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Data and Database Representation Number System Number system is a set of values used to present different quantities, and other special characters. The number system is a system of number that deals about the numbers and their representation (base and exponent or radix) in different systems. The number systems can be categorized in two board categories. a. Non-positional number system (I, II, III, IV, V) b. Positional number system ( 1,2,3,3, … ) Types of Number System 1. 2. 3. 4. Decimal or Denary Number systems Binary Number system Octal Number System Hexadecimal Number System Some Rules To Remember While Number Conversion: (A) While Number Conversion Never Multiply Or Divide Number By Base Value Of Decimal. (B) Always Remember If You Have To Convert Any Number System Into Decimal Then Multiply The Number With Base Value From The Number System You Are Converting. Other Number System To Decimal = (Multiply X) Eg. (101.11)2 Into Base 10 1x22+0x21+1x20 +1x2-1+1x2-2 Note: The Power Of Base 2 Starts With 0 From Least Significant Bit Towards Most Significant Bits For Non-Fractional Numbers, Whereas In Case Of Fractional Numbers, The Power Of Base Starts With -1. (C) Always Remember If You Have To Convert Any Decimal Number Into Any Other Number Then Divide The Number With Base Value To The Number System You Are Converting. Decimal → Other Number System = (Divide ÷) E.G. (22.22)10 Into Base 2 2 22 0 2 11 1 2 5 1 2 2 0 1 pg. 1 ↑ 2 X 0.22 = 0.44 0 2 X 0.44 = 0.88 0 2 X 0.88 = 1.76 1 2 X 0.76 = 1.52 1 2 X 0.52 = 1.04 1 ↓ Ans: (10110.00111)2 Note: Fraction Part Of Any Decimal Number Is Converted Into Binary Number By Successive Multiplication To The Given Number With Respective Base 2. The Process Is Terminated When We Get 0 In The Fraction Part Of Product. When We Fail To Get 0, Then We May Terminate The Process After 5th Round. (D) While Converting Octal To Hexadecimal And Hexadecimal To Octal, There Is No Any Direct Method To Convert From Hexadecimal To Octal And Octal To Hexadecimal. In The Case You Have To Follow Two Methods: (I) Octal To Binary To Hexadecima (Ii) Octal To Decimal To Hexadecimal (E) The Maximum Group Of Binary Bit Supported By Octal Number Is (111) And The Maximum Group Of Binary Bit Supported By Hexadecimal Number Is (1111). (F) While Converting Octal To Binary Always Convert The Equivalent Bit Of Octal Number In Three Different Bits Of A Group. I.E. (3211) = (011 010 001 001) (G) While Converting Hexadecimal To Binary Always Convert The Equivalent Bit Of Hexadecimal Number In Four Different Bits Of A Group. I.E. (3211) = (0011 0010 0001 0001). Short Answers Questions 1. Define Base Or Radix Of A Number System. Convert (11011.011) 2 Into Decimal Number. Base Or Radix Of A Number System Is Defined As The Number Of Digits Used To Represent The Number System. For E.G. Decimal Number System Uses Ten Digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) So, Its Base Is 10. The Base Of Number System Is Indicated By A Subscript And Followed By The Value Of The Number. For Example: • (1101)2 Is Of Base 2 Number System • (1607)8 Is Of Base 8 Number System Now, Converting (11011.011)2 Into Decimal Number: (11011.011)2 = 24 X 1 + 23 X 1 + 22 X 0 + 21 X 1 + 20 X 1 + 2-1 X 0 + 2-2 X 1 + 2-3 X 1 = 16 + 8 + 0 + 2 + 1 + 0 + 1 22 = 29 + 0.25 + 0.125 = 29.375 Therefore: (11011.011)2 = (29.375)10 pg. 2 + 1 23 2. What Is Binary Number System? Convert (520) 10 Into Base 16. A Number System Having Base Or Radix 2 Is Called Binary Number System. It Consists Of 2 Bits: 0 And 1. It Is Also Known As Binary Digit (BIT). The Power Of Base 2 Starts With 0 From Least Significant Bit Towards Most Significant Bits For Non-Fractional Numbers, Whereas In Case Of Fractional Numbers, The Power Of Base Starts With -1. Now Converting (520)10 Into Base 16. 