Decimal to Hexadecimal

We are now going to look at Decimal to Hexadecimal converter. So let us understand what exactly a hexadecimal number and what its digits mean. So we are going to look at three digits of hexadecimal number the first unit represents units, which is 16 to the power of zero that is one. That represents units. The second digit represents tenths, which is 16 to the power of one. And the third digit represents hundredths, which is 16 to the power of two. That is nothing but 256. So important thing to do when one is working on how to convert a decimal to hexadecimal, is the start of working out how many hexadecimal number is going to have?

Let us understand it with an example, convert decimal to hexadecimal. Say number 74, here we need to decide, what we are going to and how many digits this hexadecimal number is going to have. Now because 256 is less than 74, there is any going to be two digits. So we now going to see, that in 16 to the power of one column, here we divide 74 by 16 and the result is 4. This means 4 times 16 is 64 and we have the remainder as 10. Now 10 is a single digit in a hexadecimal, simply represents a A , that tells us 74  = 4 A.

 Let us understand with a complicated example. This time it represents 680 as a hexadecimal number. Here that we see 680 is greater than 256 so we are going to have three digits in a hexadecimal number. What we going to do first is divide 680 by 256. And the result of that is 2. Two times 256 is 512, so our remainder is 168. Next we go back as what we did in our first example, we are going to divide 168 by 16. The result of this is 10. 10 times 16 equals to 160, as we are left with the remainder 8. Now we have three digits in hexadecimal number, thus we notice that we have 10, which is represented by ( A ) . This tells us that 680 when written as a hexadecimal number as 2A8. That is, 680 = 2A8. This is how we do a decimal to hexadecimal conversion. The method to do this is to keep on dividing the decimal number by 16 till it gets the most significant remainder.

Rules of Narration for Different Types of Sentences

Narration is one of the most important concepts in English grammar. While changing narration, it is very important to follow certain rules. These rules at times differ according to the types of sentences. Let’s have a look at the rules of narration for different types of sentences in this post.
Rules of Narration for Assertive Sentences:

Rule 1: If there is no object after reporting verb, then it should not be changed. For example:
• Direct Speech: He said, “I bought a play gun from Nerf India collection for my nephew.”
Indirect Speech: He said that he bought a play gun from Nerf India collection for his nephew.
Rule 2: If there is any object after the reporting verb, then say is changed to tell, ‘says’ to ‘tells’ and ‘said’ to ‘told’. For example:
• Direct Speech: She said to me, “Pre Nan Nestle Baby is healthy and nutritious for babies.”
Indirect Speech: She told me that Pre Nan Nestle is healthy and nutritious for babies.
Rule 3: ‘said’ can be replaced by replied, stated, and added and more as per the context of the assertive sentence. For example:
• Direct Speech: She said to him, “I am going to school today.”
Indirect Speech: She replied to him that she is going to school that day.
Rules of Narration for Interrogative Sentences:
Rule 1: In interrogative sentences, ‘said’ is changed to ‘asked’ while changing from direct to indirect speech. At times, ‘said’ is also changed to ‘enquired’ or related terms as per the context.
Rule 2: If the question is formed with is/are/am/was/were etc. then it is replaced by ‘if’ or ‘whether’.
Rule 3: While changing from direct to indirect speech, the question mark is removed as the reported speech is an indirect statement and not a direct question.
For example:
• Direct Speech: She said to him, “Have you bought anything from Philips Avent India brand?”
Indirect Speech: She asked to him whether he has bought anything from Philips Avent India brand.
These are some of the rules of narration that is defined as per different types of sentences.

Interjection and its types

Interjection is one of the eight parts of speech in English grammar along with noun, pronoun, verb, adverb, adjective, conjunction and preposition. Interjection is a part of speech that conveys emotions or expresses a meaning or feelings. Interjection does not add meaning to a sentence but express the feeling of the speaker. An interjection is sometimes followed by the exclamation sign i.e. “!”. For example: The kid exclaimed, “Hurrah! I got Barbie coloring pack of pens”. Here, the interjection “hurrah!” is expressing the excitement of the kid after getting Barbie coloring pack of pens. There are five different types of interjections classified based on expressions such as greetings, joy, approval, surprise and grief. Lets’ have a closer look at each of the types of interjections.

Interjections to express Greetings:
Interjections to express greetings are type of interjections that are used to wish someone. Popularly used interjections of expressing greetings are: hello, hi and so on. For example: Hello, how have you been? Here, the speaker is wishing hello and how the other person has been by using “hello”.

Interjections to express Joy:
As the term suggests, these types of interjections convey the feeling of joy and excitement of the speaker. Commonly used interjections are: hurrah, yippee, hey and more. For example: Hey! Look Farlin India collection has real good stuffs for kids. Here, the speaker is expressing his excitement at Farlin India brand’s grand collection.

