Computer Fundamentals
Unit-I
Computer System Concepts: -A Computer is an electronic device that can perform a variety of
operations in accordance with a set of instructions called programs.
In other words, a computer is a machine that handles
data. Data are facts that are gathered and entered into the computer. The computer
stores, retrieves, sends, receives, and analyzes the data to produce
information. Information is any collection of words, numbers, and symbols,
organized so that it is meaningful to the person using it.
The
word “computer” comes from the word “compute” which means to calculate. So a
computer is normally considered to be a calculating device that can perform
arithmetic operations at enormous speed. In fact, the original objective for
inventing the computer was to create a fast calculating machine. But more than
80% of the work done by computers today is of non-mathematical or non-numerical
nature. Hence, to define a computer merely as calculating device is to ignore
over 80% of the work. More accurately, a computer may be defined as a device
that operates upon data. Data can be anything like Bio-data of various
applicants, the marks obtained by various students in various subjects etc.
Data comes in various shapes and sizes depending upon the
type of computer application. A computer can store, process and retrieve data
as and when desired. The fact that computers process data is so fundamental
that many people have started calling it a data processor. The activity of
processing data using a computer is called data processing. The computer can
access and process data millions of times faster than humans can. A computer
can store data and information in its memory, process them, and produce the
desired results. Computers can do many different tasks such as playing games,
railway reservation, weather forecasting etc.
[Data:
-
Data in computer terminology means raw facts.
For example: Mohan, 1977, A etc.
Information: - It means what
we get after processing data (meaningful data). Data are aggregated ( iw.kZ;ksx]
leqPp;] lewg ) and summarized in various meaningful ways to form the information. For
example Mohan, whose roll number is 1977 has grade A.]
A computer system consists
of a computer and supporting devices for input and output of data. The data to
be processed are supplied to the computer with the help of input devices. The
processing unit performs the desired operations on the information and the
result of calculations/processing is obtained on the output devices. Several
types of input/output devices can be attached to the computer. A computer
consists of electronic circuits only, while the input/output devices have both
electronic and mechanical components.
Computer System Characteristics: -
1. Speed: - The smallest
unit of time in the human experience is the second. A computer is a very fast
device. It can perform in a few seconds the amount of work that a human being
can do an entire year – if he worked day and night and did nothing else. While
talking about the speed of a computer, we do not talk in terms of seconds or
even milliseconds (10-3). Our units of speed are the microseconds
(10-6), the nanoseconds (10-9) and even the Pico seconds
(10-12). A powerful computer is capable of performing several
billion (109) simple arithmetic operations per second.
To classify the speeds of different computer systems, the
industry has developed the criterion of million instructions per second (MIPS).
Data processors can compare computers’ processing speeds by comparing the
number of instruction each can perform in 1 second. One computer might have a
rating of 0.5 MIPS, another rating of 10 MIPS.
2. Accuracy: - In addition to
being very fast, computers are very accurate.
The accuracy of a computer is consistently high and the degree of
accuracy of a particular computer depends upon its design. But for a particular
computer, each and every calculation is performed with the same accuracy.
Errors can
occur in a computer, but these are mainly due to human rather than
technological weakness, that is, due to imprecise thinking by the programmer or
due to incorrect input data. Computer errors caused due to incorrect input data
or unreliable programs is often referred to as Garbage-in-Garbage-out or
GIGO. Hardware errors are usually
detected and corrected by the computer system itself. Any calculating device is useless if its
results are unreliable. Computers are universally accused (nks"k
yxkuk] vkjksi yxkuk) of making mistakes on bills, cheques and statements, although most
errors attributed (fo'ks"krk] xq.k] y{k.k]
fo'ks"k.k] izrhd] Js;] ) to computers are really human errors.
4. Versatility: - Versatility
is one of the most wonderful things about the computer. One moment, it is
preparing the results of particular examination, the next moment it is busy
preparing electricity bills and in between, it may be helping an office
secretary to trace an important letter in seconds. All this work is possible by
changing the program (sequence of instructions for computers). Briefly, a
computer is capable of performing almost any task, provided that the task can
be reduced to a series of logical steps.
5. Power of
remembering: - As a human being acquires new knowledge, the brain subconsciously
selects what it feels to be important and worth retaining in its memory, and
relegates unimportant details to the back of the mind or just forgets them.
With computers, this is not the case.
