepts, Transaction Atomicity, Durability, and Isolation, Serializability. Concurrency Control: Deadlock Handling, Multiple Granularity, Lock-Based Protocols, TimestampBased Protocols, Validation-Based Protocols. Database-System Architectures: Centralized and ClientServer Architectures, Server-System Architectures, Parallel Systems, Distributed Systems, Network Types. 

References: 

1 Date C J, “An Introduction To Database System”, Addision Wesley 

2 Korth, Silbertz, Sudarshan, “Database Concepts”, McGraw Hill 

3 Elmasri, Navathe, “Fundamentals Of Database Systems”, Addision Wesley 

4 Paul Beynon Davies, “Database Systems”, Palgrave Macmillan 5 

PAPER 3: COMPUTER ORGANIZATION & ARCHITECTURE (MCA542) 

Unit 1: Generation of Computers, Functional block diagram of a computer, Hardware and Software, Generation of programming languages-Machine Level Language, Assembly Level language and High Level Language; Digital Computers ,Number Systems-Binary, Octal, Decimal Hexadecimal, and Conversion; Binary Arithmetic- Binary Addition, Subtraction etc. 

Unit 2: Logic Gates, Boolean Algebra, Minterms, Maxterms, Sum of Product Form, Product of Sum Form, realization of switching expressions by Karnaugh map ; Codes- weighted, unweighted codes, self Complementing Code, Gray Code, BCD, Excess 3 Code ; Code Conversion 

Unit 3: Adder-Half, Full, 4 and 8 bit parallel adder circuits,  and Subtractor-Half, full, 4 and 8 bit  parallel subtractor circuits; Magnitude comparator, Decoders, Encoders, Multiplexer and demultiplexer, Realization of switching expressions by decoders, encoders, multiplexer and Demultiplexer, Sequential circuits, latches and Flip Flops-SR, D, JK and T flip flops;  Analysis of clocked sequential circuits. State reduction and assignment; Counters-Ripple Counter, Ring Counter etc 

Unit 4: Introduction to microprocessors, essential and non-essential elements of a microprocessor, addressing modes, Interrupts and its types, Instruction cycle, machine cycle, T-state, pipelining, Superpipeline, Superscalar Pipeline, Pipeline Hazards. 

Unit 5: Memory Hierarchy, IO methods-Direct IO (DMA) and Indirect IO-Memory Mapped IO and IO Mapped IO; Memory Interleaving-Lower and Higher order Interleaving , Memory organization-2D and 3D, Cache Memory, addressing cells in the cache memory: Associative and Direct memory organization, Memory Management. 

References: 

1. William Stalling, “Computer Organization & Architecture”, Pearson education Asia 

2. Mano Morris, “Computer System Architecture”, PHI 

3. Zaky&Hamacher, “Computer Organization”, McGraw Hill 

4. B. Ram, “Computer Fundamental Architecture & Organization”, New Age 6 

PAPER 4: PRINCIPLES OF MANAGEMENT (MCA543) 

Unit 1: Definition, Functions, Process, Scope and Significance of Management. Nature of Management, Managerial Roles, Managerial Skills and Activities, Difference between Management and Administration. Significance of Values and Ethics in Management.  

Unit 2: Evolution of Management Thought, Approaches of Management Thought, Functions of Management.  

Unit 3:  Planning and Organizing Nature, Scope, Objective and Significance of Planning, Elements and Steps of Planning, Decision Making Organizing Principles, Span of Control, Line and Staff Relationship, Authority, Delegation and Decentralization. Effective Organizing, Organizational Structures, Formal and Informal Organizations, Staffing.  

Unit 4: Directing -Effective Directing, Supervision, Motivation, Different Theories of Motivation Maslow, Herzberg, Mc Clelland, Vroom, Porter and Lawler, Job Satisfaction. Concept of Leadership- Theories and Styles. Communication Process, Channels and Barriers, Effective Communication.  

Unit 5: Controlling and Coordinating- Elements of Managerial Control, Control Systems, Management Control Techniques, Effective Control Systems. Coordination Concept, Importance, Principles and Techniques of Coordination, Concept of Managerial Effectiveness. 

References: 1. Management: Principles and Practice by S.K. Mandal 

2. Management Principles and Practices by Parag Diwan 7 

PAPER 5: SOFTWARE ENGINEERING & CASE TOOLS (MCA544) 

Unit 1: Introduction to software engineering and software development life cycle models: Introduction to Software, Types of Software, Introduction to Software Engineering, Software Processes; SDLC: Introduction, Models. 

Unit 2: Software Requirement and Quality Assurance: Requirement Engineering, Types of Requirements, SRS, Characteristics of SRS, DFD and ERD; Verification and Validation; Software quality Assurance: definition, Objectives, Goals and Plan; CMM. 

Unit 3: System Design and Software Measurement: Design Objective, Design Principles, Modularization, Coupling and Cohesion; Software Metrics: Definition and Types. 

Unit 4: Software Testing and Maintenance: Testing Principles, Levels of Testing, White Box and Black Box Testing; Software Configuration Management, Need and Types of Maintenance, COCOMO. 

Unit 5: Risk Management, CASE Tools and Case Studies: Risk Analysis; Project Scheduling; Reverse Engineering; Re-engineering. Introduction to CASE tools, Use and Application; Case Study: To analyse a problem and prepare a SRS document including DFD and ERD. 

References:
1. Pressman, Roger S., “Software Engineering: A Practitioner’s Approach Ed. Boston: McGraw Hill, 2001 

2. Jalote, Pankaj, “Software Engineering Ed.2”, New Delhi: Narosa 2002 

3. Schaum’s Series, “Software Engineering”, TMH 

4. Ghezzi, Carlo and Others, “Fundamentals of Software Engineering”, PHI 8 

PAPER 6: DISCRETE STRUCTURES & GRAPH THEORY (MCA545) 

Unit 1: Logic: Logical Statement, Logical Operators and their Properties, Tautology, Contradiction and Contingency, Normal Forms and Properties, Implications and Biconditional, Arguments and Fallacy, Rules of Inference, Predicate Logic: Quantifier, Validity of a Predicate, Properties and Translation. 

Unit 2: Combinatorics: Permutations and Combination, Summation: Properties of Binomial Function and Generating Functions, Solution of Recurrence Relation. 

Unit 3: Set Theory: Relations: Definition of Relation, R-Relative Set, Representation of a Relation, Operations on Relations, Types of Relations, Counting of Relations and Closure of Relations, Equivalence Relations and Partial Order Relation, Properties of Equivalence Relations and Power of a Relation, Functions: Definition of Function, Domain and Range, Types of Functions, Counting of Functions, Inverse of Function, Composition, Group Theory 

Unit 4: Poset, Lattices and Boolean Algebra: Poset, Toset, Woset, Topological Sorting, Hasse Diagram, Extremal Elements of Posets, Lattice, Semi Lattice, Properties of Lattice, Types of Lattice, Boolean Algebra 

Unit 5: Graph Theory: Definition of Graph, Types of Graph, Degree of a Vertex, Special Graph, Graph Representation, Graph Traversal (BFS and DFS), Isomorphism of Graph, Connectivity of Graph, Applications: Euler’s Graph, Hamiltonian Graph, Planar Graph, Trees: Spanning Tree, Enumeration of Graph and Graph No. 

References: 1. Discrete Mathematical Structures with Application to Computer Science- Tremblay &    Manohar.   

2. Discrete Mathematical Structures – Preparata and Yeh