✅ UNIT 2 — Logic Gates, Boolean Algebra, K-Maps, Codes

🌟 2.1 LOGIC GATES

Logic gates are electronic circuits that perform logical operations on binary inputs (0 or 1).

1️⃣ Basic Gates

AND Gate

A	B	Output = A • B
0	0	0
0	1	0
1	0	0
1	1	1

OR Gate

A	B	A + B
0	0	0
0	1	1
1	0	1
1	1	1

NOT Gate

A	A'
0	1
1	0

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2️⃣ Universal Gates (NAND, NOR)

Any circuit can be built using only NAND or only NOR.

NAND Gate

Output = (A • B)’
Truth Table → Only 1 when both inputs are NOT 1.

NOR Gate

Output = (A + B)’
Truth Table → Only 1 when both inputs are 0.

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3️⃣ Exclusive Gates

XOR Gate

Output = 1 when inputs are different.
Equation: A ⊕ B = A’B + AB’

XNOR Gate

Output = 1 when inputs are same.

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🌟 2.2 BOOLEAN ALGEBRA

Important Laws

1. Identity Laws

A + 0 = A
A • 1 = A

2. Null Laws

A + 1 = 1
A • 0 = 0

3. Idempotent Laws

A + A = A
A • A = A

4. Complement Laws

A + A’ = 1
A • A’ = 0

5. De Morgan’s Laws

(AB)’ = A’ + B’
(A + B)’ = A’B’

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🌟 2.3 Minterms & Maxterms

Minterm (SOP Form)

Each minterm = product term (AND)
Example for 2 variables:
m0 = A’B’
m1 = A’B
m2 = AB’
m3 = AB

Sum of Minterms = SOP

Maxterm (POS Form)

Each maxterm = sum term (OR)
M0 = A + B
M1 = A + B’ etc.

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🌟 2.4 Simplification Using Karnaugh Map (K-MAP)

Example:

Simplify F(A, B, C) = Σ(1, 3, 5, 7)

K-MAP:

Fill 1’s in cells 1,3,5,7.

Groups formed:

• Group of four (1,3,5,7)

Final simplified function:
👉 F = B

K-map makes long Boolean expressions very small.

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🌟 2.5 NUMBER CODES

✔ 1. Weighted Codes

Each digit has a weight.
Examples:

• 8421 (BCD)

• 2421

• 5211

✔ 2. Non-Weighted Codes

Weights do NOT apply.
Examples:

• Gray Code

• Excess-3

• ASCII

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Gray Code

Only one bit changes between consecutive numbers (used in error-free encoding).

Binary to Gray:

G1 = B1
G2 = B1 ⊕ B2
G3 = B2 ⊕ B3

Example:
Binary 101 → Gray = 111

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Excess-3 Code

Add 3 to each BCD digit.

Example:
BCD 0101 (5)
Excess-3 = 0101 + 0011 = 1000

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Code Conversions Covered

✔ Binary ↔ Gray
✔ Binary ↔ BCD
✔ BCD ↔ Excess-3
✔ Hex ↔ Binary
✔ Decimal ↔ Binary

🧩 UNIT 1 — Computer Basics and Number Systems

 🌍 1.1 Generation of Computers

Computers have evolved drastically — from vacuum tubes to AI-powered processors. Each generation is marked by hardware technology, processing speed, and language level.

Generation	Years	Technology Used	Language Used	Example Computers	Features
1st Generation	1940–1956	Vacuum Tubes	Machine Language	ENIAC, UNIVAC	Large, slow, expensive, consumed a lot of power
2nd Generation	1956–1963	Transistors	Assembly Language	IBM 1401, CDC 1604	Faster, smaller, less heat, more reliable
3rd Generation	1964–1971	Integrated Circuits (ICs)	High-Level Languages (FORTRAN, COBOL)	IBM 360, PDP-8	Smaller, faster, multitasking possible
4th Generation	1971–1980s	Microprocessors (VLSI)	High-Level Languages (C, BASIC)	Intel 4004, Apple II	Personal computers introduced
5th Generation	1980s–Present	ULSI, AI, Parallel Processing	AI languages (Prolog, Python, ML)	IBM Watson, Quantum computers	AI, machine learning, natural language processing

🧠 Key Idea:
Each generation increased speed, reliability, miniaturization, and user-friendliness while reducing cost and power consumption.

