Class 9 Computer Science Chapter 1 Basics of Computer System

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Class 9 Computer Science Chapter 1 Basics of Computer System

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Basics of Computer System

Chapter – 1

COMPUTER SCIENCE

Important Terms (Basic Concepts)

● Artificial Intelligence: Artificial intelligence (AI) is wide-ranging branch of computer science concerned with building smart machines capable of performing tasks that typically require human intelligence.

● Parallel processing: Parallel processing is a method in computing of running two or more processors ( CPUs) to handle separate parts of an overall task. Breaking up different part of a task among multiple processors will help reduce the amount of time to run a program.

● Data: Data is an individual unit that contains raw material which does not carry any specific meaning.

● Information: Information is a group of data that collectively carry a logical meaning.

● Input Unit: An input device is something you connect to a computer that sends information into the computer.

● Output unit: An output device is something you connect to a computer that has information sent to it.

● CPU: A central processing unit ( CPU), also called a central processor , main processor or just processor, is the electronic circuitry that executes instructions comprising a computer program.

● Assembler: An assembler is a program that converts assembly language into machine code.

● Compiler: Compiler is a language processor that reads the complete source program written in high level language as a whole in one go and translates it into an equivalent program in machine language.

● Interpreter: An interpreter transforms or interpreter a high-level programming code into code that can be understood by the machine (machine code) or into an intermediate language that can be easily executed as well.

● ALU: An arithmetic-logic unit (ALU) is the part of a computer processor (CPU) that carries out arithmetic and logic operations on the operands in computer instruction words.

● CU: The control unit (CU) is a component of a computer’s central processing unit (CPU) that directs the operation of the processor. It tells the computer’s memory, arithmetic logic unit ant input and output devices how to respond to the instructions that have been sent to the processor.

● Memory: Computer memory is the storage space in the computer, where data is to be processed and instructions required for processing are stored.

● Registers: Registers are a type of computer memory used to quickly accept, store, and transfer data and instructions that are being used immediately by the CPU.

● Auxiliary memory: Auxiliary memory holds data and programs not currently in use and provides long-term storage.

● Flash memory: Flash memory is a long-life and non-volatile storage chip that is widely used in embedded systems.It can keep stored data and information even when the power is off.

● Program: A computer program is a collection of instructions that can be executed by a computer to perform a specific task. A computer program is usually written by a computer programmer in a programming language.

● Operating system: An operating system (OS) is a system software that manages computer hardware and software resources and provides common services for computer program requires an operating system to function.The most common operating systems are Microsoft Windows, Apple’s macOS etc.

TEXTUAL QUESTIONS AND ANSWERS

OBJECTIVE TYPE QUESTIONS

1. Choose the correct option.

(a) Which of the following is not an output device? 

(1) Speaker

(2) Mouse 

(3) Printer

(4) Monitor

Ans: (2) Mouse.

(b) Which one of the following is the  “brain” of computer?

(1) CPU 

(2) ALU

(3) CU 

(4) MU

Ans: (1) CPU. 

(c) A collection of eight bits is called______.

(1) Byte 

(2) Word 

(3) Record 

(4) Nibble 

Ans: (1) Byte.

(d) Second-generation computers were manufactured using which technology?

(1) Vacuum Tubes

(2) Transistors

(3) ICs 

(4) None of these 

Ans: (2) Transistors.

(e) Storage of 1KB means the following number of bytes:

(1) 1000

(2) 1024

(3) 1064

(4) 1012

 Ans: (2) 1024.

(f) Which of the following is not hardware?

(1) Hard disk 

(2) Printer 

(3) Assembler

(4) CPU 

Ans: (3) Assembler.

(g) Fourth generation computers used

(1) Vacuum tubes

(2) Transistors

(3) Microprocessors

(4) ICs

Ans: (3) Microprocessors.

(h) Which one of the following is a special-purpose application software?

(1) word-processing software

(2) Compiler

(3) Operating system software

(4) Payroll system

Ans: (4) Payroll system.

(i) The base of Octal Number System is _____.

(1) 2

(2) 10

(3) 16

(4) 8

Ans: (4) 8.

(j) who is known as the father of the modern computer?

(1) Charles Babbage 

(2) Herman Hollerith

(3) Blaise Pascal

(4) John Atanasoff

Ans: (1) Charles Babbage.

2. Fill in the blanks.

(a) The first-generation computers used______for storage.