A computer can store and recall any amount of information because of its
secondary storage capability. Every piece of information can be retained as
long as desired by the user and can be recalled as and when required. Even
after several years, the information recalled would be as accurate as on the
day when it was fed to the computer. A computer forgets or losses certain
information only when it is asked to do so. So it is entirely up to the user to
make a computer retain or forget particular information.
In order to explain, the idea of storage capacity, we can take an
example of CD-ROM and a hard disk. A single CD-ROM can store up to 700 MB of
data while a hard disk can have a capacity of around 80 GB (1 GB=1024MB).
6. Automatic: - A machine is
said to be automatic if it works by itself without human intervention.
Computers are automatic machines because once started on a job, they carry on
until the job is finished, normally without any human assistance. However,
computers being machines cannot start themselves. They cannot go out and fine
their own problems and solutions. They have to be instructed. That is, a
computer works from a program of coded instruction that specify exactly how a
particular job is to be done. While the job is in progress, the program is
stored in the computer, and the parts of the instruction are obeyed. As soon as
one instruction is completed, the next is obeyed automatically. Some of the
other characteristics of computers such as speed and accuracy are due to the
fact that they are automatic and work on a problem without any human
intervention.
7. No I.Q.: - A computer is not a magical device. It can only perform tasks that
a human being can. The difference is
that it performs these tasks with unthinkable speed and accuracy. It possesses
no intelligence of its own. Its I.Q. is zero, at least till today. It has to be
told what to do and in what sequence. Hence, only the user can determine what
tasks a computer will perform. A computer cannot take its own decision in this
regard.
8. No Feeling: - Computer is
devoid of emotions. They have no feelings and no instincts because they are
machine. Although men have succeeded in building a memory for the computer, but
no computer possess the equivalent of a human heart and soul. Based on our
feelings, taste, knowledge and experience, we often make certain judgments in
our day-to-day life. But computers cannot make such judgments on their own.
Their judgment is based on the instructions given to them in the form of
programs that are written by us. They are only as good as man makes and uses
them.
Capabilities of Computer:
1. It is self-directing. The user merely feeds
all the instructions to the computer at the start and later proceeds without
any need for human intervention.
2. Ability to store and retrieve information.
The computer has the ability to remember or recall data when finds the need for
them.
3. Ability to perform mathematical operations
and solve complex formula at high speed and with great precision. A very fast
computer can perform the addition of 20 million pairs of ten-digit numbers in
one second.
4. Ability to perform logic operation. The
computer is capable of comparing numbers, letters of alphabets and special
characters. Based on the results of comparison, the computer can direct to take
alternative actions.
Limitations of Computer:
1. It can do only what is designed or
programmed to do. If you ask the computer to get the total payroll for a
certain period, it will give you only the total payroll and not the net salary
or gross salary of each employee.
2. It cannot correct input data. If you
mistakenly entered an hour rate of P50 per hour, the computer cannot respond to
the actual rate of P40 per hour.
3. It cannot think and cannot drive meaning
from objects. The computer cannot interpret your favorite poem or your present
mood.
4. It can only process jobs expressed in a
number of steps leading to a precisely defined goal.
5.
It cannot
completely avoid making errors due to power fluctuations, system malfunctions,
and human disorders.
TYPES OF COMPUTER: -The computers have been classified into three categories
1) Digital Computer
2) Analog Computer
3) Hybrid Computer
DIGITAL COMPUTERS: - Digital computers represent data as numbers.
Counting on your fingers is the simplest form of digital computer. The digital
computers work upon discontinuous data. They convert the data into digits
(binary digits 0 and 1) and all operations are carried out on these digits at
extremely fast rates. A digital computer knows how to count the digits and add
the digits. Digital Computers are much faster than analog computers and far
more accurate. Computers used for business and scientific applications are digital
computers. Digital Computers can be classified in two ways:
(1)
Purpose- wise
(2)
Size and performance wise
Purpose Wise digital
computers are classified into two types:
Special-Purpose Computer is the one that
is designed to perform a specific task. The instruction (programs) to carry out
the task is permanently stored in the machine. For the specific tasks, this
type of computer works efficiently but such computers are not versatile.
General- Purpose Computer is the one that can work on different types of programs input to it
and thus be used in countless applications. The programs are not permanently
stored but are input at the time of execution. These computers are very
versatile.
