what is numeric representation

Numerals – Definition, Numeral Systems, Facts,  Examples, FAQs

What are numerals, numbers vs. numerals, what are different numeral systems, solved examples on numerals, practice problems on numerals, frequently asked questions about numerals.

Numerals are symbols or signs (or collection of symbols) used to represent numbers corresponding to numerical quantities, values, or measurements.  

Numerals often come together with a set of rules for representing larger numbers. They provide a concise and standardized way to express numerical quantities. 

Numerals help us communicate numeric values or numerical quantities effectively. In math, a number conveys a quantity. You can say that a number offers an answer to the question “how many things are there?.” A numeral helps us to write it down.

Example 1: If you have 3 apples, you can use different numerals to represent this quantity.

• Number: 3 
• Number name: Three 
• Roman numeral: III
• Symbol/Sign (using dots):  ●●●

Example 2: Take a look at the image given below. What do you see?

This image shows two cups, two soccer balls, and two ice cream cones. Here, “two” indicates a quantity. We can represent this quantity using different numerals, such as 

• Word form: Two
• Roman numerals: II 
• Using dots: ●●

So, each of these is a numeral representing the quantity “two.”  

Numerals: Definition

A numeral is a symbol or a sign that stands for a number. A numeral can be defined as a representation of a number, which can be in the form of a figure, symbol, name, or a combination of figures and symbols.

Example : Seven, VII, ७, etc. are all symbols or signs we use to indicate the number “7.” 

Each one of them is a numeral.  

Related Worksheets

The terms “numbers” and “numerals” can be confusing. The concept of a number is distinct from its written representation, which is the numeral. Let’s understand the difference.

A numeral system is a way to represent numbers. Numeral systems, also known as number systems, indeed consist of symbols and rules for representing numbers and quantities. They play a crucial role in mathematics and are used to express numerical values in a standardized and systematic manner.

There are many ways to represent a number with the help of symbols in math. In other words, we can represent a number using more than one numeral.

Note that many numeral systems have evolved across various regions and cultures, each serving a distinct purpose. Let’s discuss a few.

• Arabic numerals or Indo-Arabic numerals (Hindu-Arabic numerals):

Arabic numerals, also known as Indo-Arabic or Hindu-Arabic numerals, are the ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) we commonly use in our number system. The decimal number system is the extension of the Indo-Arabic numeral system.

• Roman numerals:  

Roman numerals are a numeral system originating from ancient Rome, characterized by the use of letters from the Latin alphabet to represent numbers. Roman numerals are still used today in specific contexts, such as numbering book chapters or indicating the date on clock faces.

I (1), II (2), V (5), X (10), L (50), C (100), D (500), M (1000), etc.

• Binary numerals:  

Binary numerals, often referred to as base-2 numerals, are a numeral system that uses only two digits: 0 and 1. It is widely used in computer systems.

• Octal numerals: 

Octal numerals, a base-8 numeral system, use eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. 

• Chinese numerals:

Chinese numerals, also known as Han numerals, are used in the Chinese writing system to represent numbers. 

$\bigcirc$ (0), 一 (1), 二 (2), 三 (3), 四 (4), 五 (5), 六 (6), 七 (7), 八 (8), 九 (9), 十 (10)

• Number names or Word form : 
• Devanagari numerals: 

Devanagari numerals are the numeric symbols used in the Devanagari script, primarily in the Indian subcontinent. They are the scripts used for languages like Sanskrit, Hindi, Marathi, and Nepali.

• Tally marks : 

Tally marks are a simple system of counting and recording numbers using vertical lines or strokes, in sets of 5. Each group of five tally marks is typically represented by four vertical lines, with the fifth line being drawn diagonally across the previous four. 

What Is the Decimal Numeral System?

The decimal numeral system is the most commonly used number system. This system is also known as the base-10 positional numeral system since it used 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to form all the numbers. It is derived from the Indo-Arabic numeral system.

Decimal numerals (often called simply as decimals refers to the notation of a number. In this system, the integer portion and the decimal portion of a numeral are separated using a decimal point. 

• What Are Place Values?

Place value refers to the value of a digit in a number by the virtue of the position in the number. The place values of digits in the decimal system are represented using the powers of 10. In decimal numbers, the whole number part and the fractional part is separated by the decimal point.

In the international place value chart, there are three periods for the nine places from right to left. Each period has three place values.

Facts about Numerals

• Numerals are symbols used to represent numbers. Different numeral systems are used worldwide, reflecting cultural and historical diversity.
• The Roman numeral system indeed did not have a symbol for zero.
• The ancient Egyptians made significant contributions to the development of numerals and mathematical systems.
• The earliest numerals used by humans were simple scratches on a rock or stone, notches on a stick, etc.

In this article, we learned about numerals. We explored a few commonly known numeral systems as well. To deepen our understanding, let’s dive into practical examples and MCQs for enhanced comprehension.

Example 1: What is the word form for 42?   

Solution : 

The word form for the number 42 is “Forty Two.” 

Example 2: How many candies are there in the bowl? Represent the numerical quantity using different numerals.    

There are 9 candies in the bowl.

Example 3: What is the time shown in the given analog clock?

The hour hand points exactly to V, which is the roman numeral for 5. 

The minute hand points exactly to XII, which is the roman numeral for 12.

So, the clock reads 5 o’clock.   

Numerals - Definition, Numeral Systems, Facts,  Examples, FAQs

Attend this quiz & Test your knowledge.

What is the roman numeral for 4?

Which of the following is not a numeral for 1, in the decimal numeral system, the base is ____., identify the numeral of 7..

What are digits in math?

A digit is a single numerical symbol used to represent numbers. A number is a mathematical concept or idea used to represent a quantity.

What is the difference between a numeral and a digit?

A numeral is a symbol or group of symbols used to represent a number, either using digits, words, other signs and symbols, etc.

What is the difference between digits, numbers, and numerals?

Number is expressed with digits, while a numeral is how we describe a number.

What is the place value of a digit?

The place value of a digit indicates its position in a number. For example, in 36, the place value of 3 is 30, while that of 6 is 6.

Are all numeral systems based on place values?

No, all numeral systems are not based on place values. For instance, the Roman numeral system is not based on place values.

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Number System

The number system or the numeral system is the system of naming or representing numbers. We know that a number is a mathematical value that helps to count or measure objects and it helps in performing various mathematical calculations. There are different types of number systems in Maths like decimal number system, binary number system, octal number system, and hexadecimal number system. In this article, we are going to learn what is a number system in Maths, different types, and conversion procedures with many number system examples in detail .  Also, check mathematics for grade 12 here.

What is Number System in Maths?

A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner. It provides a unique representation of every number and represents the arithmetic and algebraic structure of the figures. It also allows us to operate arithmetic operations like addition, subtraction, multiplication and division.

The value of any digit in a number can be determined by:

• Its position in the number
• The base of the number system

Before discussing the different types of number system examples, first, let us discuss what is a number?

What is a Number?

A number is a mathematical value used for counting or measuring or labelling objects. Numbers are used to performing arithmetic calculations.  Examples of numbers are natural numbers, whole numbers, rational and irrational numbers, etc. 0 is also a number that represents a null value. 

A number has many other variations such as even and odd numbers, prime and composite numbers. Even and odd terms are used when a number is divisible by 2 or not, whereas prime and composite differentiate between the numbers that have only two factors and more than two factors, respectively.

In a number system, these numbers are used as digits. 0 and 1 are the most common digits in the number system, that are used to represent binary numbers. On the other hand, 0 to 9 digits are also used for other number systems. Let us learn here the types of number systems.

Types of Number Systems

There are various types of number systems in mathematics. The four most common number system types are:

• Decimal number system (Base- 10)
• Binary number system (Base- 2)
• Octal number system (Base-8)
• Hexadecimal number system (Base- 16)

Now, let us discuss the different types of number systems with examples.

Decimal Number System (Base 10 Number System)

The decimal number system has a base of 10 because it uses ten digits from 0 to 9. In the decimal number system, the positions successive to the left of the decimal point represent units, tens, hundreds, thousands and so on. This system is expressed in decimal numbers . Every position shows a particular power of the base (10).

