Binary Numbers

In the previous post we have discussed about domain math and In today's session we are going to discuss about Binary Numbers. Before discussion about the Binary Numbers first we have to know about the number system that is a basic need for presenting a number. When we talk about any number it consist some of the digits in it and these digits is decided by the number system which is used to express the number. So there are basically four types of number system as decimal , binary , octal and hexadecimal number system . When we talk about the binary number system in which binary means two , so there are only two digits for expressing a number that are zero (0) and one (1). (know more about Binary Numbers, here)
In binary number system, all the values having two digits. When we talk about any number probably it is define into the decimal number system in which number having the value from 0 to 9 and all these 10 digits are used  to make different types of number and when we want to change any decimal number into the binary number that means every single digits of the given number will be multiplied with the  exponent of two that means if there is a number xyz and we want to change it in the binary number then in x y z ,digit x has a hundred position , y has a tens position and z has a ones position and then z is multiplied with the  2 >0 and y multiplied with the 2 > 1 and x is multiplied with the 2 > 2.
 Temperature Conversion Chart is used for define the temperature in different units and also describe the relation between these units that is used for changing the temperature in one unit to another.
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domain math

In mathematics, function is used to show the relationship between values. Each input values of a function gives back exactly one output value. Now we will see how to find the domain math? Suppose that we have a function and we want to find the domain of a function then first it is necessary to know about the definition of domain in function.

If we select the entire ‘x’ coordinate values of a function, all the x – coordinate values are said to be domain of a function. In the same way, the possible ‘y’ coordinate values are said to be range of a function.

Suppose we have some values (8, -15), (-10, 1), (16, -5), (-2, 6), then the domain of function is all the ‘x’ coordinate values. (know more about domain math, here)

Domain = 8, -10, 16, 6.

Range is all ‘y’ coordinate values,

Range = -15, -10, 16, 6.

let's see some steps to find domain of a function.

To finding the domain of a function we follow some steps:

Step1: To find the domain of a function first we have to assume a function which contains ‘x’ and ‘y’ coordinates.

Step2: As we know the domain of a function is all ‘x’ coordinates values.

Step3: In a function if we have values of ‘x’ and ‘y’ coordinates then we can easily find the domain and range of a function.

If we follow these steps then we can easily find the domain of a given function. This is how we can find the domain of a function. Now we will see Taylor Series Expansion. Taylor series can be defined as a series of a function about a function. It is generally used in the approximation of a function. To get more information about Taylor series then follow online tutorial of icse syllabus. In the next session we will discuss about Binary Numbers. 

Translation Math

In the previous post we have discussed about Symbolic Logic and In today's session we are going to discuss about Translation Math. In mathematics, to move a figure or a shape from one place to another we use translation. In this a figure in a plane can be move upward and downward, right, left or anywhere. It is a function that moves every point a constant distance in a particular direction. Suppose we move one point of a shape like Triangle, Square, Line, etc up to five unit in a particular direction by translation, then all the points will move by five unit in same direction. Thus only the position of the object changes but its size remains the same.

To understand better let us translate in the following graph:

The graph on the left side is translated to the graph on the right side.

The equation of the absolute value function of left hand side graph:

y = |x|.

When the function f(x) is translated ‘p’ units horizontally, then the argument of f(x) becomes x − p.

Thus as the origin is moved to (3, 4), the new equation by its translation is:

y − 4 = |x − 3|.

Let us have a rectangular on a graph with the points P(-4, 8), Q(1, 8), R(-4, 4), S(1, 4). To shift it by four unit downward we use the following steps:

As the figure is being translated by “four” unit in downward direction, there will be no changes in x- coordinate. (know more about Translation Math, here)

1. subtract by 4 in y coordinate, we get

P(-4, 8) after translation (x - 0, y – 4),

=> (-4 - 0, 8 – 5),

• (-4, 3)

2. For Q(1, 8) after translation, we get (x - 0, y - 4)

• (1 - 0, 8 - 5)
• (1, 3) translated coordinate.

3. For R(-4, 4) so, after translation (x - 0, y - 4)

=> (-4 - 0, 4 - 4)

=> (-4, 0) translated coordinate.

4. For S(1, 4), after translation,we get (x - 0, y - 4)

=> (1 - 0, 4 - 4)

=>(1, 0) translated coordinate.

So, translated figure coordinates will be points P(-4, 3), Q(1, 3), R(-4, 0), S(1, 0).