Size and Performance wise digital
computers can be classified into following four types:
Microcomputers- a microcomputer
is a computer who’s CPU is a microprocessor. A microprocessor is a processor
whose all components are on a single integrated circuit chip. Those are
normally single-microprocessors, single-user systems designed for performing
basic operations like educational, training, small business applications,
playing games etc. These are mainly used in offices, homes, schools, shops,
stores etc. IBM PCs, Apple Mac, IBM PS/2 are some popular computers of this
range.
Compared to mainframes and minis the microcomputer may be
comparatively slow and their capabilities limited, but they do provide good
value for money. The market of cheap microcomputers has tremendously
(extremely) expanded in recent years. In
Minicomputers- Minicomputers are
more powerful computers than microcomputers in terms of processing power and
capabilities. Minicomputers are mainly multi-user systems where many users
simultaneously work on the systems. Mini computers posses’ greater storage
capacity and larger memories as compared to microcomputers. These are even
capable of handling more input-output devices. The most important advantage of
a minicomputer over the mainframe is that it is cheaper in cost, small in size
and very reliable. It does not require air conditioning and can be operated at
room temperature. Examples are: PDP-11,
VAX, and 7500 MAGNUM etc.
Mini computer can accept and transfer data from I/O
devices at the maximum speed of 4 millions bytes per second. They usually
employ microprocessors (chips) in the CPU, both for data storage as well as
data manipulations.
Mainframe Computers- Mainframe
computers are designed to handle huge volumes of data and information. These
very large and expensive computers have great processing speed and very large
storage capacity and memory as compared to minicomputers. These computers even
posses and work with more than one processor at the same time. Thus, one can
say these are multi-user, multiprocessor systems. For mainframe computers very
sophisticated operating systems are needed to control and supervise their
operation. Mainframe allows its user to maintain large information storage at a
centralized location and be able to access and process this data from different
computers located at different locations. They are typically used by large
businesses and for scientific purposes. Examples are: ICL 39, CDC 6600, VAX
8842, IBM 3090/600, and IBM 4381.
Super Computers –Super computers
are the most powerful computers among digital computers. These consist of
several processors running together thereby making them immensely (hugely)
faster and powerful. These computers are capable of handling huge amounts of
calculations that are beyond human capabilities. Super computers can perform
billions of instruction per second. Some of today’s super computers have the
computing capability equal to that of 40,000 microcomputers. A Japanese
super-computer has calculated the value of Pi to 16 million decimal places.
These computers cost in 15-20 million-dollar range. A super computer can
process a great deal of information and make extensive calculations very, very
quickly. They can resolve complex mathematical equations in a few hours, which
would have taken a scientist with paper and pencil a lifetime, or, years, using
a hand calculator. Typically, super computers are used to solve multi-variant
mathematical problems of existent physical processes, such as aerodynamics,
metrology and plasma physics. These are also required by the military
strategists to simulate defense scenario. These are mainly used in application
used in applications like weather forecasting, nuclear science research,
seismology etc. Examples are: CRAY X-MP/14, CDC –205, ETA, PARAM, and ANURAG.
PARAM and ANURAG are super computers produced by
ANALOG COMPUTERS: - In analog computers, continues quantities are
used. Computations are carried out with physical quantities such as voltage,
length, current, temperature etc. The devices that measure such quantities are
analog devices e.g. voltmeter ammeter. Analog computers operate by measuring
rather than counting. Such computers do not directly deal with the numbers.
They measure continuous physical magnitudes (such as temperature, pressure and
voltage), which are analogous to the numbers under considerations. For example,
the petrol pump may have an analog computer that converts the flow of pumped
petrol into two measurements- the quantity of petrol and the price for that
quantity. The main advantage of analog
computers is that all calculations take place in parallel and hence these are
faster. It is very easy to get graphical results directly using analog
computer. But their accuracy is poor as compared to digital counterparts.
Analog computers are mostly used in engineering and scientific applications. An
electronic weighing scale is an example of analog computer.
Difference between Analog
and Digital Computer: -
|
Analog |
Digital |
|
Operates on physical
quantities like temperature, resistance, length, speed etc. |
Operates on numbers like
amount of cheque, number of miles etc. |
|
Measures |
Counts |
|
Continuous |
Discontinuous |
|
Storage capacity
relatively high |
Storage capacity
relatively low |
|
Mainly Process Control |
Scientific and Commercial
use |
HYBRID COMPUTER: - Hybrid computers utilize the best qualities
of both the digital and analog computers. In these computers some calculations
take place in analog manner and rest of them take place in digital manner.