Example of Decimal Number System:

The decimal number 1457 consists of the digit 7 in the units position, 5 in the tens place, 4 in the hundreds position, and 1 in the thousands place whose value can be written as:

(1×10 3 ) + (4×10 2 ) + (5×10 1 ) + (7×10 0 )

(1×1000) + (4×100) + (5×10) + (7×1)

1000 + 400 + 50 + 7

Binary Number System (Base 2 Number System)

The base 2 number system is also known as the Binary number system wherein, only two binary digits exist, i.e., 0 and 1. Specifically, the usual base-2 is a radix of 2. The figures described under this system are known as binary numbers which are the combination of 0 and 1. For example, 110101 is a binary number.

We can convert any system into binary and vice versa.

Write (14) 10 as a binary number.

Base 2 Number System Example

∴ (14) 10 = 1110 2

Octal Number System (Base 8 Number System)

In the octal number system , the base is 8 and it uses numbers from 0 to 7 to represent numbers. Octal numbers are commonly used in computer applications. Converting an octal number to decimal is the same as decimal conversion and is explained below using an example.

Example: Convert 215 8 into decimal.

215 8 = 2 × 8 2 + 1 × 8 1 + 5 × 8 0

= 2 × 64 + 1 × 8 + 5 × 1

= 128 + 8 + 5

Hexadecimal Number System (Base 16 Number System)

In the hexadecimal system, numbers are written or represented with base 16. In the hexadecimal system, the numbers are first represented just like in the decimal system, i.e. from 0 to 9. Then, the numbers are represented using the alphabet from A to F. The below-given table shows the representation of numbers in the hexadecimal number system .

Number System Chart

In the number system chart, the base values and the digits of different number systems can be found. Below is the chart of the numeral system.

Number System Conversion

Numbers can be represented in any of the number system categories like binary, decimal, hexadecimal, etc. Also, any number which is represented in any of the number system types can be easily converted to another. Check the detailed lesson on the conversions of number systems to learn how to convert numbers in decimal to binary and vice versa, hexadecimal to binary and vice versa, and octal to binary and vice versa using various examples.

With the help of the different conversion procedures explained above, now let us discuss in brief about the conversion of one number system to the other number system by taking a random number.

Assume the number 349. Thus, the number 349 in different number systems is as follows:

The number 349 in the binary number system is 101011101

The number 349 in the decimal number system is 349.

The number 349 in the octal number system is 535.

The number 349 in the hexadecimal number system is 15D

Number System Solved Examples

Convert (1056) 16 to an octal number.

Given, 1056 16 is a hex number.

First we need to convert the given hexadecimal number into decimal number

= 1 × 16 3 + 0 × 16 2 + 5 × 16 1 + 6 × 16 0

= 4096 + 0 + 80 + 6

= (4182) 10

Now we will convert this decimal number to the required octal number by repetitively dividing by 8.

Therefore, taking the value of the remainder from bottom to top, we get;

(4182) 10 = (10126) 8

Therefore, 

(1056) 16 = (10126) 8

Convert (1001001100) 2 to a decimal number.

(1001001100) 2

= 1 × 2 9 + 0 × 2 8 + 0 × 2 7 + 1 × 2 6 + 0 × 2 5 + 0 × 2 4 + 1 × 2 3 + 1 × 2 2 + 0 × 2 1 + 0 × 2 0

= 512 + 64 + 8 + 4

Convert 10101 2 into an octal number.

 10101 2 is the binary number

We can write the given binary number as,

Now as we know, in the octal number system,

Therefore, the required octal number is (25) 8

Convert hexadecimal 2C to decimal number.

We need to convert 2C 16  into binary numbers first.

2C → 00101100

Now convert 00101100 2 into a decimal number.

101100 = 1 × 2 5  + 0 × 2 4 + 1 × 2 3  + 1 × 2 2  + 0 × 2 1 + 0 × 2 0

= 32 + 8 + 4

Video Lesson on Numeral System

Number System Questions

• Convert (242) 10 into hexadecimal. [ Answer: (F2) 16 ]
• Convert 0.52 into an octal number. [ Answer: 4121]
• Subtract 1101 2 and 1010 2 . [ Answer: 0010]
• Represent 5C6 in decimal. [ Answer:  1478]
• Represent binary number 1.1 in decimal. [ Answer: 1.5]

Also Check: Binary Operations

Computer Numeral System (Number System in Computers)

When we type any letter or word, the computer translates them into numbers since computers can understand only numbers. A computer can understand only a few symbols called digits and these symbols describe different values depending on the position they hold in the number. In general, the binary number system is used in computers. However, the octal, decimal and hexadecimal systems are also used sometimes.

More Topics Related to Number Systems

Frequently asked questions on number system, what is number system and its types.

The number system is simply a system to represent or express numbers. There are various types of number systems and the most commonly used ones are decimal number system, binary number system, octal number system, and hexadecimal number system.

Why is the Number System Important?

The number system helps to represent numbers in a small symbol set. Computers, in general, use binary numbers 0 and 1 to keep the calculations simple and to keep the amount of necessary circuitry less, which results in the least amount of space, energy consumption and cost.

What is Base 1 Number System Called?

The base 1 number system is called the unary numeral system and is the simplest numeral system to represent natural numbers.

What is the equivalent binary number for the decimal number 43?

How to convert 30 8 into a decimal number.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

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Number Systems

Number systems are systems in mathematics that are used to express numbers in various forms and are understood by computers. A number is a mathematical value used for counting and measuring objects, and for performing arithmetic calculations. Numbers have various categories like natural numbers, whole numbers, rational and irrational numbers, and so on. Similarly, there are various types of number systems that have different properties, like the binary number system, the octal number system, the decimal number system, and the hexadecimal number system.

In this article, we will explore different types of number systems that we use such as the binary number system, the octal number system, the decimal number system, and the hexadecimal number system. We will learn the conversions between these number systems and solve examples for a better understanding of the concept.

What are Number Systems?

A number system is a system representing numbers. It is also called the system of numeration and it defines a set of values to represent a quantity. These numbers are used as digits and the most common ones are 0 and 1, that are used to represent binary numbers. Digits from 0 to 9 are used to represent other types of number systems.

Number Systems Definition

A number system is defined as the representation of numbers by using digits or other symbols in a consistent manner. The value of any digit in a number can be determined by a digit, its position in the number, and the base of the number system. The numbers are represented in a unique manner and allow us to operate arithmetic operations like addition, subtraction, and division.

Types of Number Systems

There are different types of number systems in which the four main types are as follows.

• Binary number system (Base - 2)
• Octal number system (Base - 8)
• Decimal number system (Base - 10)
• Hexadecimal number system (Base - 16)

We will study each of these systems one by one in detail after going through the following number system chart.

Number System Chart

Given below is a chart of the main four types of number system that we use to represent numbers.

Binary Number System

The binary number system uses only two digits: 0 and 1. The numbers in this system have a base of 2. Digits 0 and 1 are called bits and 8 bits together make a byte. The data in computers is stored in terms of bits and bytes. The binary number system does not deal with other numbers such as 2,3,4,5 and so on. For example: 10001 2 , 111101 2 , 1010101 2 are some examples of numbers in the binary number system.

Octal Number System

The octal number system uses eight digits: 0,1,2,3,4,5,6 and 7 with the base of 8. The advantage of this system is that it has lesser digits when compared to several other systems, hence, there would be fewer computational errors. Digits like 8 and 9 are not included in the octal number system. Just like the binary, the octal number system is used in minicomputers but with digits from 0 to 7. For example, 35 8 , 23 8 , and 141 8 are some examples of numbers in the octal number system.

Decimal Number System

The decimal number system uses ten digits: 0,1,2,3,4,5,6,7,8 and 9 with the base number as 10. The decimal number system is the system that we generally use to represent numbers in real life. If any number is represented without a base, it means that its base is 10. For example, 723 10 , 32 10 , and 4257 10 are some examples of numbers in the decimal number system.