Ans: magnetic tape.

(b) The third-generation computer replaced______with _____.

Ans: transistors, Integrated Circuits (ICs)

(c) ______are high speed temporary storage area.

Ans: Registers.

(d) _____is the short form of binary digit.

Ans: Bit

(e) A group of four bits is called ____.

Ans: Nibble.

(f) _____holds data , programs and instructions for computer.

Ans: RAM .

(g) A microphone is ____device.

Ans: input.

(h) A ____is set of instructions to perform a specific task.

Ans: program.

(i) _____software are used to scan the computers for viruses.

Ans: Antivirus.

(j)  The decimal system is composed of ____ digits.

Ans: 10.

(k) _____was the first fully electronic general-purpose computer.

Ans: ENIAC.

(l) ____was one of the first commercially available computers.

Ans: UNIVAC.

(m) An _____converts the program written in assembly language into machine language.

Ans: assembler.

(n) Processing takes place in the_____.

Ans: CPU.

(o) The ALU performs the ____and ____operations.

Ans: arithmetic, logical.

(p) RAM is ____or ____.

Ans: temporary, volatile.

(q) ROM stores basic _____instructions to operate the computer.

Ans: input / output.

(r) _____memory is an electronic non-volatile storage medium that can be electrically erased and reprogrammed.

Ans: EEPROM.

(s) Data and instructions are given to the computer through its ____device.

Ans: input.

(t) Raw data is processed by the computer to produce_____.

Ans: output.

(u) Results are obtained from the computer through its ____device.

Ans: output.

(v) 1 MB = ____ KB.

Ans: 1024.

(w) ______is an example of primary memory.

Ans: RAM.

(x) The octal number system uses the digits from _____to_____.

Ans: 0,7.

(y) A computer system comprise of both ____ and____.

Ans: hardware, software.

(z) _____represents the set of program that directs the computer how to work.

Ans: software.

3. State true or false.

(a) Another name for internal memory is primary memory.

Ans: TRUE.

(b) A hard disk can store less data than CD.

Ans: FALSE.

(c) software represent to the physical components of a computer.

Ans: FALSE

(d) A projector is input device.

Ans: FALSE.

(e) Interpreter is an utility software.

Ans: TRUE.

(f) The first-generation computers used transistors.

Ans: FALSE.

(g) Atanasoff Berry computer was the first electronic digital computer.

Ans: TRUE.

(h)  IBM 604 is an example of second-generation computers.

Ans: TRUE.

(i) UNIVAC was one of the first commercially available computers.

Ans: TRUE.

(j) ROM is volatile.

Ans: FALSE.

(k) A group of eight bits is called nibble.

Ans: FALSE.

(l) Computer does not understand any language other than machine language.

Ans: TRUE.

(m) Pen drives use flash memory to store data.

Ans: TRUE.

(n) The monitor is a soft copy output device.

Ans: TRUE.

(o) A compiler translates a program written in machine language into a program written high level language.

Ans: TRUE.

(p) Bit is the smallest unit of data in a computer.

Ans: TRUE.

DESCRIPTIVE TYPE QUESTIONS

4. Short answer questions.

1.Who is known as the ‘father of the modern computer’?

Ans: Charles Babbage.

2. What is a computer? 

Ans: Computer is an electronic device for storing and processing data, typically in binary from, according to instructions given to it.

3. Name a popular pointing device.

Ans: Mouse.

4. Who invented Jacquard’s loom?

Ans: Joseph Jacquard.

5. Give the full from of ENIAC and EDVAC.

Ans: ENIAC – Electronic Numerical Integrator and computer 

EDVAC – Electronic Discrete Variable Automatic Calculator.

6. Give two examples of second-generation computers.

Ans: IBM604, IBM1401,UNIVAC 1108

7. What is AI?

Ans: Artificial intelligence (AI) is the ability of a computer or a robot controlled by a computer to do tasks that are usually done by humans because they require human intelligence and discernment.

8. Give two examples of secondary memories.

Ans: Floppy disks, Hard disks, Compact disk.

9. What does the CPU do?

Ans: A central processing unit,or CPU, is a piece of hardware that enables your computer to interact with all of the applications and programs installed. A CPU interpreter the program’s instructions and creates the output that you interface with when you’re using a computer.