16 520 8 16 32 0 2 Therefore: (520)10 = (208)16 3. What Is Octal Number System? Convert (110111101) 2 Binary Number Into Octal Number. A Number System Having Base Or Radix 8 Is Called Octal Number System. It Consists Of 8 Digits: 0,1,2,3,4,5,6 And 7. The Power Of Base 2 Starts With 0 From Least Significant Bit Towards Most Significant Bits For Non-Fractional Numbers, Whereas In Case Of Fractional Numbers, The Power Of Base Starts With -1. Now Converting (110111101)2 Into Base 8. Separating The Given Binary Number Into Group Of Three Bits From Right To Left = 110 Calculating Equivalent Binary Bit Of Each Group: Binary 110 111 101 Octal 6 7 5 111 101 Therefore: (110111101)2 = (675)8 4. What Is Number System? Convert (567)8 Octal Number Into Hexadecimal Number. The Number System Is A Set Of Values To Represent Different Quantities, And Other Special Characters. The Number System Is A System Of Number That Deals The Numbers And Their Representation (Base And Exponent Or Radix) In Different Systems. There Are Two Types Of Number System: (A) Non-Positional Number Systems (B) Positional Number Systems Converting (567)8 Into Base 16(Octal To Binary And Binary To Hexadecimal): Separate Each Bit Of Octal Number: Equivalent Binary Bit Of Octal Number: Now, Combining All Bits: 101110111 5 6 7 101 110 111 Separating Group Of Bits Equivalent To Hexadecimal: 0001 0111 0111 Converting To Its Equivalent Hexadecimal Number: pg. 3 1 7 7 Therefore (567)8 = (177)16 5. What Is Hexadecimal Number System? Convert (111011.111) 2 Into Base 16 A Number System Having Base Or Radix 16 Is Called Hexadecimal Number System. It Consists Of 16 Digits: 0,1,2,3,4,5,6,7,8,A,B,C,D,E And F. The Power Of Base 16 Starts With 0 From Least Significant Digit Towards Most Significant Digits For Non-Fractional Numbers, Whereas In Case Of Fractional Numbers, The Power Of Base Starts With -1. Now Converting (111011.111)2 Into Base 16. Separating And Grouping Binary Bits Into 4 Bits Which Is Equivalent To Hexadecimal: 0011 Converting Binary Bits Into Hexadecimal Number: 3 Therefore (111011.111)2 = (3B.E) 16 1011 1110 11 14 1. What Is Boolean Algebra? How Is It Different From Binary Algebra? Boolean Algebra Is A Set Of Rules, Laws And Theorems By Which Logical Expression Can Be Expressed Symbolically In Equation Form And Manipulated Mathematically. Boolean Algebra Can Be State As The Branch Of Mathematics That Includes Methods For Manipulating Logical Variables And Logical Expressions. The Difference Between Boolean Algebra And Binary Algebra: 1. It Is Algebra Of Logic Based On Binary Number System. 1. It Is General Purpose Algebra Based On Decimal Number System. 2. 2. It Is Used In The Field Of Digital Electronics 3.Basic Operation Used In Boolean Algebra Are: AND, OR And NOT Operations. It Is Used In The Field Of Mathematics. 3. Basic Operation Used In Ordinary Algebra Are Addition, Subtraction, Multiplication And Division. 4. In Boolean Algebra There Are No Coefficients Or Exponents Involved. I.E. X+X=X 4. Coefficient And Power Are Used In Ordinary Algebra As A + A = 2A 5. 5. It Holds Both Distributive Laws It Holds Only One Distributive Laws. 2. Define Boolean Functions. Construct Truth Table For AND Operation Of Boolean Algebra. A Boolean Function Is An Expression Formed With Binary Variables, The Two Binary Operators OR And AND, The Unary Operator NOT, Parentheses And Equal Sign. Since The Binary Variable Can Take Either 0 Or 1, For A Given Value Of Variables The Logic Function Can Be Either 0 Or 1. I.E. Boolean Function F1 = (Abc'). AND Operator Is Represented By ".". So, A And B Can Be Represented As A.B. Other Symbols ^ And ∩, Are Used For Representing AND Operation. The Result Of AND Operation Is Exactly Same As Simple Arithmetic Multiplication. The Result Will Only Be True (1) When All The Inputs Are True. pg. 4 A 0 0 1 1 Truth Table Of AND B Result (A.B) 0 0 1 0 0 0 1 1 3. Define Operator, Operand And Operation With Suitable Example. An Operator Is A Symbol Or Sign That Causes Specific Mathematical Or Logical Manipulations To Be Performed. "Operator Is A Symbol To Signify Operation". Some Operator And Symbols Are Operator Addition Subtraction Multiplication Division Relational Logical Symbol + * / >,<,<=, >= AND, OR, NOT Operation Is An Action Upon Data. Example : 3 + 2 = 5 Addition Operation 3 * 2 = 6 Multiplication Operation Operands Are The Data Items Or Variables Or Values Of Variables Operated By Operator Example: X And Y Are Operand For X + Y A And B Are Operands For A * B 4. Construct The Truth Table Of The 'AND' And 'OR' Operations Of Boolean Algebra. AND Operation It Is Known As Logical Multiplication. It Is Carried Out By Dot (.) Operator. It Generates True Output If All The Inputs Are True Otherwise It Generates False Output. I.E: O = A . B The Truth Table Of AND Operation Is Given Below: Inputs A 0 0 1 1 Output O=A.B 0 0 0 1 B 0 1 0 1 OR Operation It Is Known As Logical Addition. It Is Carried Out By Plus (+) Operator. It Generates True Output If At Least One Input Is True