Hexadecimal Number System

The hexadecimal number system uses sixteen digits/alphabets: 0,1,2,3,4,5,6,7,8,9 and A,B,C,D,E,F with the base number as 16. Here, A-F of the hexadecimal system means the numbers 10-15 of the decimal number system respectively. This system is used in computers to reduce the large-sized strings of the binary system. For example, 7B3 16 , 6F 16 , and 4B2A 16 are some examples of numbers in the hexadecimal number system.

Conversion of Number Systems

A number can be converted from one number system to another number system using number system formulas. Like binary numbers can be converted to octal numbers and vice versa, octal numbers can be converted to decimal numbers and vice versa, and so on. Let us see the steps required in converting number systems.

Steps for Conversion of Binary to Decimal Number System

To convert a number from the binary to the decimal system, we use the following steps.

• Step 1: Multiply each digit of the given number, starting from the rightmost digit, with the exponents of the base.
• Step 2: The exponents should start with 0 and increase by 1 every time we move from right to left.
• Step 3: Simplify each of the above products and add them.

Let us understand the steps with the help of the following example in which we need to convert a number from binary to decimal number system.

Example: Convert 100111 2 into the decimal system.

Step 1: Identify the base of the given number. Here, the base of 100111 2 is 2.

Step 2: Multiply each digit of the given number, starting from the rightmost digit, with the exponents of the base. The exponents should start with 0 and increase by 1 every time as we move from right to left. Since the base is 2 here, we multiply the digits of the given number by 2 0 , 2 1 , 2 2 , and so on from right to left.

Step 3: We just simplify each of the above products and add them.

Here, the sum is the equivalent number in the decimal number system of the given number. Or, we can use the following steps to make this process simplified.

100111 = (1 × 2 5 ) + (0 × 2 4 ) + (0 × 2 3 ) + (1 × 2 2 ) + (1 × 2 1 ) + (1 × 2 0 )

= (1 × 32) + (0 × 16) + (0 × 8) + (1 × 4) + (1 × 2) + (1 × 1)

= 32 + 0 + 0 + 4 + 2 + 1

Thus, 100111 2 = 39 10 .

Conversion of Decimal Number System to Binary / Octal / Hexadecimal Number System

To convert a number from the decimal number system to a binary/octal/hexadecimal number system, we use the following steps. The steps are shown on how to convert a number from the decimal system to the octal system.

Example: Convert 4320 10 into the octal system.

Step 1: Identify the base of the required number. Since we have to convert the given number into the octal system, the base of the required number is 8.

Step 2: Divide the given number by the base of the required number and note down the quotient and the remainder in the quotient-remainder form. Repeat this process (dividing the quotient again by the base) until we get the quotient less than the base.

Step 3: The given number in the octal number system is obtained just by reading all the remainders and the last quotient from bottom to top.

Therefore, 4320 10 = 10340 8

Conversion from One Number System to Another Number System

To convert a number from one of the binary/octal/hexadecimal systems to one of the other systems, we first convert it into the decimal system, and then we convert it to the required systems by using the above-mentioned processes.

Example: Convert 1010111100 2 to the hexadecimal system.

Step 1: Convert this number to the decimal number system as explained in the above process.

Thus, 1010111100 2 = 700 10 → (1)

Step 2: Convert the above number (which is in the decimal system), into the required number system (hexadecimal).

Here, we have to convert 700 10 into the hexadecimal system using the above-mentioned process. It should be noted that in the hexadecimal system, the numbers 11 and 12 are written as B and C respectively.

Thus, 700 10 = 2BC 16 → (2)

From the equations (1) and (2), 1010111100 2 = 2BC 16

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Number Systems Examples

Example 1: Convert 300 10 into the binary number system with base 2.

Solution: 300 10 is in the decimal system. We divide 300 by 2 and note down the quotient and the remainder. We will repeat this process for every quotient until we get a quotient that is less than 2.

The equivalent number in the binary system is obtained by reading all the remainders and just the last quotient from bottom to top as shown above.

Thus, 300 10 = 100101100 2

Example 2: Convert 5BC 16 into the decimal system.

Solution: 5BC 16 is in the hexadecimal system. We know that B = 11 and C = 12 in the hexadecimal system. So we get the equivalent number in the decimal system using the following process:

Thus, 5BC 16 = 1468 10

Example 3: Convert 144 8 into the hexadecimal system.

Solution: The base of 144 8 is 8. First, we will convert this number into the decimal system as follows:

Thus, 144 8 = 100 10 → (1). Now we will convert this into the hexadecimal system as follows:

Thus, 100 10 = 64 16 → (2)

From the equations (1) and (2), we can conclude that: 144 8 = 64 16

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Practice Questions on Number Systems

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FAQs on Number Systems

What are number systems with examples.

A number system is a system of writing or expressing numbers. In mathematics, numbers are represented in a given set by using digits or symbols in a certain manner. Every number has a unique representation of its own and numbers can be represented in the arithmetic and algebraic structure as well. There are different types of number systems that have different properties, like the binary number system, the octal number system, the decimal number system, and the hexadecimal number system. Some examples of numbers in different number systems are 10010 2 , 234 8 , 428 10 , and 4BA 16 .

What are the Different Types of Number Systems?

There are four main types of number systems:

What are the Conversion Rules of Number Systems?

To convert a number from binary/octal/hexadecimal system to a decimal number system, we use the following steps:

• Multiply each digit of the given number, starting from the rightmost digit, with the exponents of the base.
• The exponents should start with 0 and increase by 1 every time we move from right to left.
• Simplify each of the above products and add them.

To convert a number from decimal system to binary/octal/hexadecimal system, we use the following steps:

• Divide the given number by the base of the required number and note down the quotient and the remainder in the “quotient-remainder” form.
• Repeat this process (dividing the quotient again by the base) until we get the quotient less than the base.
• The given number in the decimal number system is obtained just by reading all the remainders and the last quotient from bottom to top.

To convert a number from one of the binary/octal/hexadecimal systems to one of the other systems:

• We first convert it into the decimal system.
• Then we convert it to the required system.

What are the Uses of Each Number System?

There are different purposes of each number system, such as:

• The binary number system is used to store the data in computers.
• The advantage of the octal number system is that it has fewer digits when compared to several other systems, hence, there would be fewer computational errors.
• The decimal number system is the system that we use in daily life.
• The hexadecimal number system is used in computers to reduce the large-sized strings of the binary system.

What is the Importance of Number Systems?

Number systems help in representing the numbers in a small symbol set. Binary numbers are mostly used in computers that use digits like 0 and 1 for calculating simple problems. The number systems also help in converting one number system to another.

How are Number Systems Classified?

The number systems can be classified mainly into two categories: Positional and Non-positional number systems. For positional number systems, each digit is associated with a weight and its examples are binary, octal, decimal, etc. In non-positional number systems, the digit values are independent of their positions and its examples are gray code, cyclic code, aroma code, etc.

Why are Different Number Systems Used in Computers?

Computers cannot understand human languages, so to understand the commands and instructions given to the computers by programmers, different number systems are used such as the binary system, the octal system, the decimal system, and so on.

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• 4.1: Introduction
• 4.2: Hindu-Arabic Positional System
• 4.3: Early Numeration Systems
• 4.4: Converting with Base Systems
• 4.5: Addition and Subtraction in Base Systems
• 4.6: Multiplication and Division in Base Systems
• 4.7.1: Key Terms
• 4.7.2: Key Concepts
• 4.7.3: Videos
• 4.7.4: Projects
• 4.7.5: Chapter Review
• 4.7.6: Chapter Test

• School Guide
• Mathematics
• Number System and Arithmetic
• Trigonometry
• Probability
• Mensuration
• Maths Formulas
• Class 8 Maths Notes
• Class 9 Maths Notes
• Class 10 Maths Notes
• Class 11 Maths Notes
• Class 12 Maths Notes

Octal Number System

• Binary Number System
• Number System in Maths
• What is a number system?
• Hexadecimal Number System
• Number System Conversion in C
• Stella Octangula Number
• Number System in Python
• Octagonal number
• Octahedral Number
• Octal numbers in c
• Decimal Number System
• Octacontagon Number
• Pentatope number
• Octadecagonal Number
• Basic Concept Of Number System
• Classification of Number System
• Number System: Cyclicity of Numbers
• Telephone Number
• Centered Octagonal Number

Octal Number System is a number system with base 8 as it uses eight symbols (or digits) namely 0, 1, 2, 3, 4, 5, 6, and 7. For example, 22 8 , 13 8 , 17 8, etc. are octal numbers. This number system is mainly used in computer programming as it is a compact way of representing binary numbers with each octal number corresponding to three binary digits.

