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Usage Of Scientfic Calculators For Matrix Multiplication

8:32 AM sdsd

Scientific Calculators are one of the basic instruments needed for an Engineer in his career.In most of the colleges the scientific calculator prescribed will be CASIO fx-991 MS.So in this article I have written the usage of scientific calculator for the purpose of matrix multiplication.



Eventhough the usage of scientific calculator is given in the user manual this article may give you some visualisation of the application that it has on Engineering Mathematics-I.



Consider the 3x3 matrix:

|1   3   5|
|3   7   9|
|4   6   2| 
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An Introduction To Algorithms

8:42 AM sdsd

ALGORITHMS
INTRODUCTION

Algorithms are one of the most basic tools that are used to develop the problem the problem solving logic.


“An algorithm is defined as finite sequence of explicit instructions that, when provided with a set of input values produces an output and then terminates.”


In algorithm, after a finite number of steps, a solution of the problem is achieved. Algorithm can have steps that repeat (iterate) or require decisions (logic and comparison) until task is completed.


Different algorithms may accomplish the same task, with a different set of instructions, in more or less the same time, space and efforts.


CHARACTERISTICS OF ALGORITHMS

Algorithms are not computer programs, as they cannot be executed by a computer


In order to qualify as a good algorithm, it must posses he following characteristics:


1. Each and every instruction in an algorithm should be precise and unambiguous.

2. The instruction in an algorithm should not be repeated infinitely.

3. It should ultimately terminate.

4. Algorithms are written in sequence.

5. Algorithms look like normal English.

6. The desired result should be obtained only after the algorithm terminates.

QUALITIES OF A GOOD ALGORITHM

There are so many methods are logics available to solve the problem individually. All of those methods and logics may be good, for given problem there may be so many algorithms not of all equality.


The following are the primary factors that are often used to judge the quality of algorithms:


S.No.
Factors
Quality of good Algorithm
1.
Time
To execute a program, the computer system
takes some amount of time. The lesser the time
taken, the better the algorithm is.
2.
Memory
To execute a program, computer system takes
some amount of memory storage. The lesser the
memory required the better the algorithm is.
3.
Accuracy
Multiple algorithms may provide suitable or
correct solutions to a given problem, some of
these may provide more accurate results than
others, and such algorithms may be suitable.
4.
Sequence
The procedure of an algorithm must be in a
sequence and some of the instructions of an
algorithm may be repeated number of times
until a particular condition is met.
5.
General
Ability

The designed algorithm solves a single isolated
problem and more often algorithms are designed
to handle a range of input data to meet these
criteria, so the algorithms must be generalized.



REPRESENTATION OF ALGORITHMS


The algorithms can be represented in several ways. Generally the programmer follows one of the following ways to represent algorithms.

i. Normal English
ii. Flowchart
iii. Pseudocode
iv. Decision table
v. Program

1.
Normal English
The Algorithms can be easily represented in step
by step sequential order in normal English, such
algorithms are easy to understand, write and read.
2.
Flowchart
The flowchart is a pictorial representation of an
algorithm i.e. the sequential steps in an algorithm
can be represented as flowchart using the standard
symbols.
3.
Pseudocode
Pseudocode is also a formal decision tool utilized
very well with the rules of structured design and
programming.
4.
Decision Table
A decision table helps a lot in designing a specific
segment of a design.
5.
Program
The algorithms can be represented as a program
using any high level language that becomes a
program.



HOW TO MAKE AN ALGORITHM

Now let’s get into the process of making algorithm. Let’s start with simple algorithms. Different algorithms may produce the same desired result. For example in an algorithm to find the circumference of the circle the circumference could be found out either by multiplying 2 with π and radius or only π with diameter. However, performing an algorithm correctly does not guarantee a solution, if the algorithm is flawed or not appropriate to the context. For example, this algorithm fails if radius is not present.

Example 1: Algorithm to find the area and circumference of the Circle.

Step 1: Start

Step 2: Read the radius

Step 3:Find the area and the circumference of the circle using the formula
             area<--3.14*r*r
             circumference<--2*3.14*r

Step 4:Print the area and circumference of the circle

Step 5: Stop

Example 2: Algorithm to find the largest of three numbers A, B and C.

Step 1: Start

Step 2: Read three numbers say A,B,C.Find the larger number between A and B
             and store it in MAX_AB.

Step 4: Find the larger number between MAX_AB and C and store it in MAX

Step 5:Display MAX

Step 6: Stop
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How to Convert A Binary Number To Decimal Number

11:55 PM sdsd

The Decimal number system consists has ten values ranging from 0 to 9.The Binary system consists of only two values 0 and 1.
Number conversions are very useful for Engineering, especially during first semester. This article is very useful to help students convert Binary Numbers to Decimal Numbers.It is preferred that engineering students also learn How to Decimal Numbers to Binary Numbers.

In order to differentiate decimal numbers with binary numbers Base values of 10 and 2 are given in subscripts such as Binary numbers are represented as 100111(2) (read as 100111 to the base 2)and decimal numbers are represented as 39(10) (read as 39 to the base 10).To convert binary numbers to decimal numbers just follow these simple steps:
Let us consider a binary number 100111(2).In Order to convert it to decimal number
  1. Identify the position of each value of the given Binary value
  2. Write down the Given Values below the respective positions
  3. Multiply the binary values with the respective weights.
  4. The weight of first position is 2 raised to power (position-1)
  5. For example the weight of second position is 2(2-1)=21.
  6. Then just multiply the Binary value with the weights.
  7. Then add all the final values to get the decimal equivalent of the binary number.
6th5th4th3rd2nd1stPosition
100111Given Binary value
X25X24X23X22X21X20Weights
1X32+0X16+0X8+1X4+1X2 +1X1.
32+0+0+4+2+1=39(10)

Therefore the decimal equivalent of 100111(2) =39(10).
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