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Symbolic Logic

Hi friends, in this blog we are discussing an important topic that is 'Symbolic Logic'. Symbolic Logic is a method that is used to distinguish logical expressions using symbols and variables, relatively than in ordinary language. Symbolic logic is used in removing the uncertainty. In mathematical field, so many systems of symbolic logic are mention below:
(1.) Classical propositional logic,
(2.) First-order logic,
(3.) Modal logic.
In mathematics, all the symbolic logic are divided by different symbols, or exclude the use of certain symbols. Let's see some of the symbolic logic symbols. Here we will see the basic logic symbols.
(1.) (┑): - This given symbol is known as negation.
Explanation: Let we have a statement ┑A that is true if and only if the value of 'A' is given as false.
= ┑ (┑A) ⇔ A.
(2.) (∨): - This given symbol is known as logical disjunction.
Explanation: The statement A ∨ B is true if and only if the value of 'A' and 'B' both are true, or if both are false.
(3.) (⊕): - This symbol is known as exclusive disjunction.
Explanation: let we have a given statement A ⊕ B then the condition is true if value of 'A' and
'B' are true but not both the value true.
(4.) (T): - This symbol is known as Tautology.
Explanation: Here the meaning of this symbol is A ⇒ B is always true.
(5.) (∃): - This symbol is known as existential quantification.
Explanation: let we have a given statement ∃ x A (x), it means there is at least one x such that A (x) is true.
(6.) (∃!): - This symbol is known as uniqueness quantification.
Explanation: let we have a given statement ∃! x A (x), it means there is exactly one x such that A (x) is true. Solving Differential Equations is a part of trigonometry. It includes application of derivative. To get more information then we need to follow icse syllabus 2013. It helps so much for solving the differential equation.

How to Tackle Recursion

In the previous post we have discussed about How to Define Complements in Mathematics and In today's session we are going to discuss about how to Tackle Recursion. The term recursion is generally used in many subjects including the subject of the math. Many of us do not exactly know the meaning of this term in the context of the math. So in this article we will have a look on some of the important facts of the term recursion. (know more about Radical, here)

Now let us start with the definition of the term recursion. It is a method in which we repeat the items in a way which is self similar. It should be noticed that in a situation where the surfaces of any 2 mirrors are completely parallel to each other then the nested type of the images which we see can be said to be the form of an infinite type of the recursion. This term can give different types of the meanings especially to the varieties of the disciplines which range from the linguistics to the logic.
We will now discuss about some of the uses of the recursion. One of its very common uses in the field of the mathematics is the one where it is being referred to a process in which we define the functions where the function which is defined is being applied within the definition of its own.   
Particularly it can be used to define almost infinite no. of the instances that is the values of the function with the help of an expression which is finite which for some of the instances may be referred to other of the instances but in that way where any loop or a chain which is infinite cannot occur. However the term recursion is also utilized very commonly to explain any process of the objects which are repeating in a way which is self similar.
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How to Define Complements in Mathematics

In the previous post we have discussed about How to Read Binary and In today's session we are going to discuss about Complements, the word Complements can be refered as a concept that perform there different task in various field of mathematics. In a simple mean we can say that complement is a amount which can be added to something of same kind to generate its whole. The definition of Complement varies according to the different fields of mathematics.
In the geometrical mathematics the word Complements can be express as angle of 90 degree which is formed by adding two different angles. In geometry, one angle said to be complement for the other angle to make a whole angle. Suppose the measure of one angle is 35 degree and the measure of other is 55 degree then merge up of these angles form a 90 degree angle that can be consider as a whole angle.
In the same aspect of set theory, the word  Complements can be define as a inverse of any set. As we know that a set is a collection of elements that are also exists in universal set. In the same aspect the concept of complement for a set S can be define as a set of all elements that are not exists in the set A. Suppose there is a set B, so the Complements of B contains all the elements that are exists in universal set U but do not contain by set B. In the mathematical notation complement of set can be express as below given format:
Complement of B = (B)'
Suppose the set B = (1, 2, 3 ) And Universal set U contains (a, b, c, 1, 2, 3) then 
Complements of set B can be represented as in below given format:
B' = (a, b, c)
when we add both set then it make whole set which can be called as universal set. It means to say that set B + Set B' = U set.
In mathematics Green s Theorem set a relation among double integral over a plane of region D and Line integral of simple closed curve. Cbse stands for central board of secondary education which conducts the board exam for students of grade 10th and 12th. To help the students cbse provide cbse imp questions that provide the list of all imp questions that have highest possibility to come in examination.

How to Read Binary

In the previous post we have discussed about How Online Matrix Calculator and In today's session we are going to discuss about How to Read Binary. Decimal Numbers are the numbers which include 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 . We do all our mathematical processing in the form of decimal numbers. Binary numbers are the numbers which can be expressed in the form of 1 and 0 only. The data stored in the computers, calculators, chip is all in the form of digits and so it is in the form of binary codes.  These Binary numbers can be converted in the form of decimal numbers. Here we are going to learn about How To Read Binary.
Let us take the example of the binary number say 1 0 0 1. To convert the given binary number, we will start reading the data from the right hand side and place the numbers with base 2 and power 0 at the first place. The power goes on increasing by 1as we move from right to the left. SO the first digit will be 2 >0 = 1, followed by 2 >1 = 2, then we proceed as follows:
2>2 = 2 * 2 = 4
2>3 = 2 * 2 * 2  = 8
2> 4 = 2 * 2* 2 * 2  = 16
Thus the series appears as follows: 1, 2, 4, 8, 16 , 32 . . . .. .. which will be written along with the binary digits starting by right as follows
 8      4        2       1
1       0        0       1
Now we write 1 * 8 +  4 * 0 + 2 * 0 + 1 *1 = 8 + 0 + 0 + 1 = 9, which is the decimal number. (know more about Binary, here)


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