Hybrid computers are best used in hospital where analog part is responsible for
measurement of patient’s heart beat, blood pressure, temperature and other
vital signs and then the operation is carried out in digital fashion to monitor
patient’s vital signs. They are usually used for special problems in which
input data derived from measurements is converted into digits and processed by
computer. Hybrid computers are also used in weather forecasting, scientific
applications, control national defense and passenger flight radar and various
fields of engineering and in industrial control processes.
The computer can act like an analog computer, converting
measurements into numeric input. It can act as a digital computer, processing
stored data for management. Analog and hybrid computers perform specialized
task but the digital computers are used almost everywhere in business and
scientific applications.
Basic Components of a Computer System: - A computer
can be viewed as a system that comprises several units. The term computer
system refers to the whole of computer hardware, components, peripherals and
data communication equipments. It consists of a number of interrelated
components that work together with the aim of converting data into information.
A computer system essentially has the following components:
The Central Processing Unit
(CPU):- The CPU is the brain of a computer system. All major calculations and
comparisons performed by a computer are carried out inside its CPU. The CPU is
also responsible for activating and controlling the operations of other units
of the computer system.
Control Unit:- We know that
the two basic components of a CPU are the
Control Unit and the Arithmetic Logic Unit. The CU controls and guides the interpretation,
flow and manipulation of all data and information. The CU sends control signals
until the required operations are done properly by ALU and memory. Another
important function of CU is the program execution i.e. carrying out all the
instruction stored in the program. The CU gets program instruction from memory
and executes them one after the other. After getting the instruction form
memory in CU, the instruction is decoded and interpreted i.e. which operation
is to be performed. The control unit even controls the flow of data from input
devices to memory and from memory to output devices.
Although, the control unit does not perform any actual
processing on the data, it acts as a central nervous system for the other
components of the computer.
Arithmetic Logic Unit:- The arithmetic
logic unit (ALU) of a computer system is the place where the actual execution
of the instructions takes place during the processing operation. All
calculation is performed and all comparisons (decision) are made in the ALU.
The data and instruction stored in the primary storage prior to processing are
transferred as and when needed to the ALU where processing takes place. No
processing done in the primary storage unit. The ALU perform all the four
arithmetical (+, -, *, /) and some logical (<, >, =, <=, >=,
<>) operations. When two numbers are required to be added, these numbers
are sent from memory to ALU where addition takes place and the result is put
back in the memory. The same way other arithmetic operations are performed. For
logical operation also, the numbers to be compared are sent from memory to ALU
where the comparisons takes place and the result is returned to the memory. The
result of a logical operation is either TRUE or FALSE. These operations provide
the capability of decision-making to the computer.
Input/Output functions:- A computer
system also incorporates input and output devices, which are a communication
medium between a human and the computer. An input unit accepts instructions and
data from the user and communicate them to the computer. The basic task of this
unit is to gather the data and converts it into the form that the computer can
understand. Some of the input devices are keyboard, mouse, light pen and so on.
Just as humans communicate with computers with input
devices, the computer can communicate with human beings with the help of output
devices. Like input units, output units are instruments of interpretations and
communications between humans and computers. These devices take the machine
coded output results from the processor and convert them into a form that can
be used by the people or as a machine input in another processing cycle. Some
of the commonly used output devices are printers, monitor and plotters.
In addition to these, a computer also employs secondary
storage devices, which are extensively used for storing data or instructions.
The physical components or materials on which data is stored permanently are
called storage units or devices. It supplies the stored information to the
other units of computer as and when required. Some common storage devices are
floppy disks, hard disks and tape drives.
Memory:- The memory of
a computer is more like a predefined working place, where it temporarily keeps
information and data to facilitate its performance. When the task is performed,
it clears its memory and memory space is then available for the next task to be
performed. When the power is switched off, everything stored in the memory gets
erased and cannot be recalled.
The memory of
computer is often called main memory or primary memory. The memory of a computer can be thought of as
cells. Each of these cells is further broken down into smaller parts known as
bits. A bit means a binary digit i.e. either 0 or 1. A bit is an elementary
unit of the memory. A group of 8 bits is called a byte and a group of 4 bits is
called a nibble.
One byte is the smallest unit, which can represent a data
item or a character. Other units of memory are KB, MB, and GB.
1KB = 1024 BYTES = 210
1 MB = 1024 KB = 1024*1024 BYTES
1 GB = 1024 MB = 1024*1024*1024 BYTES
Since computer’s main memory
(primary memory) is temporary, secondary memory space is needed to store data
and information permanently for later use. The two most common secondary
storage media are the floppy diskette and the hard disk.