Otherwise It Generates False Output. I.E. O = A + B The Truth Table Of AND Operation Is Given Below: Inputs A 0 0 1 1 B 0 1 0 1 Output O=A+B 1 1 1 0 5. Write Truth Table Of NOR Operation Of Boolean Algebra. It Is An Electronic Circuit Used To Perform Complement Of OR Operation. It Uses Plus ( + ) Operator And Single Quote Operator ( ' ). It Is The Integration Of NOT Gate And OR Gate. It Also Accepts Two pg. 5 Or More Input And Generates Only One Output. It Generates 1 Or True Output If All The Inputs Are False Otherwise, It Generates 0 Or False Output. Inputs A B 0 0 0 1 1 0 1 1 6. A+B 1 1 1 0 Output O=(A+B)' 0 0 0 1 What Are Logical Gate? Define NAND Gate And Draw Its Logic Symbol. A Logic Gate Is An Electronic Circuit Which Generates Only One Output Signal From One Or More Input Signals. The Manipulation Of Binary Information Is Done By Logic Gate. It Is Embodied Into Integrated Circuit (IC). Each Gate Has Its Specific Function And Graphical Symbol. In A Digital Computer, There Are Three Basic Gates : AND, OR And NOT Gate. It Is An Electronic Circuit Used To Perform Complement Of Logical Multiplication Or Complement Of AND Operation. It Uses Dot Operator (.) And Single Quote Operator (‘). It Is The Integration Of NOT Gate and AND Gate. It Accepts Two Or More Inputs And Generates Only One Output. It Generates 1 Or True Output If At Least Any One Of The Input Is False Otherwise, It Generates 0 Or False Output. Graphical Symbol: Inputs A B 0 0 0 1 1 0 1 1 7. Truth Table Output O=A.B O=(A.B)’ 0 1 0 1 0 1 1 0 Venn Diagram Why NAND Gate And NOR Gate Are Known As Universal Gates? Differentiate Between NAND And NOR Gate With An Example. NAND And NOR Gates Are Known As Universal Gate Because It Is Possible To Implement Any Logical Expression Using Only NAND Gate. NAND Gates Are Sufficient To Implement Any Boolean Expression. Similarly, Only NOR Gates Are Sufficient To Implement Any Boolean Expression. The Proper Combination Of Either NAND Gate Or NOR Gate Can Be Used To Perform Each Of The AND, OR, NOT Operation. NAND Gate 1. It Is The Combination Of AND And NOT Gate. 2. It’s Output Value Is Just Complement Of Output Value Of AND Gate. 3. The Output Value Of NAND Gate Is 0 Only When All Combination Of Inputs Are 1 Otherwise Output Value Is 1. 4. Algebraic Expression: If A And B Are Two Input Signals, Then It Is Represented By 0=(A.B)’ 5. Truth Table pg. 6 NOR Gate 1. It Is The Combination Of OR And NOT Gate. 2. Its Output Value Is Just Complement Of Output Value Of OR Gate 3. The Output Value Of NOR Gate Is 1 Only When All Combination Of Inputs Are 0 Otherwise Output Value Is 0. 4. Algebraic Expression: If A And B Are Two Input Signals, Then It Is Represented By O=(A+B)’ 5. Truth Table NAND Gate Inputs Output A B O=A.B O=(A.B)’ 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 6. Graphical Symbol NOR Gate Inputs Output A B O=A+B O=(A+B)’ 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 0 6. Graphical Symbol Long Questions 1. What Is Boolean Algebra? Describe AND Gate, OR Gate, NOT Gate And NAND Gate With Gate Symbol And Truth Table. Boolean Algebra Is A Set Of Rules, Laws And Theorems By Which Logical Expression Can Be Expressed Symbolically In Equation Form And Manipulated Mathematically. Boolean Algebra Can Be State As The Branch Of Mathematics That Includes Methods For Manipulating Logical Variables And Logical Expressions. Boolean Algebra Also Referred To As The Algebra Of Logic. It Is A Two-Value System Of Algebra That Represents Logical Relationships And Operation. The Two Values Used Are 1 (True) Or 0 (False) Different Gates Used In Digital Computer Are Briefly Explained Below: (A) AND Gate AND Gate Is An Electronic Circuit Used To Perform Logical Multiplication And It Is Denoted By Dot Operator (.). It Accepts Two Or More Inputs And Generates Only One Output. It Produces High (1) Output When All Inputs Are High (1) Otherwise, The Output Will Be Low (0). Graphical Symbol Truth Table Inputs Output A B Q=A.B 0 0 0 0 1 0 1 0 0 1 1 1 Venn Diagram (B) OR Gate OR Gate Is An Electronic Circuit Used To Perform Logical Addition And It Is Denoted By Dot Operator (+). It Accepts Two Or More Inputs And Generates Only One Output. It Produces High (1) Output When One Of The Input Is High (1) Otherwise, The Output Will Be Low (0). Graphical Symbol pg. 7 Truth Table Inputs Output A B Q=A.B 0 0 0 0 1 1 Venn Diagram 1 1 0 1 1 1 (C) NOT Gate NOT Gate Is An Electronic Circuit Used To