UNIT -II:

COMPUTER ARITHMETIC & STORAGE FUNDAMENTALS:

 Binary, Binary Arithmetic,
 Number System:
o Positional & Non-Positional,
o Binary, Octal, Decimal, Hexadecimal
 Converting from one number system to another.
 Primary Vs Secondary Storage:
 Data storage & retrieval methods.
 Primary Storage: - RAM, ROM, PROM, EPROM, EEPROM.
 Secondary Storage: -Magnetic Tapes, Magnetic Disks. Cartridge tape, hard disks,
Floppy disks, Optical Disks, Compact Disks, Zip Drive, Flash Drives
List of Important Questions:
1. What is number system? Explain various types of number systems 2021,2022
2. What is binary arithmetic? How does it help in programming? 2019
3. Short note on Binary, Decimal, Octal, Hexa decimal  2021
4. Differentiate between RAM and ROM2021,2022
5. Discuss about various secondary storage devices.  2021
6. What is data storage? what are its types  2019

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What is a Number System?
 Number systems are very important because the design and organisation of a
computer system depends upon the number system.
 A number system has an ordered set of symbols known as digits with rules defined
for performing arithmetic operations like addition, multiplication etc.
Classification of Number System:
1. Positional or weighted number system
2. Non-Positional number system
Positional (or Weighted) Number System:
A positional number system is also known as weighted number system.
 Positional number systems use only few symbols called digits.
 According to its position of occurrence in the number, each digit is weighted.
For example:
1358 = 1 x 103 + 3 x 102 + 5 x 101 + 8 x 100
13.58 = 1 x 101 + 3 x 100 + 5 x 10-1 + 8 x 10-2

 Few examples of positional number system are

 decimal number system
 Binary number system (Base 2. Digits used: 0, 1)
 octal number system, ( Base 8. Digits used: 0 to 7)
 hexadecimal number system (Base 16. Digits used: 0 to 9, Letters used: A- F)
2. Non-Positional (or Non-weighted) Number System:

 Non-positional number system is also known as non-weighted number system.

 Digit value is independent of its position.
 Non-positional number system is used for shift position encodes and error detecting
purpose.
 Example of non-weighted number system:
Roman Code: I II III IV V VI VII VIII IX X

Number System: Binary, Octal, Decimal, Hexadecimal

 When we type some letters or words, the computer translates them in numbers as
computers can understand only numbers.
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 A computer can understand the positional number system where there are only a
few symbols called digits and these symbols represent different values depending on
the position they occupy in the number.
 The value of each digit in a number can be determined using −
 The digit
 The position of the digit in the number
 The base of the number system (where the base is defined as the total number of
digits available in the number system)

1. Decimal Number System

 The number system that we use in our day-to-day life is the decimal number system.
Decimal number system has base 10 as it uses 10 digits from 0 to 9.
 In decimal number system, the successive positions to the left of the decimal point
represent units, tens, hundreds, thousands, and so on.
 Each position represents a specific power of the base (10).
 For example, the decimal number 1234 consists of the digit 4 in the unit’s position, 3
in the tens position, 2 in the hundreds position, and 1 in the thousands position.
 Its value can be written as
(1 x 1000) + (2 x 100) + (3 x 10) + (4 x l)
1000 + 200 + 30 + 4
1234

 As a computer programmer or an IT professional, we must understand the following

number systems which are frequently used in computers.

1.Binary Number System

Characteristics of the binary number system are as follows −
 Uses two digits, 0 and 1
 Also called as base 2 number system
Ex: Binary Number: (10101)2
Calculating Decimal Equivalent –

Binary Number Decimal Number

(10101)2 ((1 x 24) + (0 x 23) + (1 x 22) + (0 x 21) + (1 x 20))10

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 (10101)2 (16 + 0 + 4 + 0 + 1)10

(10101)2 (21)10

Note − 101012 is normally written as 10101.

2. Octal Number System

Characteristics of the octal number system are as follows −
Uses eight digits, 0,1,2,3,4,5,6,7
 Also called as base 8 number system
Example
Octal Number:(129570)8
Calculating Decimal Equivalent −

Octal Number Decimal Number

(12570)8 ((1 x 84) + (2 x 83) + (5 x 82) + (7 x 81) + (0 x 80))10

(12570)8 (4096 + 1024 + 320 + 56 + 0)10

(12570)8 (5496)10

Note − 125708 is normally written as 12570.