There are two types of memories: Primary and Secondary.
The primary memory or the main memory is part of the main computer system. The
processor directly stores and retrieves information from it. The primary memory
itself is implemented by two types of memory technologies. The first is called
random access memory(RAM) and other is read only memory(ROM).
Random Access Memory
(RAM):-
Random access memory is a volatile memory. It means the information stored in
it remains as long as the power is switched ON. As soon as the power is
switched OFF, the information contained in it vanishes. RAM can be defined as a
block of sequential memory locations, each of which has a unique address
determining the location and those locations contain a data element.
Physically, this
memory consists of some integrated circuit chips either on the motherboard or
on a small circuit board attached to the motherboard. A computer’s motherboard
is designed so that its memory capacity can be easily enhanced by adding more
memory chips. The additional RAM chips, which plug into special sockets on the motherboard,
are also known as single in-line memory modules (SIMMs).
There are two types of RAM.
Dynamic Random
Access Memory (DRAM):- This type of RAM holds the data in dynamic manner
with the help of a refresh circuitry. Each second or even less than that the
content of each memory cell is read and the reading action refreshes the
contents of the memory. Due to this refreshing action, the memory is called
dynamic RAM. DRAMs are made from transistor and capacitor. The capacitor holds
the electrical charge if the bit contains 1 and no charge if the bit is 0. The transistors
read the contents of the capacitor. The charge is held for a short period and
than it fades away, that is, when refresh circuitry comes in.
Static Random
Access Memory (SRAM):- SRAM along with DRAM is essential for a system to
run optimally, because it is very fast as compared to DRAM. It is effective
because most programs access the same data repeatedly and keeping all this
information in the fast SRAM allows the computer to avoid accessing the slower
DRAM. Data is first written to SRAM assuming that it will be used again soon.
SRAM is generally included in a computer system by the name of cache. A static
RAM is faster, costlier, and consumes more power than dynamic RAM. Due to these
reasons, large memories use dynamic RAM, and static RAM is used mainly for
specialized applications. The main memory of most computers uses dynamic RAM.
Read Only Memory
(ROM):-
A special type of RAM, called read only memory (ROM) is a non-volatile memory
chip in which data is stored permanently and can not be altered by the
programmer. As the name suggests, read only memory can only be read, not
written. The contents of ROM are not lost even in case of sudden power failure,
making it non-volatile in a nature. Read
only memory is also random access in nature, which means the CPU can randomly
access any location within
In fact, storing data permanently
into this kind of memory is called “burning in the data”, because data in such
memory is stored by fuse-links. Once a fuse-link is burnt it is permanent. ROMs
are mainly used to store programs and data which do not change and are
frequently used. For example, the most basic computer operations are carried
out by wired electronic circuits. However, there are several higher level
operations that are very frequently used but will require very complicated
electronics circuits for their implementations. Hence, instead of building
electronics for these operations, special programs are written to perform these
operations. These programs are called micro programs because they deal with
low-level machine functions and are essentially substitutes for additional
hardware. Micro programs are written to
aid the control unit in directing all the operations of the computer systems.
ROMs are mainly used by computer manufacturers for storing these micro programs
so that they can not be modified by the users. A good example of a micro
program that is stored in a ROM chip of a computer is the set of instructions
that is needed to make the computer system ready for use when its power is
switched on. This micro programs called system boot programs, contains a set of
start up instructions to check if the system hardware like memory, I/O devices
etc are functioning properly and looks for an operating system and loads its
core part in the volatile RAM of the system to produce the initial display
screen prompt. Note that this micro program is used every time the computer is
switched on and needs to be retained when the computer is switched off.
There are various
types of ROMs, which are given below:
- Programmable
Read Only Memory (PROM)- PROM is a ROM that can be programmed to record
information using a facility known as PROM programmer. Once the chip has
been programmed, the recorded information can not be changed i. e. PROM
becomes same as
- Erasable
Programmable Read Only Memory- EPROM is another type of ROM that can
not erased and the chip can be programmed to record different information
using a special PROM program facility. Erasure to achieved by exposing the
chip to ultraviolet light. When an EPROM is in use, information can only
be read and the information remains on the chip until it is erased. EPROM
are of two kinds-UVPROM(Ultraviolet PROM) and EAPROM(Electrically
Alterable PROM).
