assignment on number system

Number System – Definition, Examples, Facts, Practice Problems

Number system, practice problems on number system, frequently asked questions on number system.

Decimal Number System: The decimal number system consists of 10 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 and is the most commonly used number system. We use the combination of these 10 digits to form all other numbers. The value of a digit in a number depends upon its position in the number. The place value table for the decimal number system is as:

Each place to the left is ten times greater than the place to its right, that is, as we move from the right to the left, the place value increases ten times with each place. 

• A decimal number system is also called the Base 10 system.
• A number 49,365 is read as Forty-nine thousand three hundred sixty-five, where the value of 4 is forty thousand, 9 is nine thousand, 3 is three hundred, 6 is sixty and 5 is five. 

Binary Number System

In the binary number system, we only use two digits 0 and 1. It means a 2 number system.

Example of binary numbers: 1011; 101010; 1101101

Each digit in a binary number is called a bit. So, a binary number 101 has 3 bits. 499787080

Computers and other digital devices use the binary system. The binary number system uses Base 2.

Hexadecimal Number System

The word hexadecimal comes from Hexa meaning 6, and decimal meaning 10. So, in a hexadecimal number system, there are 16 digits. It consists of digits 0 to 9 and then has first 5 letters of the alphabet as:

The table below shows numbers 1 to 20 using decimal , binary and hexadecimal numbers.

• The decimal number system is also called the Hindu–Arabic numeral system
• Anthropologists hypothesize that the decimal system was the most commonly used number system, due to humans having five fingers on each hand, and ten in both.

Related Worksheets

Number Systems

Attend this Quiz & Test your knowledge.

Which number from the decimal number system does the letter A represent in the Hexadecimal Number system?

Which of the following is not used to represent numbers in the hexadecimal number system, how many unique digits does the decimal number system use to represent all the numbers, the binary system uses which two numbers from the decimal number system.

What is the most commonly used number system?

The most commonly used number system is the decimal positional numeral system.

What number systems do computers use?

Computers use decimal, binary, octal , and hexadecimal number systems.

Which number system uses letters?

The hexadecimal number system uses 6 letters (A, B, C, D, E, and F) in addition to 10 digits from 0 to 9.

What is the base of the hexadecimal number system?

The base of the hexadecimal number system is 16.

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Number Systems

The number system is a way to represent or express numbers.  You have heard of various types of number systems such as the whole numbers and the real numbers. But in the context of computers, we define other types of number systems. They are:

• The decimal number system
• The binary number system
• The octal number system and
• The hexadecimal number system

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Binary Number System (Base 2)

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Practice Questions

Q 1: How would you represent 10111 in the decimal number system?

Q 2: The LSB and MSB in the following number are: 1220

A) 1 & 0

B) 0 & 1

Ans: A) 0 & 1

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Numeral and number systems. origin and development.

A number is an abstract concept used to compute or measure something.

A numeral is a symbol representing a number.

A number system is a set of numbers sharing the same characteristics.

A numeral system is a combination of specific numerals.

People have been trying to store and pass the information on as soon as they learned how to communicate. 

The first attempts to depict numbers were done using the images of sticks or stones – mostly to count the number of items. 

As civilization advanced, the need to develop numeral and number systems that would allow people to complete more complex mathematical operations grew. With the implementation of taxation systems, increased trade, evolving construction needs, interest in sciences, mathematicians were looking for more efficient ways of representing numbers.

Number Bases and Number Groups

Counting up to 10 (based on the number of fingers on one’s hand) eventually became not enough and people had to think of a way of representing larger numbers using symbols. 

Thus, the number bases and number groups emerged.

10 was a popular base (however, Babylonians, for example, used base-sixty and Mayans used base-twenty), because it was easy to count on fingers and count by 10s.

Other numbers were also used to represent groups of numbers (a dozen, for example). 

The symbols representing ones and tens first appeared in Egypt and Mesopotamia around 3400-3000 BC.

Simple grouping numeral systems were used to depict large numbers and mathematical expressions involving more than one arithmetic operation. 

Egyptians repeated the symbols up to 9, with a special symbol for 10.

Greeks and Romans had a similar way of representing large numbers and performing arithmetic operations.

Roman numerals were popular for almost 2000 years. 

The Roman numerals system was a convenient system based on letters: I, V, X, L, C, D and M. 

The system first emerged between 900 and 800 B.C and is still used in some contexts today.