In this article, we will discuss Octal Numbers System, Octal Number System Conversions, Octal Number System Examples, and Others in detail.

Table of Content

Octal Number System Definition

Octal to decimal numbers, octal to hexadecimal number, octal to binary number, octal multiplication table, what are number systems.

A number system is a method of expressing numbers. It contains sets of symbols (or digits) combined with a set of rules to represent a particular quantity. The number system is mainly classified into four types:

• Decimal number system (with base 10 and symbols ranging between 0-9)
• Binary Number system (with base 2 and symbols 0 and 1)
• Hexadecimal number system (with base 16 and symbols raging between 0-9 and from A to F )
• Octal Number system (with base 8 and symbols ranging between 0-7)

‘OCTAL’ is derived from the Latin word ‘OCT’ which means Eight. The number system with base 8 and symbols ranging between 0-7 is known as the Octal Number System. Each digit of an octal number represents a power of 8. It is widely used in computer programming and digital systems. Octal number system can be converted to other number systems and visa versa.

For example, an octal number (10) 8 is equivalent to 8 in the decimal number system, 001000 in the binary number system and 8 in the hexadecimal number system.

Octal Numbers System Table

The table added below, shows the Octal Number and Decimal Number. 3 bits of Binary Number System is equivalent to one octal numbers.

Now, we will learn about the conversion of octal number system to other number systems one by one. So let’s get started.

A decimal number system has a base 10 consisting of digits 0-9. We can easily convert an octal number to a decimal number by following these simple steps:

• Step 1: Write the octal number.
• Step 2: Multiply each digit of the given octal number with an increasing power of 8 starting from the rightmost digit.
• Step 3: Sum all the products obtained in step 2.

Example: Represent 123 8 as a Decimal Number.

123 8 = 1 × 8 2 + 2 × 8 1 + 3 × 8 0 ⇒ 123 8 = 1 × 64 + 2 × 8 + 3 × 1 ⇒ 123 8 = 64 + 16 + 3 ⇒ 123 8 = 83 10 Hence 83 10 is decimal representation of 123 8 .

Decimal to Octal Number

To convert a decimal number to an octal number follow these simple steps:

Step 1: Divide the given decimal number by 8. Step 2: Write down the quotient and remainder obtained. Step 3: Divide the quotient obtained by 8. Step 4: Repeat step 2 and step 3 until the quotient becomes 0. Step 5: Write the obtained remainder in reverse order.

Let’s Consider an example for better understanding.

Example: Represent 164 10 as Octal Number.

164/8 , Quotient = 20 and Remainder = 4 20/8 , Quotient = 2 and Remainder = 4 2/8 , Quotient = 0 and Remainder = 2 Now, By writing obtained remainders in reverse order we get, 244. Hence 244 8 is octal representation of 164 10

The image added below shows binary to octal conversion.

A hexadecimal number system has a base 16 and it is an alphanumeric number system consisting of digits from 0 to 9 and alphabets from A to F. To convert an octal number to a hexadecimal number: First convert the octal number to the decimal number; Then convert the obtained decimal number to the hexadecimal number.

Steps to Convert Octal Number to Decimal Number

Steps to convert decimal number to hexadecimal number.

• Step 1: Divide the decimal number by 16.
• Step 2: Write down the quotient and remainder obtained.
• Step 3: Divide the quotient obtained by 16.
• Step 4: Repeat step 2 and step 3 until the quotient becomes 0.
• Step 5: Write the obtained remainder in reverse order.
• Step 6: Convert each obtained remainder to its corresponding hexadecimal digit.

Corresponding value of 0-9 remains the same in hexadecimal and 10-15 corresponds to A-F in hexadecimal that is represented as,

Example: Convert 174 8 to a hexadecimal number.

Step 1: Convert 174 8 to decimal 174 8 = 1 × 8 2 + 7 × 8 1 + 4 × 8 0 174 8 = 1 × 64 + 7 × 8 + 4 × 1 174 8 = 64 + 56 + 4 = 124 We get 174 8 = 124 10 Step 2: Covert 124 10 to hexadecimal 124/16, Quotient = 7, Remainder = 12 7/16, Quotient = 0, Remainder = 7 Converting the obtained remainders to corresponding hexadecimal number and writing it in reverse order we get: 124 10 = 7C 16 Hence we get 174 8 = 7C 16

Hexadecimal to Octal Number

To convert a Hexadecimal number to an Octal number we have to First convert the Hexadecimal number to a Decimal number and then the Decimal number to an Octal number.

Steps to Convert Hexadecimal Number to Decimal Number

We can use following steps to convert hexadecimal number to decimal numbers.

Step 1: Write the corresponding decimal value for the given hexadecimal number. Step 2: Multiply each digit of the obtained number with an increasing power of 16 starting from the rightmost digit. Step 3: Sum all the products obtained in step 2.

Steps to Convert Decimal Number to Octal Number

We can use following steps to convert decimal number to octal numbers.

Let’s consider an example for better understanding.

Example: Convert 9B 16 to Octal Number.

Step 1: First convert 9B 16 to decimal number: Corresponding decimal value of 9 and B are 9 and 11 respectively. 9B 16 = 9 × 16 1 + 11 × 16 0 9B 16 = 9 × 16 + 11 × 1 9B 16 = 144 + 11 = 155 We get 9B 16 = 155 10 Step 2: Convert 155 10 to Octal Number 155/8, Quotient = 19, Remainder = 3 19/8, Quotient = 2, Remainder = 3 2/8, Quotient = 0, Remainder = 2 Writing the obtained remainders in reverse order we get: 155 10 = 233 8 Hence we get 9B 16 = 233 8

The conversion of an octal number to a binary number is very simple, we have to simply write the corresponding binary value of each digit of the given octal number. Corresponding values of octal and binary numbers are as follows:

Example: Convert 213 8 to a binary number.

Write the corresponding binary value of each digit of the given octal number: 2 —> 010 1 —> 001 3 —> 011 Hence we get 213 8 = 010001011 2

Binary to Octal Number

We can easily convert a binary number to an octal number by following these steps:

• Step 1: Split the binary number into sets of three digits, starting from the right.
• Step 2: Write the corresponding octal value of each binary triplet obtained in step 1.

Example: Convert 100111001 2 to an octal number.

Split 100111001 into sets of three digits and write its corresponding octal value 100 —> 4 111 —> 7 001 —> 1 Hence we get, 100111001 2 = 471 8

The binary-to-decimal conversion is added in the image below,

Octal Multiplication table is added below,

• Whole Numbers
• Natural Numbers
• Irrational Numbers

Examples on Octal Numbers System

Example 1: What is Decimal Equivalent of 1121 8 ?

1121 8 = 1 × 8 3 + 1 × 8 2 + 2 × 8 1 + 1 × 8 0 1121 8 = 1 × 512 + 1 × 64 + 2 × 8 + 1 × 1 1121 8 = 512 + 64 + 16 + 1 = 593 Hence 1121 8 = 593 10

Example 2: Convert 27 8 into the binary number.

Write binary equivalent of each digit of 27 8 2 —> 010 7 —> 111 Hence 27 8 = 010111 2

Example 3: Find the octal equivalent of 1001001 2

Breaking 10101111 into groups of three starting from rightmost digit and adding leading zeroes we get: 010 , 101, 111 Write the octal equivalent of the groups formed 010 —> 2 101 —> 5 111 —> 7 Hence we get 10101111 2 = 257 8

Practice Questions on Octal Number System

Q1: Convert 121 10 to an octal number.

Q2: What is Octal Value of 100010000 2 ?

Q3: Find the Decimal Equivalent of 55 8 .