10. Why we use secondary memory?

Ans: We use the secondary memory because:

● secondary memory devices are used to store data and programs permanently for later use.

● The secondary memory is non-volatile.

● Primary memory has a limited storage capacity. So secondary memory devices are used to store large amount of data.

11. Give two examples of pointing devices?

Ans: Mouse, Trackball, Joystick, Stylus.

12. Which input device is used to record sound?

Ans: Microphone.

13. What is the use of barcode reader?

Ans: A barcode reader is used to read information stored in a barcode. Barcode is a system of representing data using machine-readable lines.

14. What is system software? Give two examples.

Ans: System software is a set of programs designed to operate hardware and control the internal operations of a computer. System software provides a platform for running application software. Examples- Operating system, antivirus software, Encryption/Decryption software etc.

15. What is the role of CU?

Ans: CU is the control unit. It decodes the instructions,and controls all the other internal components of the CPU to make it work.

16. What is the function of ALU?

Ans: ALU is the Arithmetic and logic Unit which performs all the arithmetic and logical operations such as addition, subtraction, logical AND,OR etc.

17. What do you understand by memory word?

Ans: computer memory is the storage space in the computer. The memory unit provides space for storing data and instructions, space for intermediate results, and also space the final results.

18. What is the function of Compiler?

Ans: The name “compiler” is primarily used for programs that translate source code from a high-level programming language to a lower level language .(e.g., assembly language, object code, or machine code) to create an executable program.

19. What is the main limitation of a computer?

Ans: The main limitation of a computer are: 

● The computer system does not have the power to make decisions on their own because they do not possess all the essentials of decision making.

● It cannot respond in a particular situation unless that situation is already programmed into them.

20. Mention three main features of a computer.

Ans: The main features of a computer are: 

● Speed: A computer works with much higher speed.

● Accuracy: Computer perform calculation with 100% accuracy.

● Diligence: A computer can perform millions of tasks or calculations with the same consistency and accuracy.

● Storage: A computer can store lot of information which can be used at any time in future.

21. What is a computer program?

Ans: A computer program is a collection of instructions that can be executed by a computer to perform a specific task.A computer program is usually written by a computer programmer in programming language.

22. What are the fundamental components of a computer system?

Ans: The fundamental components of a computer system are:

● Input device

● Output device

● Central Processing Unit (CPU)

23. What is application software?

Ans: Applications software is a set programs developed to carry out complete operations for a specific purpose. These are the programs written by the programmers to perform a specific task payroll processing software, examination processing software etc. are examples of application software.

24. Mention various categories of application software?

Ans: Application software can be divided into two categories:

● General-Purpose Application software (Package)

● Specific-Purpose Application software.

25. What do you understand by computer memory?

Ans: Computer memory is the storage space in the computer. The memory unit provides space for storing data and instructions, space for intermediate results, and also space for the final results.

26. What is the binary equivalent of hexadecimal 15 ?

Ans: (00010101)₂

Long answer questions

1. Mention four features of a computer system.

Ans: ● Speed of computer: Computers are much faster to perform mathematical calculations than human. The computer is capable of performing millions of tasks per second.

● Accuracy of computer: A computer is very accurate. It does not make any kind of mistake in calculating. sometimes we get some error but these are because of the mistake performed by us.

● Diligence of computer: A person gets tired of doing some work in a few hours and a computer has the ability to do any work continuously for many hours, days, months.

● Reliability of computer: Reliability is a very big characteristics of computer. Today almost all the big industries or big e-commerce companies like Amazon and Flipkart, and big search engine companies like  – Google and Bing, all these companies are dependent on computers.

● Versatility of computer: Versatility is the characteristics of a computer. Its means is that the computer is capable of working in almost every field.

Today computers are being used almost everywhere like schools, colleges, hospitals, offices, railway stations, hotels, etc.

● Storage capacity of computer: Computer systems have a very large capacity to store any type of data .A computer can store and resell any information due to its storage capacity.

Computers have the ability to store all types of data such as data, pictures,files, programs, games, and sound for many years and later we can get any data in a few seconds at any time for taking that information and for future retrieval.

● Automatic: A computer is an automatic machine because once started on a job they carry on until the job is finished without any human assistance.

● Quick Decision: The computer takes the decision very quickly, given by the user which is the instruction arithmetic data or logic data.

● Multitasking: Multitasking is also a very special feature of computers. A user can do different types of tasks on the computer at the same time.

