Contents
1.
DEFINE BOOLEAN
ALGEBRA
2.
COMPLEXITY OF THE
QUICKSORT ALGORITHM
3.
BRIEFLY DESCRIBE
HOW A CPU WORKS WITH THE HELP OF BASIC BUILDING BLOCK DIAGRAM WITH AN EXAMPLE
4.
ASSEMBLY LANGUAGE
5.
OPERATING SYSTEM
6.
ANALOG COMPUTER
AND DIGITAL COMPUTER
7.
COMPUTER PROGRAMMING
LANGUAGE
ü DEFINE BOOLEAN ALGEBRA
A class of elements B together with two binary operations +
and . is a Boolean algebra, if the fooling for postulates hold :-
P1:- Both the operations +
and . are commutative, i.e. for any two
elements a and b of B, a+b=b+a and a∙b=b∙a.
P2:- Each of the
operations + and . are distributive over the other, i.e., for any elements a, b
and c in B, a+b∙c=(a+b)∙(a+c)
and a(b+c) =a∙b+a∙c .
P3:- There exist in B
distinct is identity elements 0 and 1 (0 ≠1) for the operations + and ∙
respectively, such that for any element a of B. a+0=0+a=a and a∙1=1∙a=a.
P4:-For every element
a of B, there exists an element a’ (called the complement of a) in B, such that
a+a’=1 and a∙a’=0.
ü COMPLEXITY OF THE QUICKSORT
ALGORITHM
The running time of a sorting
algorithm is usually measured by the number f(n) of comparisons required to
sort n elements. The algorithm has a worst-case running time of n2/2, but an average-case running time of other n log n.
The 1st elements will require
n-comparisons to recognize that it remains in the 1st position. The
1st sub list will be empty, but the 2nd sub list will
have n-1 elements. The 2nd element will require n-1 comparisons to
recognize that it the 2nd position. And so on. Consequently, there
will be a total of f(n)= n+(n-1)+……+2+1= n(n+1)/2 = n2/2+0(n)=0(n)2 comparisons.
The complexity f(n)=0 (n log n) of the
average case come from the fact that, on the average, each reduction step of the algorithm produces two sub lists. Accordingly,
1. Reducing the initial list places 1
element and produces two sub lists.
2. Reducing the two sub list places 2
elements and produces four sub lists.
3. Reducing the four sub list places 4
elements and produces eight sub lists.
4. Reducing the eight sub list places 8
elements and produces sixteen sub lists.
And so on. Hence, here will be approximately
log2n levels of reductions steps. Each level uses at most n-
comparisons, so f(n)=0(n log n). Mathematical analysis and empirical evidence
have both shown that, f(n)≈1∙4[n log
n] is the expected number of comparisons for the quick sort algorithm.
ü
BRIEFLY DESCRIBE HOW A CPU WORKS WITH
THE HELP OF BASIC BUILDING BLOCK DIAGRAM WITH AN EXAMPLE
INPUT UNIT::- A computer accepts the coded information
through the input unit. The simplest is the keyboard which is electronically
connected to the processing part of the computer. Other example is mouse which
is one of the important components in the GUI environment. Here GUI means
graphical user interface.
MEMORY UNIT::- the function of the memory unit is to store programmers
and data. there are two classes of memory devices called the primary and
secondary storage.
The primary
memory or the main memory or the main memory is a fast memory capable of
operating at the electronic speeds. Programmes are stored in main memory during
their execution. The main consists of a large number of semi conductor storage
cells each capable of storing I bit of information. Instruction and data can be
written into the memory and read out under the control of a processor. The
secondary memory unit may be used to data information and final output.
ARITHMATIC AND LOGICAL UNIT ::- This unit does the octal
processing (arithmetic and logical operations) under programmes control. It performs the additions,
subtraction, multiplication and divination as arithmetical operation and also
the logical operation like AND, OR, NOT etc. The ALU works under the directions
of control unit.