Q4: Convert 12F 16 to Octal number.

Q5: What will be the binary value of 57 8 ?

Octal Number System – FAQs

What are octal number system.

Number system with base 8 and symbols ranging between 0-7 is known as the Octal Number System. Each digit of an octal number represents a power of 8. It is widely used in computer programming and digital systems.

What is Octal Equivalent of (100) 10 ?

(144) 8 is Octal Representation of (100) 10

What are Types of Number Systems . ?

The four types of number system are, Decimal Number System (with base 10 and symbols ranging between 0-9) Binary Number System (with base 2 and symbols 0 and 1) Hexadecimal Number System (with base 16 and symbols raging between 0-9 and from A to F) Octal Number System (with base 8 and symbols ranging between 0-7)

What are Symbols of Octal Number System?

The base of an octal number system is 8 nd hence it consists of 8 symbols which are 0, 1, 2, 3, 4, 5, 6, and 7.

How to Convert Octal Number to Hexadecimal Number?

To convert an octal number to a hexadecimal number, First convert the octal number to the decimal number; Then convert the obtained decimal number to the hexadecimal number.

What is Octal Equivalent of (1010) 2 ?

Breaking 1010 into groups of three starting from rightmost digit and adding leading zeroes, 001 , 010 Write Octal Equivalent of Groups, 001 —> 1 010 —> 2 Hence we get (1010) 2 = (12) 8

What is 123 in Octal Number System?

123 in Octal Number System is equal to 173.

What are uses of Octal Number System?

Octal Number system are used in Computer applications sectors, aviation sector and research purposes.

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Data Representation in Computer: Number Systems, Characters, Audio, Image and Video

Table of Contents

• 1 What is Data Representation in Computer?
• 2.1 Binary Number System
• 2.2 Octal Number System
• 2.3 Decimal Number System
• 2.4 Hexadecimal Number System
• 3.4 Unicode
• 4 Data Representation of Audio, Image and Video
• 5.1 What is number system with example?

What is Data Representation in Computer?

A computer uses a fixed number of bits to represent a piece of data which could be a number, a character, image, sound, video, etc. Data representation is the method used internally to represent data in a computer. Let us see how various types of data can be represented in computer memory.

Before discussing data representation of numbers, let us see what a number system is.

Number Systems

Number systems are the technique to represent numbers in the computer system architecture, every value that you are saving or getting into/from computer memory has a defined number system.

A number is a mathematical object used to count, label, and measure. A number system is a systematic way to represent numbers. The number system we use in our day-to-day life is the decimal number system that uses 10 symbols or digits.

The number 289 is pronounced as two hundred and eighty-nine and it consists of the symbols 2, 8, and 9. Similarly, there are other number systems. Each has its own symbols and method for constructing a number.

A number system has a unique base, which depends upon the number of symbols. The number of symbols used in a number system is called the base or radix of a number system.

Let us discuss some of the number systems. Computer architecture supports the following number of systems:

Binary Number System

Octal number system, decimal number system, hexadecimal number system.

A Binary number system has only two digits that are 0 and 1. Every number (value) represents 0 and 1 in this number system. The base of the binary number system is 2 because it has only two digits.

The octal number system has only eight (8) digits from 0 to 7. Every number (value) represents with 0,1,2,3,4,5,6 and 7 in this number system. The base of the octal number system is 8, because it has only 8 digits.

The decimal number system has only ten (10) digits from 0 to 9. Every number (value) represents with 0,1,2,3,4,5,6, 7,8 and 9 in this number system. The base of decimal number system is 10, because it has only 10 digits.

A Hexadecimal number system has sixteen (16) alphanumeric values from 0 to 9 and A to F. Every number (value) represents with 0,1,2,3,4,5,6, 7,8,9,A,B,C,D,E and F in this number system. The base of the hexadecimal number system is 16, because it has 16 alphanumeric values.

Here A is 10, B is 11, C is 12, D is 13, E is 14 and F is 15 .

Data Representation of Characters

There are different methods to represent characters . Some of them are discussed below:

The code called ASCII (pronounced ‘􀀏’.S-key”), which stands for American Standard Code for Information Interchange, uses 7 bits to represent each character in computer memory. The ASCII representation has been adopted as a standard by the U.S. government and is widely accepted.

A unique integer number is assigned to each character. This number called ASCII code of that character is converted into binary for storing in memory. For example, the ASCII code of A is 65, its binary equivalent in 7-bit is 1000001.

Since there are exactly 128 unique combinations of 7 bits, this 7-bit code can represent only128 characters. Another version is ASCII-8, also called extended ASCII, which uses 8 bits for each character, can represent 256 different characters.

For example, the letter A is represented by 01000001, B by 01000010 and so on. ASCII code is enough to represent all of the standard keyboard characters.

It stands for Extended Binary Coded Decimal Interchange Code. This is similar to ASCII and is an 8-bit code used in computers manufactured by International Business Machines (IBM). It is capable of encoding 256 characters.

If ASCII-coded data is to be used in a computer that uses EBCDIC representation, it is necessary to transform ASCII code to EBCDIC code. Similarly, if EBCDIC coded data is to be used in an ASCII computer, EBCDIC code has to be transformed to ASCII.

ISCII stands for Indian Standard Code for Information Interchange or Indian Script Code for Information Interchange. It is an encoding scheme for representing various writing systems of India. ISCII uses 8-bits for data representation.

It was evolved by a standardization committee under the Department of Electronics during 1986-88 and adopted by the Bureau of Indian Standards (BIS). Nowadays ISCII has been replaced by Unicode.

Using 8-bit ASCII we can represent only 256 characters. This cannot represent all characters of written languages of the world and other symbols. Unicode is developed to resolve this problem. It aims to provide a standard character encoding scheme, which is universal and efficient.

It provides a unique number for every character, no matter what the language and platform be. Unicode originally used 16 bits which can represent up to 65,536 characters. It is maintained by a non-profit organization called the Unicode Consortium.

The Consortium first published version 1.0.0 in 1991 and continues to develop standards based on that original work. Nowadays Unicode uses more than 16 bits and hence it can represent more characters. Unicode can represent characters in almost all written languages of the world.

Data Representation of Audio, Image and Video

In most cases, we may have to represent and process data other than numbers and characters. This may include audio data, images, and videos. We can see that like numbers and characters, the audio, image, and video data also carry information.

We will see different file formats for storing sound, image, and video .

Multimedia data such as audio, image, and video are stored in different types of files. The variety of file formats is due to the fact that there are quite a few approaches to compressing the data and a number of different ways of packaging the data.

For example, an image is most popularly stored in Joint Picture Experts Group (JPEG ) file format. An image file consists of two parts – header information and image data. Information such as the name of the file, size, modified data, file format, etc. is stored in the header part.

The intensity value of all pixels is stored in the data part of the file. The data can be stored uncompressed or compressed to reduce the file size. Normally, the image data is stored in compressed form. Let us understand what compression is.

Take a simple example of a pure black image of size 400X400 pixels. We can repeat the information black, black, …, black in all 16,0000 (400X400) pixels. This is the uncompressed form, while in the compressed form black is stored only once and information to repeat it 1,60,000 times is also stored.

Numerous such techniques are used to achieve compression. Depending on the application, images are stored in various file formats such as bitmap file format (BMP), Tagged Image File Format (TIFF), Graphics Interchange Format (GIF), Portable (Public) Network Graphic (PNG).

What we said about the header file information and compression is also applicable for audio and video files. Digital audio data can be stored in different file formats like WAV, MP3, MIDI, AIFF, etc. An audio file describes a format, sometimes referred to as the ‘container format’, for storing digital audio data.

For example, WAV file format typically contains uncompressed sound and MP3 files typically contain compressed audio data. The synthesized music data is stored in MIDI(Musical Instrument Digital Interface) files.

Similarly, video is also stored in different files such as AVI (Audio Video Interleave) – a file format designed to store both audio and video data in a standard package that allows synchronous audio with video playback, MP3, JPEG-2, WMV, etc.

FAQs About Data Representation in Computer

What is number system with example.