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💻 1.2 Functional Block Diagram of a Computer

Every computer follows a simple structure known as the Von Neumann Architecture.

+--------------------------------------------+
|                USER INTERFACE              |
+--------------------------------------------+
| INPUT → CPU (ALU + CU + Registers) → OUTPUT |
|                 ↑          ↓                |
|              MEMORY (Primary + Secondary)  |
+--------------------------------------------+

1️⃣ Input Unit:
Takes data and instructions (e.g., keyboard, mouse, scanner).

2️⃣ Output Unit:
Displays results to the user (e.g., monitor, printer).

3️⃣ Memory Unit:
Stores data temporarily or permanently.

• Primary Memory: RAM, ROM

• Secondary Memory: Hard Disk, SSD

4️⃣ CPU (Central Processing Unit):

• ALU (Arithmetic Logic Unit): Performs calculations and logical operations.

• CU (Control Unit): Controls the flow of data and instruction execution.

• Registers: High-speed storage inside CPU for quick data access.

🧩 Flow:

Input → Process (CPU) → Output
          ↑
        Memory

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🧠 1.3 Hardware vs Software

Aspect	Hardware	Software
Definition	Physical components of a computer	Set of programs/instructions
Examples	Keyboard, CPU, Hard disk	OS, MS Word, Browser
Tangibility	Can be touched	Intangible
Failure	Hardware wears out	Software bugs
Dependency	Needs software to function	Runs on hardware

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💬 1.4 Types of Programming Languages

Type	Description	Example
Machine Language	Binary (0s and 1s), directly understood by computer	10110100 01100001
Assembly Language	Uses mnemonics for machine instructions	MOV A, B
High-Level Language	Human-readable, needs compiler/interpreter	C, Java, Python

Conversion Tools:

• Assembler: Assembly → Machine

• Compiler: High-Level → Machine (all at once)

• Interpreter: High-Level → Machine (line by line)

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🔢 1.5 Number Systems

System	Base	Digits Used	Example
Binary	2	0, 1	1011
Octal	8	0–7	27
Decimal	10	0–9	45
Hexadecimal	16	0–9, A–F	2F

Conversions:

• Binary → Decimal: Multiply each bit by 2ⁿ and sum.
  Example: 1011₂ = 1×8 + 0×4 + 1×2 + 1×1 = 11₁₀

• Decimal → Binary: Divide by 2 repeatedly and write remainders in reverse.
  Example: 13₁₀ → 1101₂

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➕ 1.6 Binary Arithmetic

Operation	Example	Result
Addition	101 + 10	111
Subtraction	101 – 10	11
Multiplication	101 × 10	1010
Division	1010 ÷ 10	101

Binary Addition Rules:

+	0	1
0	0	1
1	1	10 (carry 1)

Addition of Two 8-bit Numbers (in Assembly)

 

Program 1: Addition of Two 8-bit Numbers

Add values at C050H and C051H and store result in C052H.

LDA C050H
MOV B, A
LDA C051H
ADD B
STA C052H
HLT

sql query practice

 

1️⃣ Create Employee Table

CREATE TABLE Employee(
    EmpID INT PRIMARY KEY,
    EName VARCHAR(50),
    Job VARCHAR(50),
    Salary DECIMAL(10,2),
    City VARCHAR(50)
);

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2️⃣ Add Columns HRA, PF, DA with Domain (numeric)

ALTER TABLE Employee
ADD HRA DECIMAL(10,2);

ALTER TABLE Employee
ADD PF DECIMAL(10,2);

ALTER TABLE Employee
ADD DA DECIMAL(10,2);

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3️⃣ Insert 5 Records (Using Keyboard / Manual Insert)

INSERT INTO Employee(EmpID, EName, Job, Salary, City) VALUES
(101,'Adarsh','Manager',50000,'Delhi'),
(102,'Riya','Clerk',30000,'Mumbai'),
(103,'Amit','Developer',40000,'Lucknow'),
(104,'Neha','Analyst',35000,'KNP'),
(105,'Sara','Tester',28000,'ALLD');

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4️⃣ Update HRA, PF, DA (Percent of Salary)