- Electrically
Erasable PROM (EEPROM)- This type of ROM can be programmed and erased
by electrical signals. It does not require exposure to ultraviolet light
to erase its contents as EPROM memory does and provides an easy means to
load and store temporary or permanent information in a form of ROM memory.
Information loaded in this memory can be retained for many years without
any power supplied, one of its new applications is as a backup to RAM
memory whose contents are lost in
a power failure. When power is returned, the EEPROM memory can be used to
replace the lost contents of the RAM memory and the microcomputer can
continue working just as if nothing had happened. Even newer devices are
combining RAM and EEPROM memory in a single integrated circuit. Due to the ease with which stored
programs can be altered, EEPROM is also known as flash memory. Flash memory
is used in many new I/O and storage devices. The intelligence of these
devices can be upgraded by simply down-loading new software from a
vendor-supplied disk to flash memory.
Cache Memory:- Cache memory is an extremely fast, small
memory between CPU and main memory whose access time is closer to the
processing speed of the CPU. It acts as a high-speed buffer between CPU and
main memory and is used to temporarily store very active data and instructions
during processing. Since the cache memory is faster than main memory, the
processing speed is increased by making data and instructions needed in present
processing available in the cache.
Data Representation and Codes:- We know that a
computer stores data internally in a format that is not easily readable by
human beings. Every computer stores numbers, letters and other special
characters in codes form. Therefore, you have to understand number system
before codes. Basically, there are two types of number system.
1) Non-Positional Number Systems:- In early days,
human beings counted on fingers. When counting beyond ten fingers, they used
stones, pebbles, or sticks to indicate values. This method of counting uses
known as non-positional number system. In this system, we have symbols such as
I for 1, II for 2, III for 3, IIII for 4, IIIII for 5 etc. Each symbol
represents the same value regardless of its position in a number, and to find
the value of a number, one has to count the number of symbols present in the
number. Since it is very difficult to perform arithmetic with such a number
system, positional number systems were developed.
2) Positional Number System:- In a positional
number system, there are only a few symbols called digits. These symbols
represent different values, depending on the position they occupy in a number.
The value of each digit in such a number is determined by three considerations:
a) The digit itself,
b) The position of
the digit in the number, and
c) The base of the
number system(where base is defined as the total number of digits available in
the number system).
In our day-to-day life, we use
decimal number system. In this system, base is equal to 10 because there are
altogether ten symbols or digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9). You know
that in decimal number system, successive positions to the left of the decimal
point represent units, tens, hundreds, thousands, etc. However, notice that
each position represents a specific power of the base (10). For example,
decimal number 2586(written as 258610) consists of digit 6 in unit’s
position, 8 in tens position, 5 in hundreds positions, and 2 in thousands positions,
and its value can be written as:
(2*103)+(5*102)+(8*101)+(6*100)=2000+500+80+6=2586
The principles that apply to decimal number system, also
apply to any other positional number system. It is important to keep track of
only the base of the number system in which we are working. The value of the
base in all positional number systems suggests the following characteristics:
- The value of
the base determines the total number of different symbols or digits available
in the number system. The first of these choices is always zero.
- The maximum
value of a single digit is always equal to one less than the value of the
base.
Decimal:- The primary
number system used is a base ten number system or decimal number system. The
decimal system is the system, which we use every day while counting. The name
is derived from the Latin word Decem, which means ten. This number system
includes the ten digits from 0 through 9. These digits are recognized as the
symbols of the decimal system.
Starting at the decimal point and moving to the left,
each position is represented by the base (radix) value (10 for decimal) raised
to a power. The power starts at 0 for the position just to the left of the
decimal point. The power is incremented for each position that continues to the
left.
Binary:-- Binary number
system is like decimal number system, except that the base is 2, instead of 10.
You can use only two symbols or digits (0 and 1) in this number system. Note
that the largest single digits are 1(one less than the base). Each position in
a binary number represents a power of the base (2). Hence, in this system, the
rightmost positions is units (20) position, the second position from
the right is 2’s (21) and so on. Therefore, decimal equivalent of
binary number 10101(written as 101012) is:
(1*24)+(0*23)+(1*22)+(0*21)+(1*20)=16+0+4+0+1=21
Hence, we can write
101012=2110
The
short form of “binary digit” is bit. Hence, a bit in computer terminology means
either a 0 or 1. An n-bit number is a binary number consisting of ‘n’ bits. All
3-bit numbers along with their decimal equivalent is shown in table.