Let us discuss some of the number systems. Computer architecture supports the following number of systems: 1. Binary Number System 2. Octal Number System 3. Decimal Number System 4. Hexadecimal Number System

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Numerical Representation

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The numerical system used in the Western World today is a place-value base-10 system inherited from India through the intermediary of Arabic trade; this is why the numbers are often called Arabic numerals or more correctly Indo-Arabic numerals. However, this is not the only numerical system possible. For centuries, the Western World used the Roman system instead, which is a base-10 additive-value system (digits of a number are summed and subtracted from each other to get the value represented), and that system is still in use today, notably in names and titles. Other civilizations experimented with other bases: some precolonial Australian cultures used a base-5 system, while base-20 systems arose independently in Africa and in pre-Columbian America, and the ancient Babylonians used a base-60 counting system. Even today, despite the prevalence of the base-10 system, systems in other bases continue to be used every day: degrees, minutes, and seconds are counted in the base-60 system inherited from Babylonian astrologers, and base-12 is used to count hours in the day and months (or zodiacs) in the year.

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Khoury, R., Harder, D.W. (2016). Numerical Representation. In: Numerical Methods and Modelling for Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-21176-3_2

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What Is The Pound Symbol ( # ) And How Do You Use It?

• What Is A Pound Symbol?
• When To Use It
• Try Grammar Coach

Time to learn about the pound symbol! #educational

Although the pound symbol isn’t used often in formal writing, the average social media user is likely very familiar with this particular character. If you have avoided social media, you might wonder what this strange symbol means or if it even has a use in writing at all.

What is a pound symbol ?

The pound symbol (#), also known by many other names that include pound sign , number sign , hash mark , and hashtag , is a typographical symbol that is rarely used in formal writing. However, this symbol is used often in informal writing, specifically on social media.

Note:  the name pound symbol is also used to refer to the symbol (£) used to represent a denomination of British currency called the pound or pound sterling . We won’t be looking at this particular symbol, but don’t be surprised if you see the name pound symbol used to refer to it.

✏️ Example usage of the pound symbol

The following examples show some ways that the pound symbol could be used:

• Yay! The Wildcats are ranked #2 in the country!
• You will need a calculator to solve problem #7 on the exam.
• The catchy pop song reached #1 on the Billboard Hot 100.
• Going to #Disneyland tomorrow! So excited! #vacation 

When do you use a pound symbol?

The pound symbol is rarely ever used in formal writing. Typically, most writers will opt for alternative words or abbreviations rather than use a pound symbol. However, the pound symbol is a popular symbol among social media users.

Substitute for the word number

One fairly common use for the pound symbol is to represent the word number , and it can be used for this reason if word count is a concern. However, this usage is typically avoided in formal writing unless the symbol is commonly used in a specific title of something, such as a musical composition. Here are some examples of the pound symbol used to represent the word number:

• Quarterback Jeff Jeffreys wears #5 (number 5), the same number he wore in college.
• She poked me with a #2 (Number Two) pencil.
• The orchestra performed Mozart’s Symphony #25 (Number 25).
• What is the answer to questions #7 and #9 (number 7 and number 9)?

Speaking of numbers, how much do you know about countable nouns?

Social media

On social media, the pound symbol is commonly referred to as the hashtag . The hashtag is used with words or phrases on social media to tag a message, photo, video, or other content as being related to a certain topic. For example, a person might label a photo of the Eiffel Tower with #France or #Paris . The word hashtag is used both to refer to the pound symbol as well as a tag using a pound symbol.

Hashtags allow social media users to easily search for content that (probably) has something to do with a certain topic or subject. For example, a fan of Star Wars could search the hashtags #StarWars , #Chewbacca , or #LukeSkywalker on social media to find content related to Star Wars.

Here are some examples of how the pound symbol might be used on social media:

• Ugh! Final exams tomorrow! #cramsession
• Been stuck in line for two hours… #DMV #boring
• I think the crows in my yard are plotting against me. #CrowConspiracy

Take this quiz to see how much you know about the pound symbol and other typographical symbols.

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Mathematics > Rings and Algebras

Title: on the sumsets of exceptional units in quaternion rings.

Abstract: We investigate sums of exceptional units in a quaternion ring $H(R)$ over a finite commutative ring $R$. We prove that in order to find the number of representations of an element in $H(R)$ as a sum of $k$ exceptional units for some integer $k \geq 2$, we can limit ourselves to studying the quaternion rings over local rings. For a local ring $R$ of even order, we find the number of representations of an element of $H(R)$ as a sum of $k$ exceptional units for any integer $k \geq 2$. For a local ring $R$ of odd order, we find either the number or the bounds for the number of representations of an element of $H(R)$ as a sum of $2$ exceptional units.

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LGBTQ representation in government is growing but still disproportionate: Graphics explain

Those identifying as gay represented the largest share of lgbtq elected officials, with 544 gay men in public office within local, state and federal governments.

Nearly 1,300 elected officials in the U.S. are a part of the LGBTQ community − a number that continues to grow every election cycle but still falls far short of being representative of the LGBTQ community.

About 7.6% of U.S. adults now identify as lesbian, gay, bisexual, transgender, queer, or as something other than heterosexual, according to a recent Gallup poll . That’s compared to 3.5% in 2012, the year the national polling agency began measuring sexual orientation and transgender identity.

While 7.6% of adults identify as LGBTQ+, less than 1% of elected officials in the U.S. identify the same, though there's no way to quantify those who hold office but haven't come out publicly.

In order for the government to be fully representative of the queer population, more than 35,000 LGBTQ people would need to be elected, according to the Victory Institute , a nonprofit focused on training LGBTQ+ leaders to run for office.

Although the LGBTQ community is underrepresented in government, an annual report by the organization did identify gains in several areas.

LGBTQ+ representation in government

According to the most recent year of data available (2022), those identifying as gay represented the largest share of LGBTQ elected officials, with 544 gay men in public office within local, state and federal governments.

The following groups made gains between 2021 and 2022:

• Non-binary and genderqueer elected officials increased from nine to 12
• Transgender elected officials grew from 41 to 45
• Bisexual elected officials increased from 71 to 90 during the same time period

The growing number of adults identifying as LGBTQ+ represents a greater sense of societal acceptance and/or support systems for those who identify as queer, Brandon Robinson, an associate professor and department chair of gender and sexuality studies at the University of California, Riverside, previously told USA TODAY.

"More people identifying as LGBTQ is often a sign that more people feel safe and/or comfortable to openly claim an LGBTQ identity," they said.

Map shows which states have LGBTQ+ representation in public office

Alabama, Wyoming and Idaho all have one elected official that identifies as queer. California, Illinois, Pennsylvania, Massachusetts and Michigan all have more than 50 LGBTQ+ elected officials serving in local, state and federal office.

Ten states have fewer LGBTQ+ elected officials in 2022 compared to 2021. During the same time period, 22 states have more LGBTQ+ elected officials, the Victory Institute reported.

Between June 2021 and 2022, the share of LGBTQ+ elected officials who were affiliated with the Democratic Party increased from 73.1% to 75.1%. The share of LGBTQ elected officials that are affiliated with the Republican party was much smaller, at 3%.

"LGBTQ elected officials are on the front lines of defending our rights and freedoms, which are under threat at every level of government," Victory Institute President and CEO Annise Parker, also the mayor of Houston, says on the group's website. "LGBTQ elected officials represent the strength and diversity of not only who we are as a society now, but also the America we aspire to build for future generations."

Data trends: Portion of US adults identifying as LGBTQ has more than doubled in last 12 years

More than just 'firsts': LGBTQ elected officials carve space for a future generation of politicians

Contributing: Marc Ramirez

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Explained: The representation of women in the incoming Lok Sabha, how it compares to previous years

Over the years, lok sabha’s gender composition has shown a general trend towards increasing women’s representation. but progress has been slow and not linear..

India has elected 74 women MPs to Lok Sabha this year, four fewer than in 2019 and 52 more than in India’s first elections in 1952. These 74 women make just 13.63% of the elected strength of the Lower House, much less than the 33% that will be reserved for women after the next delimitation exercise.