3. Hexadecimal Number System

Characteristics of hexadecimal number system are as follows −
 Uses 10 digits and 6 letters, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
 Letters represent the numbers starting from 10. A = 10. B = 11, C = 12, D = 13, E =
14, F = 15
 Also called as base 16 number system
Example:
Hexadecimal Number: (19FDE)16
Calculating Decimal Equivalent –

Hexa Decimal Number Decimal Number

(19FDE)16 ((1 x 164) + (9 x 163) + (F x 162) + (D x 161) + (E x 160))

(19FDE)16 ((1 x 164) + (9 x 163) + (15 x 162) + (13 x 161) + (14 x 160))
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 (19FDE)16 (65536+ 36864 + 3840 + 208 + 14)10

(19FDE)16 (106462)10

Note – (19FDE)16 is normally written as 19FDE.

Number Conversion:
There are many methods or techniques which can be used to convert numbers from one
base to another.
Decimal to Binary Binary to Decimal
Decimal Number: (29)10 Binary Number: (11101)2
Calculating Binary Equivalent − Calculating Decimal Equivalent −
Division Quotient Remainder Binary Decimal Number
by 2 Number
29 / 2 14 1 (11101)2 ((1 x 24) + (1 x 23) + (1 x 22) + (0 x 21) +
14 / 2 7 0 (1 x 20))10
7/2 3 1 (11101)2 (16 + 8 + 4 + 0 + 1)10
3/2 1 1 (11101)2 (29)10
1/2 0 1 Binary Number: (11101)2 = Decimal Number: (29)10
Decimal Number: 2910 = Binary
Number: (11101)2.

Decimal to Octal Octal to Decimal

Decimal number (100)10

Convert Octal number (144)8 to a Decimal
To convert decimal numbers to octal numbers,
we need to divide 100 by the octal base number number.
i.e. 8. (144)8 = (1 × 82 ) + (4 × 81 )+ (4 × 80 )
(144)8 = (1x64) + (4x8 ) + (4x1)
Division by 8 Quotient Remainder (144)8 = 64 + 32 + 4
100/8 12 4
(144)8 = 100
12/8 1 4
1/8 0 1 Therefore, (144)8 = (100)10
Therefore, (100)10 = (144)8
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 Decimal to Hexa decimal Hexa decimal to Decimal
Convert the (740)10 decimal to hexadecimal Convert (2E4)16 to decimal number
number.
Division quotient Remainder in (2E4) 16 = (2x 162) +(14 x161 ) + (4x 160)
Fact Hexadecimal
740 /16 46 4 (2E4) 16 = (2x 256) + (14 x 16) + (4x1)
46 / 16 2 14 = E (2E4) 16 = 512 + 224 + 4
(14 is represented (2E4) 16 = (740)10
by ‘E’ in
hexadecimal
system)
2 / 16 0 2

Now, write the remainders from bottom to

top (in the reverse order). (740)10 = (2E4)16

Binary Arithmetic:
 Binary arithmetic is essential part of all the digital computers and many other digital
systems.

Binary Addition

There are four rules of binary addition.

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In fourth case, a binary addition is creating a sum of (1 + 1 = 10) i.e. 0 is written in the given
column and a carry of 1 over to the next column.
Example − Addition

Binary Subtraction

Subtraction and borrow, these two words will be used very frequently for the binary
subtraction. There are four rules of binary subtraction.

Example − Subtraction

Binary Multiplication

Binary multiplication is similar to decimal multiplication. It is simpler than decimal

multiplication because only 0s and 1s are involved. There are four rules of binary
multiplication.

Example − Multiplication

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Binary Division

Binary division is similar to decimal division. It is called as the long division procedure.
Example – Division

Primary Vs Secondary Storage:

 A memory is just like a human brain.
 It is used to store data and instructions.
 Computer memory is the storage space in the computer, where data is to be
processed and instructions required for processing are stored.
 The memory is divided into large number of small parts called cells.
 Each location or cell has a unique address

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Comparison Between Primary and Secondary Memories
1. Primary memory is the computer’s main memory and stores data temporarily.
2. Secondary memory is external memory and saves data permanently.
3. Data stored in primary memory can be directly accessed by the CPU, which cannot be
accessed in secondary memory.
4. Primary memory is lost during a power outage, while secondary memory saves the
data.
5. Primary memory is volatile, while secondary memory is non-volatile.
6. Primary memory is stored on semiconductor chips, while secondary memory is
stored on external hardware devices.
7. Primary memory is classified into cache memory and random-access memory, while
secondary memory has no such categories.
8. Primary memory is faster than secondary memory.
9. Primary memory uses the computer’s current data, while secondary memory can
save data in various formats that can be accessed at any time.