Like we are using MS Word in computer as well as listening to songs and also getting printouts.

2. Mention the characteristics features of third- generation computers.

Ans: characteristics of Third Generation of computers: 

(1) Use of Integration Circuits (IC) instead of transistors

(2) Use of semiconductor memory 

(3) Small size than previous generation computers

(4) Use of magnetic storage device

(5) Improved faster operations and more dependable output

(6) Use of monitors and line Printers

(7) Use of high level programming language

3. What do you understand by generation of computers? Mention two disadvantages of first – generation computers.

Ans: Generation in computer terminology is a change in technology a computer is/was being used. Initially, the generation term was used to distinguish between varying hardware technologies. Nowadays, generation includes both hardware and software which together make up an entire Computer system.

The disadvantages of first- generation computers:

● The computers were very larger in size.

● They consumed a large amount of energy.

● They heated very soon due to thousands of vacuum tubes.

● They were not reliably.

● Air conditioning is required.

● Constant maintenance was required.

● Not- portable.

● Costly commercial production.

4. Describe the functioning of CPU.

Ans: 

The function of CPU are: 

(1) The CPU receives the data when the computer inputs the data through input device such as a keyboard or mouse.

(2) After this, the CPU process these input data by performing calculations and technical algorithm.

(3) And then CPU provides the processed data through output devices such as on the monitor screen.

(4) The CPU also stores the process data in the from of a cache for future use.

5. Discus Draw a block diagram of a computer system.

Ans: A computer basically performs five major operations: 

● Accepting data or instructions

● Processing data

● storing data

● Displaying results

● Controlling and coordinating all operations inside a computer 

A computer system consisted of a unit to perform each of the above functions.

6. What are the categories of printers? Explain.

Ans: A printer is a device that takes the text and graphics information obtained from a computer and prints it on a paper. The output produced on a paper is called the hard copy.Printers can be divided into two distinct categories:

(1) Impact printer: In these Printers, there is a physical contact between the print head and paper. Impact printers are subdivided into line Printers and character printers.

Line Printer prints one line of text at a time. Examples of line Printers are : drum printer and chain printer.

Character printer prints one character of at a time. Examples of character printer s are-Dot matrix printer, letter-quality printer.

(2) Non-impact printer: In these Printers, there is no physical contact between the print head and paper. Non-impact printers are faster than impact printer. The main types of Non-impact printers are inkjet printer, thermal printer, electromagnetic printer, and laser printer.

 7. What is a bus? Explain three types of buses.

Ans: The buses are electrical wires which connects the various components and transfer data between them.

There are three main buses. These are:

Data bus: It carries data from the memory to the CPU and the CPU to the memory.

Address bus: Is carries address from the CPU to the memory.

Control bus: Is carries instructions between the CPU and other parts of the computer.

8. What are functions of primary storage area?

Ans: A primary storage device is a medium that holds memory for short periods of time while a computer is running. Although it a much lower access time and faster performance, it is also about two orders of magnitude more costly than secondary storage. RAM (Random Access Memory) and cache are both examples of a primary storage device.

9. Explain three types of ROM.

Ans: The different types of ROM are: PROM ( programmable Read Only Memory) is read-only memory that can be programmed to store information only once by a user.It is not erasable.

EPROM (Erasable Programmable Read Only Memory) can be reprogrammed to record different information. The recorded information can be erased by exposing it to ultraviolet light.

EEPROM (Electrically Erasable Programmable Read Only Memory)can be programmed and erased electrically.

10. What is a purpose of a language processor? Explain the three language processors.

Ans: Language processors are system software that translates programs written in assembly level language or high level language into its equivalent machine language program. Assembly, Compiler and interpreter are language processors.

An assembler converts the program written in assembly language into machine language. A compiler and an interpreter convert the program written in high level language into machine language. A key difference between Compiler and interpreter is that a compiler convert the program in one go while an interpreter translates the program line by line .

11. Differentiate between data and information.

Ans: Data is an individual unit that contains raw material which does not carry any specific meaning. Information is a processed, organised data presented in a given context and is useful to humans. Information is a group of data that collectively carry a logical meaning.

12. Write short note on fifth-generation  computers.

Ans: In 1982, the fifth-generation computer system was begun by Japan’s Ministry of International Trade and Industry. In this generation, the VLSI technology has advanced and become ULSI technology, stands for Ultra Large-Scale Integration.