|
Binary |
Decimal Equivalent |
|
000 |
0 |
|
001 |
1 |
|
010 |
2 |
|
011 |
3 |
|
100 |
4 |
|
101 |
5 |
|
110 |
6 |
|
111 |
7 |
Remember that we have only
two digits, 0 and 1, in binary number system and hence, binary equivalent of
decimal number 2 has to be stated as 10(read as one, zero). Another important
point to note is that with 3 bits (positions), only 8(23) different
patterns of 0s and 1s are possible, as shown in table. In fact, any decimal
number in the range 0 to 2n-1 can be represented in binary form as
an n-bit number. Every computer stores numbers, letters, and other special
characters in binary form. There are several occasions when computer
professionals need to know the raw data contained in a computer’s memory. A
commonly used way of doing this is to print memory contents on a printer. This
printout is called a memory dump. Memory dumps, which are in binary numbers,
would have many pages of 0s and 1s. Working with these numbers would be very
difficult and error prone for computer professional. Hence, two number systems-
octal and hexadecimal are often used as shortcut notations for binary.
Octal: In octal number
system, the base is 8. Hence, there are only eight symbols or digits:
0,1,2,3,4,5,6 and 7. The largest single digit is 7(one less than the base 8).
Each positions in an octal number represents a power of the base (8). Therefore,
decimal equivalent of octal number 2057(written as 20578) is:
(2*83)+(0*82)+(5*81)+(7*80)=1024+0+40+7=1071
Hence, 20578=107110
Observe that there are only
8 digits in octal number system, 3 bits( 23=8) are sufficient to
represent any octal number in binary.
Hexadecimal System: In hexadecimal
number system, the base in 16. Hence, there are 16 symbols or digits. The first
10 digits are the same digits of decimal number system- 0, 1, 2, 3, 4, 5, 6, 7,
8, and 9. The remaining six digits are denoted by the largest single digit is F
or 15(one less than the base 16). Each position in hexadecimal number system
represents a power of the base (16). Therefore, decimal equivalent of hexadecimal
number 1AF (written as 1AF16) is:
(1*162)+(A*161)+(F*160)=(1*256)+(10*16)+(15*1)=256+160+15=431
Hence, 1AF16=43110
Observe that since there are
only 16 digits in hexadecimal number system, 4 bits (24=16) are
sufficient to represent any hexadecimal number in binary.
Inter Conversion: Numbers
expressed in decimal number system are much more meaningful to us, than are
numbers expressed in any other number system. However, you can represent any
number in one number system in any other number system. Because the input and
final output values are to be in decimal, computer professionals are often
required to convert numbers in other number system to decimal and vice-versa. Many
methods or techniques can be used to convert numbers from one base to another.
Converting
to Decimal from Another Base:-- The following three steps are used to convert to
a base 10 value from any other number system:
Step 1: Determine the column
value of each digit(this depends on the position of the digit and the base of
the number system).
Step 2: Multiply the
obtained column values by the digits in the corresponding columns.
Step 3: Sum the products
calculated in step 2. The total is the equivalent value in decimal.
For Example: 110012=?10
Step 1: Determine Column
Values
Column Number Column
Value
1
20 = 1
2
21 = 2
3
22 = 4
4
23 = 8
5
24 = 16
Step 2: Multiply column
values by corresponding column digits
16 8 4 2 1
*1 *1 *0 *0 *1
Step 3: Sum the products
16+8+0+0+1=25
Converting from a Base 10 to
a new base(Division-Remainder Technique):
The following four steps are
used to convert a number from base 10 to a new base:
Step 1: Divide the decimal
number to be converted by the value of the new base.
Step 2: Record the remainder
from step 1 as the rightmost digit(least significant digit) of the new base
number.
Step 3: Divide the quotient
of the previous divide by the new base.
Step 4: Record the remainder
from step 3 as the nest digit, (to the left) of the new base number.
For Example: 2510
= ?2
Steps 1 & 2: 25/2= 12
and remainder 1
Steps 3 & 4: 12/2= 6 and
remainder 0
Steps 3 & 4: 6/2= 3 and
remainder 0
Steps 3 & 4: 3/2= 1 and
remainder 1
Steps 3 & 4: ½= 0 and
remainder 1
Hence, 2510=
110012
Computer Codes:-- Numeric data is not the only form of data
handled by a computer. We often requires to process alphanumeric data also. An
alphanumeric data is a string of symbols, where a symbol may be one of the
letters A, B, C,…….Z, or one of the digits 0,1,2,…..9, or a special character,
such as + - * / , . () = (space or blank) etc. An alphabetic data consists of
only the letters A, B,C,……Z, and blank character. Similarly, numeric data
consists of only the digits 0,1,2,….and 9. However, the bits 0 and 1 must
represent any data internally. Hence, computers use binary coding schemes to
represent data internally.