HRA = 12%, PF = 10%, DA = 65%

UPDATE Employee
SET HRA = Salary*0.12,
    PF  = Salary*0.10,
    DA  = Salary*0.65;

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5️⃣ Deduct PF from Salary Column

UPDATE Employee
SET Salary = Salary - PF;

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6️⃣ Delete Employees with EmpID 105, 107, 109 AND City in ('ALLD','KNP','Lucknow')

DELETE FROM Employee
WHERE EmpID IN (105,107,109)
   OR City IN ('ALLD','KNP','Lucknow');

Note: Ye deletion condition me OR use kiya kyunki aapne dono criteria diye hain (empid OR city)

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7️⃣ Delete the Column City

ALTER TABLE Employee
DROP COLUMN City;

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8️⃣ List Name, Salary, Total Salary (Salary + HRA + PF + DA)

SELECT EName,
       Salary,
       (Salary + HRA + PF + DA) AS TotalSalary
FROM Employee;

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✅ Explanation of Steps:

1. Table created with basic employee info.

2. HRA, PF, DA columns added separately with numeric domain.

3. 5 sample records inserted.

4. HRA, PF, DA calculated as % of Salary.

5. PF deducted from Salary column.

6. Unwanted employees deleted using EmpID or City criteria.

7. City column removed from table.

8. Final output displays employee name, net salary after PF deduction, and total salary including HRA, PF, DA.

📝 DBMS – Unit 1 + Unit 2 (Long Answer Questions & Answers)

 

Unit 1: Introduction to DBMS

1️⃣ Define Database, DBMS and Explain Features of DBMS

Database: Collection of logically related data stored systematically to serve multiple applications.

DBMS: Software that manages databases, allowing users to store, modify, retrieve, and manage data efficiently.

Features of DBMS:

• Data Independence: Application programs do not depend on physical data storage.

• Efficient Data Access: Uses indexes, queries to retrieve data quickly.

• Data Security: Only authorized users can access.

• Data Integrity: Maintains accuracy and consistency using constraints.

• Data Concurrency: Multiple users can access data simultaneously without conflicts.

• Backup & Recovery: Provides automatic backup and recovery in case of failure.

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2️⃣ Difference Between DBMS and File System

File System	DBMS
Data stored in files	Data stored in structured database
Redundancy & Inconsistency	Minimizes redundancy & maintains consistency
Limited data security	High-level security features
Difficult to update & manage	Easy update, retrieval, management
No support for concurrent access	Supports multiple concurrent users
Example: MS Excel	Example: MySQL, Oracle, PostgreSQL

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3️⃣ Explain DBMS Architecture

Three levels of DBMS Architecture:

1. Internal Level: Physical storage of data, low-level description.

2. Conceptual Level: Logical structure of entire database, hides physical details.

3. External Level: User views or application views of data.

Diagram:

       +----------------+
       |   External     |
       |   Views        |
       +----------------+
              |
       +----------------+
       | Conceptual     |
       | Schema         |
       +----------------+
              |
       +----------------+
       |   Internal     |
       |   Storage      |
       +----------------+

Explanation:

• External level → user interface

• Conceptual → database structure for DBMS

• Internal → physical storage details

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4️⃣ Advantages of DBMS

• Reduced data redundancy

• Data consistency & integrity

• Efficient data access via queries

• Data security & authorization

• Multi-user concurrent access

• Backup and recovery facilities

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Unit 2: ER Model & Relational Model

1️⃣ Explain Entity, Attribute, Relationship & ER Diagram

Entity: Object or thing in real world (e.g., Student, Employee)
Attribute: Property of an entity (e.g., Name, Age, Roll No)
Relationship: Association among entities (e.g., Student enrolls in Course)

ER Diagram Example:

[Student]───Enrolled_In───[Course]
   | Name                    | CName
   | RollNo                  | CID

Types of Attributes:

• Simple / Composite

• Single-valued / Multi-valued

• Derived

Types of Relationships:

• One-to-One (1:1)

• One-to-Many (1:N)

• Many-to-Many (M:N)

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2️⃣ Explain Keys in DBMS

Primary Key: Unique identifier for entity (e.g., RollNo)
Candidate Key: Possible key that can act as primary key
Foreign Key: Attribute referencing primary key of another table
Super Key: Any set of attributes that uniquely identifies entity

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3️⃣ Relational Model Concepts