Perform Logical Complement (Or NOT Operation) And It Is Denoted By Single Quote Or Bar Operation (` Or -). It Accepts Only One Input And Generates Only One Output. It Produces High (1) Output When Input Is Low (0) Or Vise Versa Graphical Symbol Inputs A 0 1 Truth Table Output Q=A.B 1 0 Venn Diagram (D) NAND Gate It Is An Electronic Circuit Used To Perform Complement Of Logical Multiplication Or Complement Of AND Operation. It Uses Dot Operator (.) And Single Quote Operator (‘). It Is The Integration Of NOT Gate And AND Gate. It Accepts Two Or More Inputs And Generates Only One Output. It Generates 1 Or True Output If At Least Any One Of The Input Is False Otherwise, It Generates 0 Or False Output. Graphical Symbol: Truth Table Inputs A B 0 0 0 1 1 0 1 1 pg. 8 O=A.B 0 0 0 1 Venn Diagram Output O=(A.B)’ 1 1 1 0 Database System Data Data is a collection of raw facts and figures which is isolated, uninterested and unorganized, but able to organize into useful information. Data can be manipulated to produce output. Dta are the raw facts from which we start to get information. Information Information is the processed data i.e. after processing the data we can get information. Information of one thing may be the data of another. Hence information data arranged in an order that is useful to people who receive it. Database A database is a collection of related information about a subject organized in a useful manner that provides a base or foundation for procedure, such as retrieving information, drawing conclusion and make decision. A Database is a collection of interrelated data of certain place or person or thing in such a way that it can be easily access by an application program like DBMS (Database management System) Why Database ? Traditional file system have been used from the beginning for managing data in a computer . In the traditional file system, the data can be duplicated, they cannot be shared and security and integrity cannot be maintained very well. It is also very difficult to search data. So it is not easy to work in file system where everything is kept in file. Problems with File system. a. Data Duplication b. Data dependence c. Lack of data integration DBMS ( Database Management System) A DBMS is a set of programs that manages the database files. The DBMS allows to access the files. Update the records, and retrieve data as requested. The DBMS acts as an interface between the application program and the data in the database. Objectives of DBMS To provide storage area for mass amount of relevant data. To make access to the data easy for the end user. To provide prompt response to users request for data To make the latest modification to the database available immediately. To eliminate data redundancy (duplication of data) To allow multiple user to be active at one time To protect the data from the physical harm and unauthorized access. Advantage of DBMS pg. 9 1. Data Sharing: Data stored in a database can be share. For example with a DBMS the data for the entire company is effectively made available to all managers and end users, which need them 2. Reduced data Redundancy: In traditional file processing the same data may be duplicated at many times or places is also called data redundancy. A DBMS reduces the duplication of data from a database. 3. Integrity can be maintained: Integrity ensures that the data stored in a database is correct or accurate. So the problem of integrity is the problem of ensuring that the data in the database is correct. 4. Data Independence: The DBMS keeps description of data separate from application that use the data. Thus changes in the data definition can occur without requiring changes in every application program that uses the data. 5. Security can be enforced: In an organization, there should be many confidential data, such data should not be available to all users. In a DBMS, certain restriction can be applied for security by giving different authority to different users. 6. Providing multiple user interface: DBMS provides variety of interfaces for various users. Disadvantage of DBMS 1. 2. 3. 4. 5. 