The computer made in the fifth generation was created with the help of logic programming and massively parallel computing. This generation of computers was based upon parallel processing hardware and AI (Artificial intelligence) software. Artificial intelligence has the ability to illustrates the means and method of making.computers think the same as human beings.

In this generation, all kinds of high-level languages such as C and C++, .Net, Java and more are used. The computers made in the fifth generation are more powerful, functional, fast in speed, even if they are still in the development phase.

There are some advantages of the computers that use ULSI ( Ultra Large-Scale Integration) technology, which are given below: 

● The computers of fifth-generation use AI (artificial intelligence) technology that includes: Development of expert systems, Game Playing, Robotics, Natural language understanding, and Neutral Networks.

● The AI technology made these computers to understand human language as well as recognize graphs and pictures.

● The development of fifth-generation computers is intended to solve highly complex problems, including working with natural language.

● Hopefully, they will be able to use more than one CPU and less expensive compared to the recent generation.

● It is very easy to take these Computers from one place to another and to repair them.

● The computers made in the fifth generation can be handle easily.

13.What are basic differences between the four generations of computers? 

Ans: Over the years, many computing devices were invented that are used by the humans to solve different types of problems. All these computing devices can be classified into five generations which refer to the phases of improvement made to different computing devices resulted in a small, cheap, fast, reliably and productive computer. The technological development in the field of computers not only refers to the improvements made to the hardware technologies, but also the improvements made to the software technologies.

14. Write a short note on MARKI.

Ans: In 943, American computer Engineer device the first electromechanical computer named Mark-I. It was able to multiple two 10-digit numbers in 5 second. Mark-I was the first machine which could perform to pre programmed instruction automatically. It was the first operational general purpose computer.

15. Explain the two main types of secondary memory.

Ans: The secondary storage devices which are built into the computer or connected to the computer are known as a secondary memory of the computer. It is also known as external memory or auxiliary storage.

The main types of secondary memory are: Hard disks, Pen Drive, SD Card, Compact Disk (CD), Digital Video Disk (DVD) etc.

16. Describe various types of magnetic media.

Ans: The various types of magnetic media are: 

(1) Floppy disks: A floppy disk is a flexible disk with a magnetic coating on it 1.44 MB of data . Now floppy disks are not used due to very less memory storage.

(2) Hard disks: A hard disk is a basically a set of disks known as platters, each with its own read/write head. These rotating disks are coated with a magnetic material and stacked with space between them. Data is recorded on the surface of the disks magnetically.

(3) Magnetic taps: Magnetic tapes can hold a large amount of data. Magnetic tapes are available the form of cassettes, reels, and cartridges.

17. Mention some areas where computer are used widely.

Ans: Today, computers are used almost everywhere. Here are some of the areas where computers are in use widely.

Education: Computers are used in education sector through online classes, online examinations, referring e-books, online tutoring etc. A computer is a powerful teaching aid. Teachers use computers to prepare lessons. Students use computers to access Internet do projects and research works.

Home: computers are used at homes for several purpose like watching movies, online bill payment, home tutoring, playing games, internet access, social media access,etc. Computers help to avail work from facility for corporate employees.

Medical Field: Computers have become an important part in hospitals, labs and pharmacies. Computers are used to keep records of patients and medicine. Computers are used diagnostic system and patient monitoring system.

Business: Almost every business uses computers nowadays. Computers are used for maintaining staff records, transaction processing, sale forecasting, production planning crate presentation and reports, etc.

Government: Various government department use computers to improve the quality and efficiency of their services. Computers are used to keep records on legislative actions, Internal Revenue service, etc.

Banking and Finance: In the banking sector, computers are used to store the details of customers and conduct transactions. People can also use computer to access information on stock markets, trade stock, and manage investment.

Communication: Computers are used to communicate through emails, chat, and video conferencing.

Entertainment: Computers are used to listen to music, watch movies online, play games. Computers are used to create cartoons, animation, videos, etc. Computers are used in recording music.

Reservation: Computers are used for airline/railway/bus reservation. People can book their tickets irrespective of their location. For example, a person in Guwahati may book a ticket from Kolkata to New Delhi.

Science and Engineering: Computers with high performance are used for engineering purpose and to stimulate dynamic process in Science. Computers are used by the scientist for research works.