Slow change

Over the years, Lok Sabha’s gender composition has shown a general trend towards increasing women’s representation. But progress has been slow and not linear. ( See chart)

In 1952, women made up just 4.41% of the strength of the Lower House. This number increased to more than 6% in the election held a decade later, but again dipped to below 4% in 1971 (ironically, with Indira Gandhi, India’s first and only woman Prime Minister, at the helm). Since then, there has been a slow, but steady rise in women’s representation (with a few exceptions), which crossed the 10% mark in 2009, and peaked in 2019 at 14.36%. India still lags behind several countries — 46% of MPs in South Africa, 35% in the UK, and 29% in the US, are women.

Party-wise share

In 2024, women Lok Sabha MPs come from 14 parties. The BJP leads this list with 31 women MPs, followed by the Congress (13), TMC (11), SP (5), DMK (3), and Chirag Paswan -led LJPRV and JD(U), both with two. Seven parties have one woman MP each. Among the 3 parties with double-digit women MPs in the Lok Sabha, the TMC boasts the highest proportion (37.93%), followed by Congress (13.13%) and BJP (12.92%).

New faces, younger

Of the 74 women MPs elected, 43 are first time MPs, and one (Misa Bharti of the RJD) is a first time Lok Sabha MP. This is higher than the overall percentage of newcomers in the House (59% vs 52%).

Women MPs have only 0.76 Lok Sabha terms of experience (one term is generally 5 years long) .

Women MPs, with an average age of 50 years, are also younger. The overall age of the House is 56. They are as educated as their male counterparts, with 78% completing undergraduation.

Candidates’ composition

Out of the total 8,360 candidates, who stood in the 2024 Lok Sabha elections, just around 10% were women. This number too has increased over time — it stood at 3% in 1957. This is the first time that women candidates’ proportion touched 10%. Roughly 16% of BJP’s candidates were women, as opposed to 13% of Congress candidates — both higher than the overall average.

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Lok Sabha election results 2024: How number of women MPs has fallen from 2019

In Lok Sabha elections 2024, a total of 797 women contested the elections, with 74 of them getting elected. Which states have the best and worst women’s representation in the Lok Sabha? Which state has the most women MPs? Which party has the most women MPs? We tell you what the numbers say read more

Following the 2024 Lok Sabha elections, 74 women have been elected as Members of Parliament (MP). This means that only 13.6 per cent of the 543 members of the Lower House of the Parliament are women. That despite the fact that they form roughly 50 per cent of India’s population.

The number is slightly lower than the record-high seen in 2019, when 78 women (14.3 per cent of the total 543 MPs) were elected to the Lok Sabha.

We tell you what the numbers say about women’s participation and election in the 2024 Lok Sabha polls 2024.

A comparison with 2019

According to data provided by the Election Commission, in 2019, 726 women had contested in the elections. Of them, 78 women - 10.74 per cent of total women candidates - were elected.

In 2024, a total of 797 women contested the elections, with 74 of them getting elected. That means that 9.7 per cent of the women who were in the electoral race won. Only 13.6 per cent of the 543 members of the Lower House of the Parliament are women.

States/UTs with best women representation

Tripura is tied with the Union territory of Dadra and Nagar Haveli and Daman and Diu for the top spot when it comes to women’s representation. The Northeastern state and the union territory have two Lok Sabha constituencies each. They have each elected one woman. This means that 50 per cent of the population in each of these places are represented by women.

Here’s how that calculation works, illustrated with the example of Tripura:

The state of Tripura has 2 constituencies. All eligible voters are registered to cast their ballot for one of the two seats. Theoretically, that means that 100 per cent of the population is represented (in the Lok Sabha) by the two people who are elected. So each candidate represents roughly 50 per cent of the state’s population.

The National Capital Territory of Delhi takes the third rank when it comes to women’s representation in Lok Sabha in percentage. Delhi has 7 seats. Two of those– New Delhi and West Delhi– have been won by women.

This means that 28.57 per cent of the population in Delhi is represented by women in the Lok Sabha.

States sending most female representatives to Lok Sabha

West Bengal takes the crown when it comes to this. The state, which has 42 seats, has elected 11 women. All of them are from the Mamata Banerjee-led Trinamool Congress.

Maharashtra and Uttar Pradesh are tied for second place. Both states have elected seven women to the Lok Sabha. However, given that Maharashtra has 48 seats, while UP has 80, it is clear that the former’s proportion of women elected is better.

States with worst women representation in Lok Sabha

According to Firstpost’s analysis of Election Commission data, there are 13 states/Union territories with no women representatives elected to the Lok Sabha.

Five of these states – Arunachal Pradesh, Manipur, Meghalaya, Nagaland, and Sikkim – are in the Northeast.

Five Union territories – Andaman and Nicobar Islands, Chandigarh, Ladakh, Lakshadweep, and Puducherry – each having only one seat, saw men representing their entire populations in the Lok Sabha.

The Union Territory of Jammu and Kashmir, which sent five representatives to the Lok Sabha, and where six women, including former chief minister Mehbooba Mufti were in the fray, also saw no women getting elected.

In Goa, which has two Lok Sabha constituencies, BJP’s Pallavi Shrinivas Dempo was the runner up for the South Goa seat. She lost to Congress’ Captain Viriato Fernandes by a margin of 13,535 votes.

Kerala is an especially disappointing presence on this list. There are 20 constituencies in the state- much more than any other state or union territory that did not elect any women representatives. No women representatives were chosen despite 71.72 per cent of women voters turning out to cast their ballots.

Party-wise distinction

As many as 31 of the elected women belong to the BJP, which contested the most seats of any party in the country. Congress, with 14 women members elected to the Lok Sabha, takes the second spot. TMC is in the third place.

Five of the elected women belong to Samajwadi Party. This includes top party leader Akhilesh Yadav’s wife, Dimple Yadav, too.

Dravida Munnetra Kazhagam (DMK), the ruling party in Tamil Nadu, has three women elected to the Lok Sabha. Janata Dal (United) and Lok Janshakti Party (Ram Vilas) have two women members who have been elected to the Lok Sabha.

One woman member each from Telugu Desam Party (TDP), Yuvajana Sramika Rythu Congress Party (YSRCP), Shiromani Akali Dal (SAD, Rashtriya Janata Dal (RJD), Apna Dal, and Jharkhand Mukti Morcha (JMM) have been elected to the Lok Sabha.

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Here's What Angel Number 444 Is Trying to Tell You

In numerology, this number mean big things for your relationships, career and health.

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What does it mean when you see the number 4?

Love and relationships, finances and career.

Angel numbers take various forms, each carrying its unique significance. For instance, the number 2 signifies connection , while 8 symbolizes achievement and balance . If the number 5 appears, it may indicate a readiness for adventure or change . However, when you encounter specific numbers like 4, 44, or 444, Berry advises against dismissing them.

Laura Widney, Chief Innovation Officer for Soaak , a private health clinic and mindfulness, mental health, and wellness app, explains that spiritually, the number 4 implies the presence of your angels, who are guiding, encouraging, and providing you with positive energy, confidence, and inner strength. As Widney emphasizes, when a number consistently reappears in your life, it's a clear sign from the universe, urging you to remain open and receptive to its meaningful message.

Number 4 spiritual meaning

In the spiritual sense, the lesson the number 4 can bring to you has to do with dreams, goals and aspirations. To achieve what you want, you have to be willing to serve, be dependable, and put in consistent hard work, according to our astrological experts.

The number 4 can represent the four elements: air, fire, water, and earth. These signify the importance of working together to achieve our goals, Widney says.

The number 4 can also represent the four sacred directions: north, south, east, and west, Widney explains. This reminds us that “we are all connected and need to respect and care for others to achieve our goals and aspirations.”

According to Berry, the number 4’s purpose is to build something of real value by being practical and hardworking. “It shows the need for security and structure, being motivated by things of a practical nature and being responsible for achieving what is wanted and understanding the value of self-discipline and rules,” Berry adds.

According to Vincent Genna , psychic therapist, spiritual teacher, and author of The Secret That’s Holding You Back , “If the angels need to send you a sign regarding the number 4, it means you are in need of important guidance.” It may mean that you’re off your ultimate life path, and you need to get back on track.