Relation: Table with rows (tuples) and columns (attributes)
Tuple: Row of a table (one record)
Attribute: Column of a table (property)
Domain: Set of possible values for an attribute

Example: Student Table

RollNo	Name	Age
101	Adarsh	21
102	Riya	20

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4️⃣ Convert ER Diagram to Relational Schema

ER Diagram Example:

• Entities: Student(SID, Name), Course(CID, CName)

• Relationship: Enroll(SID, CID)

Relational Schema:

• Student(SID, Name)

• Course(CID, CName)

• Enroll(SID, CID)

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5️⃣ Advantages of ER Model

• Easy to understand for users

• Helps in database design

• Visual representation of entities, relationships

• Identifies primary keys and constraints

Unit 1: Basics, Algorithm & Operators ( Programming in C Language)

1️⃣ Explain Algorithm with Example and Properties.

Definition:
Algorithm is a step-by-step procedure to solve a problem in a finite number of steps.

Example: Add two numbers

1. Start

2. Read two numbers, A and B

3. Calculate Sum = A + B

4. Print Sum

5. Stop

Properties of a good algorithm:

• Input: Accepts zero or more inputs

• Output: Produces at least one output

• Definiteness: Steps are clear and unambiguous

• Finiteness: Algorithm must terminate after finite steps

• Effectiveness: Steps are basic, feasible, and solvable manually or by machine

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2️⃣ Draw Flowchart and Explain Sum of First 10 Numbers

Flowchart:

   ┌───────┐
   │ Start │
   └───┬───┘
       ↓
   i=1, sum=0
       ↓
 ┌── i ≤ 10 ? ──┐
 │ Yes        No│
 ↓             ↓
sum=sum+i     Print sum
i=i+1         ↓
 │          ┌───────┐
 └─────────► Stop  │
             └─────┘

Explanation:

• Initialize i=1 and sum=0.

• Check condition i ≤ 10.

• Add i to sum and increment i.

• Repeat until i > 10.

• Print final sum and stop.

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3️⃣ Explain Compilation & Execution Process in C

Steps:

1. Editing: Write source code in .c file.

2. Preprocessing: Removes comments, expands macros, includes header files.

3. Compilation: Converts source code to assembly code.

4. Assembly: Converts assembly code into object code (.o file).

5. Linking: Combines object code with libraries to produce executable.

6. Execution: OS loads and runs the executable file.

Example:

#include <stdio.h>
int main() {
    printf("Hello, World!");
    return 0;
}

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4️⃣ Explain Keywords, Identifiers, and Constants in C

Keywords: Reserved words in C with predefined meaning.
Example: int, float, if, else, return

Identifiers: User-defined names for variables, functions, arrays, etc.
Example: sum, age, myFunction

Constants: Fixed values that do not change.
Example: #define PI 3.14 or const int x = 5;

Difference between Keywords and Identifiers:

Keywords	Identifiers
Reserved by C	User-defined names
Cannot be used as variable names	Can be used as variable or function names
Example: int, float	Example: sum, age

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5️⃣ Explain Operators in C with Examples

Types of operators:

1. Arithmetic: + - * / %

2. Unary: ++ --

3. Relational/Logical: > < == != && || !

4. Bitwise: & | ^ << >>

5. Assignment: = += -= *= /= %=

6. Conditional: ?:

Examples:

int a=5, b=3;
int c;
c = a + b;  // 8
c = a & b;  // 1 (bitwise AND)
c = a << 1; // 10 (left shift)

Precedence & Associativity:

• Precedence decides which operator evaluated first

• Associativity decides order for operators with same precedence

Example:

10 + 20 * 5  // 110, '*' has higher precedence
100 / 10 * 5 // 50, '/' and '*' have same precedence, left-to-right

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Unit 2: Control Structures, Functions, Arrays

6️⃣ Explain Control Structures in C with Examples

Definition: Control structures manage the flow of execution in a program.