BCD Numbers: Binary Coded
Decimal (BCD) code is one of the early computer codes. The idea of this coding
scheme is to convert each digit of a decimal number into its binary equivalent
instead of converting the entire decimal value into a binary number. This makes
the conversion process easier.
|
Decimal Digits |
BCD Equivalent |
|
0 |
0000 |
|
1 |
0001 |
|
2 |
0010 |
|
3 |
0011 |
|
4 |
0100 |
|
5 |
0101 |
|
6 |
0110 |
|
7 |
0111 |
|
8 |
1000 |
|
9 |
1001 |
Figure shows BCD equivalent of each decimal
digit. Since 8 and 9 require 4 bits, all decimal digits are represented in BCD
by 4 bits. As you, know that 4210 is equal to 1010102. However, converting 4210 into BCD
produces the following result:
4210=0100 0010 or 01000010 in BCD
Note that each decimal digit
is independently converted to a 4-bit binary number, and hence, the conversion
process is very easy. Also note that when four bits are used, altogether 16 (24)
combinations are possible. However, from figure you can see that only the first
10 of these combinations are used to represent decimal digits. The remaining
six arrangements (1010, 1011, 1100, 1101, 1110 and 1111) have decimal values
from 10 to 15. These arrangements are not used in BCD coding. That is 1010 does
not represent 1010 in BCD. Instead,
1010= 0001 0000 or
00010000 in BCD
4-bit BCD coding system can be used to represent only
decimal numbers because four bits are insufficient to represent the various
characters used by a computer. Hence, instead of using four bits with only 16
possible characters, computer designers commonly use six bits to represent
characters in BCD code. In 6-bit BCD code, the four BCD numeric place positions
are retained but two additional zone positions are added. With six bits, it is
possible to represent 64(26) different characters. This is
sufficient to code the decimal digits (10), alphabetic letters(26), and other
special characters(28).
EBCDIC:- The major
problem with BCD code is that it can represent only 64(26) different
characters. This is not sufficient for providing decimal numbers (10), lowercase
(small) letters (26), uppercase (capital) letters (26), and a large number of
other special characters (28+). Hence, BCD code was extended from a 6-bit code
to an 8-bit code. The added two bits are used as additional zone bits,
expanding the zone to four bits. The resulting code is called the Extended
Binary-Coded Decimal Interchange Code (EBCDIC). In this code, it is possible to
represent 256(28) different characters, instead of 64 (26).
In addition to the various characters, this also allows a large variety of
printable characters and several non-printable control characters. The control
characters are used to control such activities as printer vertical spacing,
movement of cursor on terminal screen etc. All of the 256 combinations have not
yet been assigned characters. Hence, the code can still grow, as new
requirements develop. Developed by IBM, EBCDIC code is used in most IBM models,
and in many other computers.
ASCII Codes: Another widely
used computer code is the American Standard Code for Information Interchange (ASCII).
Several American computer manufactures have adopted ASCII as their computer’s
internal code. This code is popular in data communications, is used almost
exclusively to represent data internally in microcomputers and is frequently
found in larger computers produced by some vendors.
American National Standards Institute (ANSI) published
ASCII standard in 1963. However, the standard lacked lowercase letters and ANSI
subsequently revised ASCII in 1967. Later revisions in 1968, 1977 and finally
in 1986 brought it in its present form. Today, ASCII is one of the most popular
and widely supported character-encoding standards.
ASCII is of two types- ASCII-7 and ASCII-8. ASCII-7 is a
7-bit code that can represent 128(27) different characters.
Computers using 8-bit byte and 7-bit ASCII either set the 8th bit
(leftmost bit) of each byte as zero or use it as a parity bit.
ASCII-8 is an extended version of ASCII-7. It is an 8-bit
code that can represent 256(28) different characters. The additional bit is
added to the left of the 7th bit(leftmost bit) of ASCII-7 codes.
ASCII-7 uses only 7 bits whereas all the 8 bits are used in ASCII-8. Hence, the
codes of first 128 characters (symbols) are identical in ASCII-7 and ASCII-8.
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