Data storage & retrieval methods.

Data storage and retrieval methods can be broadly classified into two categories:

 Local storage: This involves storing data on a device that is physically connected to
the computer or device that is accessing the data. Common local storage devices
include hard drives, solid-state drives (SSDs), and optical drives (CDs, DVDs, and Blu-
rays).
 Remote storage: This involves storing data on a device that is not physically
connected to the computer or device that is accessing the data. Common remote
storage methods include cloud computing and network-attached storage (NAS).

Local storage methods

 Hard drives: Hard drives are the most common type of local storage device. They are
relatively inexpensive and have a large storage capacity. However, hard drives can be
slow and noisy.
 Solid-state drives (SSDs): SSDs are faster and more durable than hard drives, but
they are also more expensive. SSDs are a good choice for applications that require
fast data access, such as gaming and video editing.

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  Optical drives: Optical drives are used to store data on CDs, DVDs, and Blu-rays.
Optical drives are relatively slow and have a limited storage capacity, but they are
portable and can be used to share data with others.

Remote storage methods

 Cloud computing: Cloud computing is a service that allows users to store and access
data over the internet. Cloud computing offers a number of advantages over local
storage, including scalability, accessibility, and security. However, cloud computing
can be more expensive than local storage, and there may be concerns about data
privacy and security.
 Network-attached storage (NAS): NAS is a storage device that is connected to a
network. NAS devices can be used to share data between multiple computers on the
network. NAS devices are a good choice for applications that require centralized data
storage and sharing.

Data retrieval methods

Once data has been stored, it needs to be able to be retrieved efficiently. Some of the most
common data retrieval methods include:

 File systems: File systems are used to organize data on storage devices. They allow
users to create, delete, and modify files, and to move files between different storage
devices.
 Databases: Databases are used to store structured data in a way that makes it easy
to retrieve and analyse. Databases use a variety of techniques to index and organize
data, which allows users to quickly and easily find the data they need.
 Search engines: Search engines are used to search for data on the internet. They
index websites and other online content, and they allow users to search for specific
keywords or phrases.
 Data mining: Data mining is a process of extracting knowledge from large amounts of
data. It can be used to identify trends, patterns, and relationships in data.

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Primary Storage: - RAM, ROM, PROM, EPROM, EEPROM:

 Primary storage (also known as main memory) is the component of the computer
that holds data, programs and instructions that are currently in use.
 Primary storage is located on the motherboard. As a result, data can be read from
and written to primary storage extremely quickly.
 This gives the processor fast access to the data and instructions that the primary
storage holds.
 There are two types of primary storage:
1. Random access memory (RAM)
2. Read Only Memory (ROM)

RAM:
 RAM (Random Access Memory) is the internal memory of the CPU for storing data,
program, and program result.
 It is a read/write memory which stores data until
the machine is working.
 As soon as the machine is switched off, data is
erased.
 Data in the RAM can be accessed randomly but it is
very expensive.

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  RAM is volatile, i.e., data stored in it is lost when we switch off the computer or if
there is a power failure.
 Hence, a backup Uninterruptible Power System (UPS) is often used with computers.
RAM is small, both in terms of its physical size and in the amount of data it can hold.

 RAM is of two types −

1. Static RAM (SRAM)
2. Dynamic RAM (DRAM)
ROM
 ROM stands for Read Only Memory.
 The memory from which we can only read but
cannot write on it.
 This type of memory is non-volatile.
 The information is stored permanently in such
memories during manufacture.
 A ROM stores such instructions that are required
to start a computer.
 This operation is referred to as bootstrap.
 ROM chips are not only used in the computer but
also in other electronic items like washing machine and microwave oven.
PROM: (Programmable Read-Only Memory)
 It is a chip on which data can be written only once.
Once a program has been written onto a PROM, it
remains there forever.
 The difference between a PROM and a ROM
(read-only memory) is that a PROM is
manufactured as blank memory, whereas a ROM
is programmed during the manufacturing process.
 To write data onto a PROM chip, you need a
special device called a PROM programmer or
PROM burner.