6. Initial investment is high for implementing DBMS Proper training is require for staff to work properly in the database system When some fault occurs in one part of the database it affects the other parts as well. It is complex to understand and implement Overhead cost for providing security, recovery, and integrity functions. Cost for the maintenance of the hardware, software, backup, recovery and its upgrade remains forever. Database Model Data model describes the structure of a database. Data model is collection of conceptual tools for describing data, relationship etc. Types of Database Model 1. Hierarchical Database Model In a hierarchical database model records are logically organized into a hierarchy of relationships. It is arranged logically in an inverted tree patterns. It is based on parent child. A parent record can have several children,, but a child can have only one parent. Department Job Description Education Required • pg. 10 Background Required Employee Education Job History A hierarchical database model is a data model in which the data is organized into a tree-like structure. • The hierarchical data model is the oldest type of data model, developed by IBM in 1968. • Records are inter-related through hierarchical or tree-like structures. • A parent can have several children, but a child can have only one parent. • One to one and one to many relationships. Advantages • It is the easiest model of database. • A database owner is more secured because nobody else can see and modify a child without consulting its parent. • Searching is fast and easy, if parent is known. • It is very efficient in handling 'One-to-many' relationship. • It helps to build complex system from simple components. Disadvantages • It is old fashioned, outdated database model. • It is non-flexible database model (Modification and addition of child without consulting the parent is impossible or very complex process). • It can't handle 'Many- to-Many' relationships. • It increases data redundancy as same data can be saved in different places. • When parent node is deleted, all the children nodes are deleted automatically. Network Data Model • Network Database Model Network database model is a modified version of the hierarchical database. • In network database structure each node may have several parents. • Operation and maintenance of this structure becomes complicated, as the number of points in the network increases. • It is less user-friendly when compared to the hierarchical structure. • It Support Many to Many Relationship Advantages • It is more flexible than hierarchical model because accepts 'many-to-many' relationship. • It reduces redundancy because data shouldn't be repeated if same data is needed. • Searching is fast because of multidirectional pointers. pg. 11 Disadvantage • It is one of the complex database models. • It needs larger programs to handle the relationships. • It is less secured compared to hierarchical model, as it is open to all. Entity Relation Data Model • The ER data models is based on a perception of real world that consist of a collection of basic objects called entities and relationship among these objects. • Database can be modeled as a collection of entities, and relationship among entities. • Overall logical structure of a database can be expressed graphically by E-R diagram. Basic Component of Diagram • Rectangle (represent entity sets) • Ellipses (represents attributes) • Diamonds (represent relationship sets among entity sets) • Lines (link attributes to entity sets and entity sets to relationship sets) Relational Database Model In a relational Database model, data are arranged in two dimensional table, which are easy for a user to develop and understand. This type of model can also be described mathematically. Because many managers often work with tabular form data, it is easy for most of them to understand the structure used in a relational database. Advantages: Since on table is linked with other, some common fields and rules implemented on one table can easily be implemented to another. It is very less data redundancy Normalization of the database is possible Rapid processing of database is possible Disadvantage: It is more complex than other models Too many rules makes database non-user-friendly Database Language Language that are used to interact with database management systems are called database language. DBMS provides two languages: Data Definition Language (DDL) Database language that is used to create, delete or modify database schema is called data definition language. Results of DDL Statements are recorded in special file called data dictionary. Structured query language supports following DDL Statements. pg. 12 Create Statement Drop Statement Alter Statement