Military: Computers are largely used in defence. Computers are used in military communication, missile control, military operation and planning etc.

18. What are the major operations performed by a computer? 

Ans: Basic Operations of a computer system:

● Accepting data or instructions

● Processing data 

● Storing data

● Displaying results

● Controlling and coordinating all operations inside a computer.

19. Differentiate between the following pairs:

1. Input Unit and Output unit.

Ans: The difference between Input unit and Output unit are:

2. RAM and ROM.

Ans: The difference between Ram and Rom are:

3. Hard copy and soft copy.

Ans: The difference between Hard copy and soft copy are:

4. Primary memory and secondary memory.

Ans: The difference between Primary memory and secondary memory are:

5. Impact-printer and Non-impact printer.

Ans: The difference between Impact-printer and Non-impact printer are:

6. Assembler and Compiler.

Ans: The difference between Assembler and Compiler are:

7. Hardware and software.

Ans: The difference between Hardware and Software are: 

8. System software and application software.

Ans: The difference between system software and application software are: 

20. Carry out the following conversation:

(a) (135)₁₀ =(?)₂

Solⁿ.                 

∴ (135)₁₀= (10000111)₂ .

(b) (1100110)₂ = (?)₁₀

Solⁿ. (1100110)₂

= 1×2⁶+1×2⁵+0×2⁴+0×2³+1×2²+1×2¹+0×2⁰

= 64+32+0+0+4+2+0

 ∴ (1100110)₂ = (102)₁₀ .

(c) (110.110)₂ = (?)₁₀  

Solⁿ.(110.110)₂

= 1×2²+1×2¹+0×2⁰+1×2⁻¹+1×2⁻²+0×2⁰

= 4+2+0+1/2+1/4+0

= 6+0.5+0.25

= (6.75)₁₀ .

(d) (35.375)₁₀=(?)₂

Solⁿ. (35.375)₁₀

∴ (35.375)₁₀=(100011.011)₂ .

(e) (265)₁₀=(?)₈

Solⁿ. 

∴ (265)₁₀=(411)₈ .

(f) (205.375)₁₀=(?)₈

Solⁿ.

Integer part       

Fraction part 3       

0.375×8=3.0

∴ (250.375)₁₀=(372.3)₈ .

(g) (375)₈=(?)₁₀

Solⁿ. (375)₈

= 3×8²+7×8¹+5×8⁰

= 3×64+7×8+5×1

= 192+56+5

= (253)₁₀ .

(h) (25.6)₈= (?)₁₀

Solⁿ. (25.6)₈

= 2×8¹+5×8⁰+6×8⁻¹

= 2×8+5×1+6/8

= 16+5+6/8

= 21+6/8

= 21+0.75

= (21.75)₁₀ .

(i) (125)₁₆=(?)₁₀

Solⁿ . (125)₁₆

= 1×16²+2×16¹+5×16⁰

= 1×256+2×16+5×1

= 256+32+5

= (293)₁₀ .

(j) (436)₁₀=(?)₁₆      

Solⁿ.                

∴ (436)₁₀=(1B4)₁₆

Note: 10₁₀=A₁₆           13₁₀=D₁₆

11₁₀=B₁₆                      14₁₀=E₁₆

12₁₀=C₁₆                      15₁₀=F₁₆

(k) (213.03125)₁₀=(?)₁₆

Solⁿ .    

∴ (213.03125)₁₀=(D5.08)₁₆ .

(l) Impact-printer and Non-impact printer.

Ans: The difference between Impact-printer and Non-impact printer are:

(m) Assembler and Compiler.

Ans: The difference between Assembler and Compiler are:

(n) Hardware and Software.

Ans: The difference between Hardware and Software are:

(o) System software and Application software.

Ans. The difference between system software and application software are:

21. Carry out the following conversation:

(a) (135)₁₀  =(?)₂

Solⁿ.             

∴ (135)₁₀ =(10000111)₂ .

(b) (1100110)₂ = (?)₁₀

Solⁿ. (1100110)₂

= 1×2⁶+1×2⁵+0×2⁴+0×2³+1×2²+1×2¹+0×2⁰

= 64+32+0+0+4+2+0

∴ (1100110)₂ = (102)₁₀ .

(c) (110.110)₂ = (?)₁₀

Solⁿ. (110.110)₂

= 1×2²+1×2¹+0×2⁰+1×2⁻¹+1×2⁻²+0×2⁰

= 4+2+0+1/2+1/4+0

= 6+0.5+0.25

= (6.75)₁₀ .