Modern Numeral System

The decimal numeral system that we use today originated in India and was further developed in Persia. 

The Chinese system was also a decimal system, where counting was based on ten numerals represented by symbols. It had special characters to represent ten, a hundred, a thousand, ten thousand, as well as other multiples of ten.

The modern numerals system is called Hindu-Arabic: 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0.

The system is positional, which means that the position of a symbol determines the place value of that symbol within the number (235 is two hundred + thirty + five).

Around 1500 BC – 500, Indians were really interested in Astronomy and thus, the calculations involved very large numbers. They expressed these numbers using a place-value notation, giving names for the powers of 10.

The full system was first described outside India in Al-Khwarizmi’s On the Calculation with Hindu Numerals ( in 825).

The earliest European manuscript, Codex Vigilanus , containing these numerals was written in Spain in 976. An Italian mathematician, Fibonacci, further popularized the system in Europe.

Number Systems

Numbers are classified into number systems based on their characteristics and properties.

There are 5 main number systems that we use to classify numbers:

• Natural Numbers
• Rational Numbers 
• Real Numbers
• Complex (Imaginary) Numbers

Natural numbers – positive integers that we use to count. 

Integers – a combination of a zero, negative and positive whole numbers. Zero is neither positive nor negative. Negative numbers are numbers that are less than zero. We use them to depict opposites, deficits, etc.

The abstract concept of negative numbers was described around 100 B.C.. – 50 B.C. in the Chinese ”Nine Chapters on the Mathematical Art” (Jiu-zhang Suanshu) which provided explanations on how to find areas of figures where red lines were used for positive coefficients and black were used for negative coefficients.

Greek mathematician Diophantus described integers and integer equations in his work Arithmetica. 

Rational numbers – numbers that can be expressed as fractions with an integer numerator and a non-zero natural number denominator. The denominator cannot be 0 since we cannot divide by 0. But a value of the whole fraction can equal 0.

Fractions can be positive and negative. 

Integers are part of the set of all rational numbers, since every integer can be given as a fraction with a denominator 1. 

Rational numbers could be found in the texts of Ancient Egypt, describing how to convert fractions. Indian and Greek mathematicians studied rational numbers as part of the number theory. 

Irrational numbers are numbers that cannot be expressed as repeating, terminating decimals or as a ratio of two integers. Two special examples of irrational numbers are numbers 𝚎 and 𝛑 . 

The need for understanding and considering irrational numbers was established around 500 BC by a Greek mathematician Pythagoras.

These numbers do not have their own set symbol.

In the 17th century, Rene Decartes introduced the term “real” to describe roots of a polynomial (distinguishing them from imaginary numbers). Although with the development of Calculus real numbers sets and the concept of infinity were widely used, real numbers were for the first time formally defined in 1871 by Georg Cantor.

Complex (imaginary) numbers result from taking a square root of a negative number. The resulting number is denoted by i , a symbol assigned by Leonhard Euler. 

Every preceding set of numbers is a subset for the subsequent number system.

Binary Number System

A Binary number system is the simplest of all positional systems and is widely used in Computer Science (computers use the binary number system to manipulate and store all of their data including numbers, words, videos, graphics, and music).

The base of the binary system is 2 and only two numbers are used: 0 and 1.

Gottfried Leibniz, the co-creator of Calculus, first published his invention of the binary system in the 17th century. 

In a binary number system the first 10 numbers would be represented as:

0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, and 1010

We can convert binary numbers into decimal numbers. 

To convert 10101 from binary to decimal system we would do the following (a subscripts represents the base – 2 for binary and 10 for decimal):

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• CBSE Class 9 Maths Worksheet Chapter 1 Number System

CBSE Class 9 Maths Worksheet Chapter 1 Number System - Download Free PDF with Solution

When it comes to Maths as a whole, not many people excel in this subject as it is a subject that solely relies on the logical reasoning functions of the brain. That is why the number system can be intimidating to most students. In Chapter 1, Number System for Class 9, students will learn the number system and their types and how to solve the equations. 

So, what is the number system, and what does the number system syllabus contain? A number system can be defined as an arithmetic system or practice of writing numbers to express them. It is the mathematical notation for continuously representing numbers of any given set by using a certain set of digits, symbols, or other characters. It offers a unique representation of every number. It signifies the arithmetic and algebraic structure of the given figures, permitting us to carry out mathematical calculations such as addition, subtraction, and division. 