EPROM: (Erasable Programmable Read-Only Memory)

 EPROM is a special type of memory that retains its
contents until it is exposed to ultraviolet light.
 The ultraviolet light clears its contents, making it
possible to reprogram the memory.
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  To write to and erase an EPROM, you need a special device called a PROM
programmer or PROM burner.
EEPROM: (Electrically erasable programmable read-only
memory)
 EEPROM is a special type of PROM that can be
erased by exposing it to an electrical charge.
 Like other types of PROMS, EEPROM retains its
contents even when the power is turned off.

Secondary Storage:
 Secondary storage is a memory that is stored external to the computer.
 It is mainly used for the permanent and long-term storage of programs and data.
 Hard Disk, CD, DVD, Pen/Flash drive, SSD, etc, are examples of secondary storage.
1. Magnetic Tapes:
 In magnetic tape only one side of the ribbon is used
for storing data.
 It is sequential memory which contains thin plastic
ribbon to store data and coated by magnetic oxide.
 Data read/write speed is slower because of
sequential access.
 It is highly reliable which requires magnetic tape
drive writing and reading data.

2. Magnetic Disks.
 A magnetic disk is a type of secondary memory.
 It is used to store various programs and files.
 Magnetic disks are less expensive than RAM and can store large amount of data, but
the data access rate slower than main memory.
 Data can be modified or can be deleted easily in the magnetic disk memory.

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  It also allows random access to data.

3. Cartridge tape:
 A tape cartridge is a storage device that
contains a spool of magnetic tape used to
store different kinds of data, from corporate
data to audio and video files.
 Each cartridge is designed to fit into a
compatible audio/video recorder system or
computer system.
4. hard disks:
 A computer hard disk drive (HDD) is non-volatile data
storage device.
 All computers need a storage device, and HDD are
just one example of a type of storage device.
 Hard disks are usually installed inside desk-top
computers.
 Most basic hard drives consist of several disk platters
-- a circular disk made of either aluminium, glass or
ceramic -- that are positioned around a spindle inside
a sealed chamber.
5. Floppy disks:
 A floppy disk is a magnetic storage medium for
computer systems.
 The floppy disk is composed of a thin, flexible
magnetic disk sealed in a square plastic carrier.

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  In order to read and write data from a floppy disk, a computer system must have a
floppy disk drive (FDD).
 A floppy disk is also referred to simply as a floppy. Since
the early days of personal computing, floppy disks were
widely used to distribute software, transfer files, and
create back-up copies of data.
 When hard drives were still very expensive, floppy disks
were also used to store the operating system of a
computer.
6. Optical Disks:
 An optical disk is any computer disk that uses optical
storage techniques and technology to read and write
data.
 It is a computer storage disk that stores data digitally
and uses laser beams (transmitted from a laser head
mounted on an optical disk drive) to read and write
data.
 An optical disk is primarily used as a portable and
secondary storage device.
 It can store more data than the previous generation of magnetic storage media,
and has a relatively longer lifespan.
 Compact disks (CD), digital versatile/video disks (DVD) and Blu-ray disks are
currently the most commonly used forms of optical disks.
These disks are generally used to:
 Distribute software to customers
 Store large amounts of data such as music, images and videos
 Transfer data to different computers or devices
 Back up data from a local machine.

7. Compact Disks:
 Abbreviated as CD, a compact disc is a flat, round, optical storage medium invented
by James Russell.
 The first CD was created at a Philips factory in Germany on August 17, 1982.
 The main material of the CD is plastic
 The shape of the plastic is circular and one side of the circular plastic is coated with
the reflecting metal coating, usually aluminium.

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8. Zip Drive:
 A Zip drive is a medium-capacity and portable magnetic
disk storage system launched by Iomega in the mid-
1990s.
 It was popular at the time of launch as cost per storage
unit was lower than that of hard disks, and it could store
a larger amount of data than a floppy disk.
 The Zip drive was capable of fast data transfer and was
durable and reliable.
 The rise of other devices that later came to market, such
as USB drives, were favoured over the Zip drive and Zip
disk, and these became obsolete soon afterward.

9.Flash Drives:
A USB flash drive is a device used for data storage that includes a flash memory and an
integrated Universal Serial Bus (USB) interface.
 Most USB flash drives are removable and rewritable.
 Physically, they are small, durable and reliable.
 The larger their storage space, the faster they tend to
operate.
 USB flash drives are mechanically very robust because
there are no moving parts.
 They derive the power to operate from the device to
which they are connected (typically a computer) via the
USB port.

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