(d) (35.375)₁₀ = (?)₂

Solⁿ. (35.375)₁₀ 

∴ (35.375)₁₀ =(100011.011)₂ .

(e) (265)₁₀ = (?)₈

Solⁿ. 

∴ (265)₁₀ = (411)₈ .

(f) (250.375)₁₀ = (?)₈

Solⁿ. 

Fraction par

Integer part 3

0.375×8=3.0

∴ (250.375)₁₀ = (372.3)₈ .

(g) (375)₈ = (?)₁₀

Solⁿ . (375)₈

= 3×8²+7×8¹+5×8⁰

= 3×64+7×8+5×1

= 192+56+5

= (253)₁₀ .

(h) (25.6) = (?)₁₀

Solⁿ. (25.6)₈

= 2×8¹+5×8⁰+6×8⁻¹

= 2×8+5×16/8

= 16+5+6/8

= 21+6/8

= 21+0.75

= (21.75)₁₀. 

(i) (125)₁₆ = (?)₁₀

Solⁿ. (125)₁₆

= 1×16²+2×16¹+5×16⁰

= 1×256+2×16+5×1

= 256+32+5

= (293)₁₀ .

(j) (436)₁₀ = (?)₁₆

Solⁿ.        

∴ (436)₁₀ = (1B4)₁₆

Note: 10₁₀ = A₁₆               13₁₀ = D₁₆

11₁₀ = B₁₆                         14₁₀ = E₁₆

12₁₀ = C₁₆                         15₁₀ = F₁₆ .

(k) (213.03125)₁₀ = (?)₁₆

Solⁿ.                 

∴ (213.03125)₁₀ = (D5.08)₁₆.

(l) (55.08)₁₆ = (?)₁₀

Solⁿ. (55.08)₁₆  

= 5×16¹+5×16⁰+0×16⁻¹+8×16⁻²

= 5×16+5×1+0+8/16²

= 80+5+8/256

= 85+0.03125

= (85.03125)₁₀.

(m) (1100110111)₂ = (?)₁₆

Solⁿ. (1100110111)₂

0011 0011 0111

Now,

(0011)₂ = 0×2³+0×2²+1×2¹+1×2⁰

= 0+0+2+1×1

= 2+1

= 3

(0111)₂ = 0×2³+1×2²+1×2¹+1×2⁰

= 0+1×4+1×2+1×1

= 4+2+1

= 7

∴ 0011/3  0011/3  0111/7

∴ (1100110111)₂ = (337)₁₆ .

(n) ( 10011001.10111001)₂ = (?)₁₆

Solⁿ . 1001  1001  1011 1001

Now, 

1001 = 1×2³+0×2²+0×2¹+1×2⁰

= 8+0+0+1×1

= 8+1

= 9

1011 = 1×2³+0×2²+1×2¹+1×2⁰

= 8+0+1×2+1×1

= 8+2+1

= 11

= B [11₁₀ = B₁₆]

∴ 1001/9  1001/9  1011/B 1001/9

(10011001.10111001)₂ = (99.B9)₁₆

(o) (B59E)₁₆ = (?) 

Solⁿ.              

∴ (B59E)₁₆

= (1011010110011110)₂

Table: Binary equivalent of hexadecimal digits.

(P) (1001100111)₂ = (?)₈

Solⁿ. (1001100111)₂

001  001  100  111

Now, 

001 = 0×2²+0×2¹+1×2⁰

= 0+0+1×1

= 1

100 = 1×2²+0×2¹+0×2⁰

= 4+0+0

= 4

111 = 1×2²+1×2¹+1×2⁰

= 4+2+1×1

= 4+2+1

= 7

∴ 001/1  001/1  100/4  111/7

∴ (1001100111)₂ = (1147)₈ .

(q) (6017)₈ = (?)₂

Solⁿ.         

∴ (6017)₈

= (110000001111)₂

Table : Binary equivalents of octal digits. 

Dev Kirtonia

Hi, I’m Dev Kirtonia, Founder & CEO of Dev Library. A website that provides all SCERT, NCERT 3 to 12, and BA, B.com, B.Sc, and Computer Science with Post Graduate Notes & Suggestions, Novel, eBooks, Biography, Quotes, Study Materials, and more.