CONTROL UNIT::-the control unit selects, interprets and
corries out the execution of program instruction in their proper sequence. The
operations in the ALU are also carried out under the supervision of cu unit.
OUTPUT UNIT::- The output unit is the reverse order of the
input unit. Its main function is to send information to the outside would i.e.
the output devices are used to record the results obtained by the computers and
present them to the outside world. Common output device are VDU, printer
etc.
The input
devices are used to transfer information into the memory unit of the computer
under the direction of cu. Each instruction is retrieved in proper squeegee
from the memory and interpreted. Control unit signals the ALU about the precise
operation to be performed and transferred to the ALU necessary data for
operation. The ALU then carries out all computations and comparisons. Results
are then passed to the main memory for temporary storage and are finally terns fared
to output devices. All these events take place under the direction of control
unit.
ü ASSEMBLY LANGUAGE
The
writing of program in machine languages is very difficult, tiresome and boring
job for a programmer. Moreover, it is error prone. To solve this problem and to
facilitate programmer easily understandable languages have been developed.
Assembly language is one of them. Programs can easily be written in
alphanumeric symbols instead of 0s and 1s. Meaningful and easily remember-able
symbols are selected for this purpose. For example, ADD for addition, SUB for
subtraction, CMP for comparison, etc. Such symbols are known as mnemonics. A
program written in mnemonics is called assembly language program. (The writing
of programs in assembly language is easier and faster as compared to the
writing of programs in a machine language.)
ü OPERATING SYSTEM
An operating system can be regarded as a set pf ptogrammes which permit
the continuous operation of a computer from programme to programme with the
minimum amount of operator intervention, it acts as an interface between the
operation, computer and the processing programme. According to ANSI (American
National Standard Institute) the definition of an operating system is the
software which control the execution of the computer programme and which may
provide scheduling, debugging, input/output control, account, compilation,
storage assignment, data management and related services.
An operating
system may thus be defined as a set of system programmes that control and
coordinate the operation of a computer system. Some of the major facilities
provided by a modern system are:-
1) Easy interaction between human and
computer.
2) Starting computer programmes
automatically when the power.
3) Loading and scheduling users
programme along with necessary computers.
4) Controlling input and output.
5) Controlling programme execution.
6) Scheduling processes.
7) Managing us of main memory.
8) Managing and manipulating files.
9) Providing security to users jobs and
files.
10)
Accounting
resource wage.
Every operating
system is a kernel which permanently resides in the main memory of a computer
to perform some and of the basic functions of operating system and access other
portion as they needed. The reaming in part of the operating system are
normally stored in the disc ready to be loaded into the main memory when
required and order to do by the kernel. 
ü ANALOG COMPUTER AND DIGITAL
COMPUTER
Many
physical systems can be described mathematically by differential equations
whose solutions as a function of time give the complete mathematical behavior
of the process. An analog computer performs a direct simulation of a physical
system. Each section of the computer is the analog of some particular portion
of the process under study. The variables in the analog computer are represented
by continuous signals, usually electric voltages that vary with time. (The
signal variables are considered analogous to those of the process and behave in
the same manner. The term analog signal is sometimes substituted for continuous
signal because analog computer has come to mean a computer that manipulates
continuous variables.)
To simulate a physical process in a
digital computer, the quantities must be quantized. When the variables of the
process are presented by real-time continuous signals, the latter are quantized
by an analog-to-digital conversion device. A physical system whose behavior is
described by mathematical equation is simulated in a digital computer by means
of numerical methods. When the problem to be processed is inherently discrete,
as in commercial application, the digital computer manipulates the variables in
their natural from. 
ü COMPUTER PROGRAMMING LANGUAGE
A programming language is a language
of computer programming which establishes communication between user and the
computer. It easily consists of all symbols, characters and all the rules of
using them so that it becomes easily understandable to the computer. Every
programming language contains instruction of the following types-----1) input,
output, 2) calculation/manipulation 3) logic/compression 4) storage/retrieval.
The programming language may be
broadly described into two categories à
1) Low level language
and 2) High level language.
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