Eg. CREATE TABLE account ( Account-number CHAR (10) Balance INTEGER, Branch CHAR (10) ) Data Manipulation Language (DML) Database language that enables insert, delete, update and retrieve data from database is called data manipulation language (DML). Query language is only a part of data manipulation language. Structured Query Language (SQL) supports following DML statements. Insert statement Delete Statement Update Statement Select Statement Eg. Insert into Employee values (“A01”, 7676, “Patan”); Database Architectures • Database architecture defines the overall design and inter connection of different components. • Types : • Centralized Architecture • Distributed databases Centralized Architecture Centralized database systems are those that run on a single computer system. A computer system may be single user or multiuser. Database system designed for a single user systems do not provide many of the facilities that a multiuser database system provides. In this system users have access to computer resources via hundreds of remote communication devices including on line terminals used to input data and printer to obtain reports. Client/Server Database System In a distributed database system the database is stored on several computers. Distributed database are databases located at different places. They facilitate easy access of data from any location. It has problem of control of security, increased problem of control of database and need more computer resources. It can manage by people with functional knowledge. This mode of processing incurs more expense with limited security, control and protection of data. pg. 13 Data Warehouse A data warehouse is a repository of combined information, available for queries and analysis. Data and information are extracted from mixed sources as they are generated, making it easier and more efficient to run queries over data that originally came from different sources. Data integration: It is the process of standardizing the data definitions and data structures of multiple data sources by using a common structure thereby providing a unified view of the data for enterprise level planning and decision making Data cleansing: It is the process of detecting and correcting incorrect irrelevant, out of data corrupt redundant and inconsistent records from a record set, table or database. Data consolidation: It refers to the collection and integration of data from multiple sources into a single destination. During this process, different data sources are put together or consolidated into a single data store Data Mining Data Mining is defined as extracting information from huge sets of data. Data mining is the procedure of mining knowledge from data. The information or knowledge extracted so can be used for any of the following applications – Market Analysis, Fraud Detection, Customer Retention, Production Control, Science Exploration etc. Application of data mining Data mining is widely used in diverse areas. There are a number of commercial data mining systems available today. Some of the candidate areas of data mining applications are discussed below: Financial Data Analysis: Banks and Financial institutions use data mining for Loan payment prediction and customer credit policy analysis, classification and clustering of customers for targeted marketing. Retail Industry : Data mining in telecommunication industry helps in identifying the telecommunication patterns, catch fraudulent activities, make better use of resources and improve quality of service. Biological Data Analysis : Biological data mining is a very important part of Bioinformatics. It can be used in alignment, indexing, similarity search and comparative analysis multiple nucleotide sequence, discovery of structural patterns and analysis of genetic networks and protein pathways etc. Short Answer Questions: 1. Which gate is universal gate and why? Explain the gate with proper diagram and truth table. 2. What is meant by data ware house & data mining? Explain both in your own word. Long Answer Questions: pg. 14 1. Convert the number (1894.75)10 into equivalent binary, octal and hexadecimal numbers. 2. Convert the numbers (11100010.101)2, (5634.25)8, and (A84D)16 into equivalent binary numbers. 3. Perform the operations a. (3452.50)10 + (2387.25)10 and b. (3452)10 + (3421)10 in binary. 4. List different logic gates? Explain each of the gate with suitable diagram and truth table. pg. 15