Types:

1. Sequential: Statements executed line by line.

2. Decision Making (Selection): if, if-else, switch-case

3. Loops (Iteration): for, while, do-while

4. Jump Statements: break, continue, goto

Examples:

For Loop (Factorial):

int n=5, i, fact=1;
for(i=1;i<=n;i++) fact*=i;
printf("%d", fact);

While Loop (Even Numbers):

int i=2;
while(i<=10){ printf("%d ",i); i+=2; }

Switch-Case:

int day=3;
switch(day){
  case 1: printf("Mon"); break;
  case 2: printf("Tue"); break;
  default: printf("Other"); 
}

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7️⃣ Explain Functions in C with Types and Examples

Definition: Block of code that performs a specific task and can be reused.

Advantages: Code reusability, easy debugging, modularity

Types:

• Library functions: printf(), scanf()

• User-defined functions

Categories based on arguments & return type:

1. No arguments, no return:

void hello(){ printf("Hi"); }

2. Arguments, no return:

void sum(int a,int b){ printf("%d",a+b); }

3. No arguments, return value:

int getNum(){ return 10; }

4. Arguments & return:

int add(int a,int b){ return a+b; }

Call by value vs Call by reference:

• Call by value → function gets a copy, original variable not changed

• Call by reference → function gets address, original variable can be changed

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8️⃣ Explain Arrays in C with Examples

Definition: Array = collection of elements of same type in contiguous memory.

Types:

• 1D Array: int arr[5]={1,2,3,4,5};

• 2D Array: int mat[2][2]={{1,2},{3,4}};

• Multidimensional Array

Example Programs:

Sum of 1D Array:

int arr[5], i, sum=0;
for(i=0;i<5;i++){ scanf("%d",&arr[i]); sum+=arr[i]; }
printf("Sum=%d", sum);

Matrix Addition (2D Array):

int a[2][2], b[2][2], sum[2][2], i,j;
for(i=0;i<2;i++) for(j=0;j<2;j++) scanf("%d",&a[i][j]);
for(i=0;i<2;i++) for(j=0;j<2;j++) scanf("%d",&b[i][j]);
for(i=0;i<2;i++) for(j=0;j<2;j++) sum[i][j]=a[i][j]+b[i][j];
for(i=0;i<2;i++){ for(j=0;j<2;j++) printf("%d ",sum[i][j]); printf("\n"); }

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9️⃣ Program Based Long Questions

1. Factorial using recursion:

int fact(int n){ if(n<=1) return 1; else return n*fact(n-1);}

2. Sum of first 10 numbers using loop & function:

int sum10(){ int i, sum=0; for(i=1;i<=10;i++) sum+=i; return sum; }

3. Matrix addition program → See 2D array example above.

4. Demonstrate Bitwise Operators:

int a=5,b=3;
printf("%d %d %d %d %d", a&b, a|b, a^b, a<<1, a>>1);

Unit 1 (Programming in C with Data Structures) – Short Notes (6 Marks Type)

 Q1. Define Algorithm and its properties.

Answer:
An algorithm is a step-by-step finite process to solve a specific problem.

Properties:

1. Definiteness → Steps must be clear.

2. Finiteness → Algorithm must end after finite steps.

3. Input → Zero or more inputs accepted.

4. Output → At least one output produced.

5. Effectiveness → Steps must be simple and feasible.

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Q2. What is a Flowchart? List its advantages.

Answer:
A flowchart is a graphical representation of an algorithm using symbols like oval (Start/End), rectangle (Process), diamond (Decision), parallelogram (I/O).

Advantages:

• Easy to understand.

• Helps in debugging before coding.

• Improves communication between developers.

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Q3. Explain the structure of a C program.

Answer:
Basic structure:

1. Preprocessor directives (#include <stdio.h>)

2. Main function (int main() { ... })

3. Declarations (variables)

4. Statements (logic/code)

5. Return statement (return 0;)

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Q4. Explain Compilation & Execution of a C program.

Answer:
Steps:

1. Writing → Save program as .c file.

2. Compilation → Compiler converts C code → machine code.

3. Linking → Connects with libraries.

4. Execution → Run the program → output is shown.

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Q5. What are Data Types in C?

Answer:
Data types define the kind of data stored in variables.

• Basic: int, float, char, double.

• Derived: arrays, functions, pointers.

• User-defined: structures, union, enum.

• Void: no value.

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Q6. What are Identifiers and Keywords in C?

Answer:

• Identifiers: Names given to variables, functions, etc. (e.g., marks, sum).

• Keywords: Reserved words with special meaning, cannot be used as identifiers (e.g., int, while, return).