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Do you find that your life is a little chaotic? Or, do you keep hitting dead ends as you try to pursue a goal? If you see the number 4 during these trying times, it may mean that your angels are trying to get you to stop and chill out. You should ground yourself, be still, and re-evaluate. On the other hand, if you are achieving your goals and you see the number 4, your angels are validating your journey, says Genna.“You might see or hear the number everywhere you turn,” Widney points out. “For example, you might see 4:44 on the clock, the number 4 on your receipts, or hear the same number repeatedly on the radio and in conversations.” What should you do when this happens? What does it mean if the number four being presented repeatedly becomes your reality? According to Widney, “the practicality and responsibility represented by the number 4 encourages us to work hard and harmoniously towards achieving our goals. The stability and solid foundation of the number 4 reminds us to stay focused and productive to achieve our aspirations.” To Berry, the number 4 signifies that the universe is offering support and angels are helping you with truth and self-worth. “It tells [you] to trust in feelings and heartfelt thoughts and continue with emotional strength and dedication in a positive direction,” she adds.  

When it comes to double 4s, that’s double the angel involvement, Berry points out.  “The number 44 shows angels surrounding with love and protection, ensuring safety. Also receiving help to share truth to the world with loving self-guidance and direction.” Widney believes that,  “The angel number 44 encourages you to pay special attention to your intuition and to stay on your current path because your drive and determination will lead you to success.”   

Now, the number 4 in a series that appears as “444” signifies that there are legends of angels lending assistance, Berry says.  “Miracles are happening now. The tables are turning in a favorable position and obstacles are being lifted.”  Berry reminds that for the person who sees 444, hard work is in order to overcome a challenge or to see changes for the better.  “This number is a reminder that processes have to be followed to reach the desired goals.” “The angel number 444 tells you that your connection with the angels and the angelic realm is powerful and that you can trust the guidance they are giving you,” Widney adds. “The number 444 is also a sign of love and wholeness. It represents your deep love for something or someone.”

When it comes to your love life, when you see the number 4 repeated three times, the universe is telling you to establish a stable foundation for that relationship. “I’m always telling my clients, male and female, that even though we are sexual beings, in order for any love relationship to truly work and develop into a soulmate or twin-flame-like relationship, you must develop an emotional foundation before a physical one,” Genna cautions.

While a physical connection is also important, stability will give your relationship longevity. When you see the angel number 4, it could mean that you need to find peace in your current love life. “It's important to create a sense of peace when making decisions and establishing the direction of the relationship,” Berry explains.

Likewise, Genna says, if you recently began a new love interest and relationship, seeing any of the combinations of the number 4 means you should establish a stable foundation for that relationship to work. "Remember, a strong foundation will withstand the winds of life — the natural and unnatural stressors that come along throughout one’s life," Genna advises. "The highs and lows, the good times and bad times, in sickness and in health can all be faced between a couple when a strong, stable foundation has been created." Seeing the number 4, 44 or 444 are a good reminder.

In case you’re not familiar, a twin flame is your soul split in half . “It is an exact mirror of the soul that supposedly each soul created for itself in a lifetime,” says Genna. “The idea upon splitting the soul is that if you get to meet up with your twin soul and partner with it in love, this will allow you to evolve and grow faster. In this way you have the chance to see your weaknesses and strengths outside yourself.”

According to Berry, a "twin flame" friendship or romantic relationship is the kind of soulful union in which each person reflects the best part of the other and reminds them of their true worth. Through this, both individuals in the situation can live their lives to the fullest — truthful and free from obligations where there are no secrets, and there is positive feedback and constructive criticism.

So when you see the number 4, 44, or 444, it’s a sign you’re on the right path and are heading in a positive direction with that partner. “Trusting inner instincts is the foundation of this number when involved in moving forward in the relationship,” Berry reminds.

Knowing your twin flame means you get the opportunity to see your weaknesses and strengths outside yourself.

If you follow this concept, your twin-flame relationship might actually prove to be the most difficult kind. Think about it? "If you have a hard enough getting along with yourself, how much more difficult would it be to get along with yourself as a partner?" Genna asks. "Whatever issues and weaknesses you carry would be doubly difficult to resolve and heal."

“The number 444 can help keep you focused and determined to reach your career goals and boost your finances because of your drive and determination,” explains Widney.

Remember that the number 4 gives off the energy of dependability and being practical. As it relates to your finances and your career, seeing the number 4 could be a sign that you need discipline, structure, and to be more conscientious when it comes to your money matters or job. “This number values excellence in work and career, so when it appears, more attention should be directed toward persistence and precision in areas of work and business,” adds Berry.

Genna says that the number 4 can sometimes be a message from the angels for you to either keep going (and that they’re going to be helping you!) or that you may actually need a new job. Continue to look for the signs, so you can be directed towards the right path.

When it comes to your health and wellness, you can factor in discipline too when the angel number 4 presents itself to you. It’s a sign you need to prioritize your health. Seeing the number 4 can be the angels telling you to ground yourself, slow down, and have a sense of calm, especially if the surrounding energy is chaotic. Genna suggests trying meditation among other things. “A better lifestyle may be necessary for you to regain your wellness and strength,” he says. “In order to heal the physical body, the angels know you must heal the mental body first and foremost.”

Writing or journaling about your thoughts and emotions when you experience an angel number is a great practice says Widney. “Taking the physical action of journaling during your angel number experience helps you make the most of these powerful moments.”

Ysolt Usigan is a lifestyle writer and editor with 15+ years of experience working in digital media. She has created share-worthy content for publishers Shape , What To Expect , Cafe Mom , TODAY , CBS News , HuffPo , The Bump , Health , Ask Men , and Best Gifts . A working mom of two, her editorial expertise in parenting, shopping, and home are rooted in her everyday life. 

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India election results

Results of the six-week-long election to the lower house of India’s Parliament started pouring in Tuesday morning

Results of the Indian general elections were out on Tuesday with the National Democratic Alliance (NDA), led by the Bharatiya Janata Party (BJP), winning a majority, even if their seat tally reduced significantly compared to the 2019 elections.

Stacked bar chart shows the number of seats won or led by the BJP and its allies, the Congress and its allies, and others, for 2024 and 2019.

Counting of over 640 million votes that were cast in the 2024 Indian general elections began early on Tuesday. The polling to elect 543 members of the Lok Sabha, lower house of the Indian parliament, concluded on June 1.

The ruling BJP along with its allies was competing for a third term under Prime Minister Narendra Modi’s leadership. The Indian National Congress (INC), which has the second largest national footprint after the BJP, helped stitch a new coalition called the Indian National Developmental Inclusive Alliance (INDIA) last year, hoping to wrest power from Modi through a united opposition.

Elections were held in seven phases in constituencies spread across 36 states and federal territories.

Map shows the winner or leader in each of India’s 543 Lok Sabha constituencies

The BJP seized power from the Congress and its allies with a decisive victory in 2014, marking the first time in three decades that a single party achieved a majority of its own. Its strength increased in the subsequent 2019 election. However, the party did not end up with enough seats this year to form a majority by itself.

Its previous victories had come from the more populous northern and western parts of India. It lost some of that turf to the Congress-led alliance this year.

Four maps show winners or leaders in each of India’s 543 Lok Sabha constituencies in 2009, 2014, 2019 and 2024.

India's political landscape has significantly evolved over time. Until three decades ago, the Congress was the dominant force. However, the BJP began gaining substantial electoral strength and emerged as the leading party. Its wins in the 2014 and 2019 elections relegated Congress to historically low levels of influence, winning less than 10% of the seats each time. This year, however, the Congress almost doubled its tally.

Stacked bar chart shows seats won by BJP, INC and others in each general election from 1962 to 2019, and the results for 2024

All major exit polls had predicted a historic victory for the BJP, anticipating its best performance to date.

Some allies of BJP and INC have changed between 2019 and 2024.

Election Commission of India; Trivedi Centre for Political Data; DataMeet; Natural Earth

Simon Scarr, Anand Katakam and Raju Gopalakrishnan