Interjections to express Approval:
Interjections to express approval are used to express or congratulate on someone’s effort. Commonly used interjections of expressing approval are: bravo, wow etc. For example: Bravo! You won the match. Here, the speaker is congratulating some for winning the match.

Interjections to express Surprise:
Interjections to express surprise are used to express the emotion of surprise by the speaker. Commonly used interjections of expressing surprise are: oh, eh and so on. For example: Oh! Nuby baby brand is giving away annual sale this month. Here, the speaker is expressing his surprise at Nuby baby brand’s annual discount.

Interjections to express Grief:
Interjections to express grief as the term describes is used to express sorrow or grief by the speaker. Commonly used interjections expressing grief are: alas, ouch and more. For example: Alas! The man is dead. Here, the speaker is using “Alas” to express his grief on the man’s death.

Set Theory and Various Types of Sets

Set theory is one of the important theories in mathematics. It can help in solving of various mathematical problems. The problems can be represented in the graphical form with the help of set theory. A set is nothing but a collection of objects. There can be intersection of sets and union of sets. On performing the intersection operation the common elements of both the sets are got. The union of two sets gives all the elements present in both the sets. Basically a set can consist of various objects in it. But usually in mathematics sets usually deal with the objects which are related to mathematics.

The concept of set theory is very ancient. In the 1870’s itself good research was done on this topic and considerable progress was made. A Venn diagram is best used to represent the operations on sets. The process of intersection and union can be easily represented on the Venn diagram. There can be bigger set and a smaller which is part of it is called its subset. This can be explained with the help of an example. If a set contains the elements {1, 2, 3, 4} and there is another set which contains the elements {1, 2} then the latter set is subset of the former set. It simply means the all the elements present in the second set are also present in the first set. First set covers the whole of the second set in it.

The compliment of a set is nothing but a set containing elements which are present in the universal set but are not present in the given set. The set complement can be explained with the help of an example. If there are elements like {a, b, c, d, e} in the universal set and elements in the given set whose compliment is to be found out, are {a, c, e} then the complement set is given by { b, d}. So, the elements b, d is contained in the universal set but is not present in the set whose compliment has to be found. So, these elements are part of the required set. The compliment of a set X can be represented by the notation X’. This is a simple notation and there is another method of representing the same. Instead of the apostrophe symbol the letter ‘c’ can also be used to represent compliment.

Introduction to polygon basics

The polygon is a basically called plane figure and that is surrounded with closed path, collected of a fixed series in straight line segments with a nearer polygonal chain. And these segments are called its edges or sides. Let us discuss  the topic called polygon basics. (Source – Wikipedia)

Types of Polygon Basics

Names of polygons basics with different number of sides:

• Triangle : Triangle consists of three sides
• Quadrilateral :Quadrilateral consists of four sides
• Pentagon: Pentagon consists of five sides
• Hexagon:Hexagon consists of six sides
• Octagon:Octagon consist of eight sides.
• Nanogon : Nonagon consists of nine sides
• Decagon : Decagon consists of ten sides
• Heptagon:Heptagon consists of sevensides.
• Triskaidecagon or Tridecagon : Trikaidecagon or tridecagon consists of  thirteen sides. 

• Tetrakaidecagon or Tetradecagon : Tetrakaidecagon or tetradecagon consists of fourteen sides.
• Pendedecagon : Pendedecagon consists of fifteen sides.
• Hexdecagon: Texdecagon consists of  sixteen sides.
• Heptdecagon: Heptdecagon seventeen sides.
• Octdecagon: Octdecagon eighteen sides.
• Enneadecagon: Enneadecagon consists of nineteen sides
• Icosagon: Icosagon consists of twenty sides.
• Triacontagon : Triacontagon consists of thirty sides.
• Teracontagon: Teracontagon consists of forty sides.
• Tetracontagon: Tetracontagon consists of fifty sides.
• Pentacontagon: Tentacontagon consists of sixty sides.

 The triangle is the basic method in polygon and it has three angles. This involves three sides and three vertices.

 Triangle

Square

The octagon

The drawn diagramatic representation are the  basics form in polygon.

Problems Based on Polygon Basics

Example 1 :

Determine the side distance end to end of hexagon is 12 cm. Mention the area of the hexagon.

Solution:

            Given:

                        Side distances  (t) = 12 cm

            Formula:

                        Area of the hexagon (A) = t2 2.6

                                                = 122 x 2.6

                                                = 144 x 2.6

                                                = 374.4

Example 2:

The side distances of hexagon is 13cm. Find the area of the hexagon.

Solution:

            Given:

                        Side length (t) = 13 cm

            Formula:

                        Area of the hexagon (A) = t2 2.6

                                                = 132 x 2.6

                                                = 169 x 2.6

                                                = 439.4

              Area of the hexagon = 439.4 cm2