All these figures carry their values, which can be determined by looking at the digit, the position in the number, and the base of the number. A number is a mathematical value used to count, measure, or label objects. Regarding the number system, these numbers are used as digits. 

With the help of worksheets such as the Number System Class 9 worksheet, Class 9 Maths Chapter 1 worksheet pdf, and worksheet for Class 9 Maths Chapter 1 with solutions and the operations on Real Numbers Class 9 worksheet, students will have a better understanding of what number systems are and how to solve them accurately.

Access Worksheet for Class 9 Maths Number System

1. It is impossible to represent a rational number in decimal form.

Terminating

Non- terminating

Repeating or Non- Terminating

Non-repeating or Non- terminating

2. Between two rational numbers

There is no rational number.

There is exactly one rational number.

There are infinitely many rational numbers.

There are only rational numbers and no irrational numbers.

3. The product of any two irrational numbers,

is always an irrational number.

is always a rational number.

is always an integer.

can be rational or irrational.

4. Which of the following is irrational?

$\sqrt{81}$

$\dfrac{\sqrt{12}}{\sqrt{3}}$

$\dfrac{\sqrt{4}}{9}$

5. What is the value is $\sqrt{4} \times \sqrt{81}$?

6. Fill in the blanks;

Any two integers are separated by a finite number of others …..

There are an ….. amount of rational numbers between 15 and 18.

X+Y is a rational number if x and y are both ……

Value of $\sqrt[3]{8}$ …….

7. Match the Column:

8. Using two irrational numbers as an example:

Product is an irrational number.

Difference is an irrational number.

Division is an irrational number.

9. Simplify; $(\sqrt{5}+\sqrt{6})(\sqrt{5}-\sqrt{6})$.

10. Simplify; $\sqrt[3]{1331}-\sqrt{100}+\sqrt{81}$.

11. Calculate the value of $\dfrac{11^{\dfrac{1}{2}}}{11^{\dfrac{1}{4}}}$.

12. Calculate the $\dfrac{x}{y}$ form of $0.777 . . . . .$, where $\mathbf{x}$ and $\mathbf{y}$ are integers and $\mathbf{y}$ does not equal to zero.

13. Find three rational number between $\dfrac{9}{11}$ and $\dfrac{5}{11}$.

14. The value of $\dfrac{\sqrt{8}+\sqrt{12}}{\sqrt{32}+\sqrt{48}}$.

15. The value of $a^b+b^a$, if $\mathbf{a}=2$ and $\mathbf{b}=3$

16. Simplify; $2^{\dfrac{2}{3}} \cdot 2^{\dfrac{1}{5}}$

17. Find the value of $\dfrac{1}{a^b+b^a}$, where $a=5, \mathbf{b}=2$

18. Arrange in ascending order $\sqrt[3]{2}, \sqrt{3}, \sqrt[6]{5} \text {. }$

19. Simplify $(4 \sqrt{5}+3 \sqrt{7})^2$

20. Find the value of a, If $\left(\dfrac{y}{x}\right)^{2a-8}=\left(\dfrac{x}{y}\right)^{a-1}$.

21. Rationalize the denominators of $\dfrac{1}{\sqrt{7}}$.

22. Recall, $\pi$ is defined as the ratio of circumference (say c) to its diameter (say d). That is $\pi=\dfrac{c}{d}$. This seems to contradict the fact that $\pi$ is irrational. How will you resolve this contradiction?

23. Express $0 . \overline{001}$ in the form of $\dfrac{p}{q}$, where $\mathrm{p}$ and $\mathrm{q}$ are integers and $\mathrm{q} \neq 0$.

24. Find five rational numbers between $\dfrac{3}{4}$ and $\dfrac{4}{5}$

25. Find six rational numbers between 3 and 4.

Answers to the Worksheet:

A rational number cannot have a non-terminating or non-repeating decimal form.

2. (c) 

Between two rational numbers, there are infinitely many rational numbers. 

E.g. $\dfrac{3}{5}$ and $\dfrac{4}{5}$ are two rational numbers, then $\dfrac{31}{50} \dfrac{32}{50} \dfrac{33}{50} \dfrac{34}{50} \dfrac{35}{50} \ldots$ are infinite rational number between them.

3. (d) 

The product of two irrational numbers can be rational or irrational depending on the two numbers.

For example, $\sqrt{3} \times \sqrt{3}$ is 3 which is a rational number whereas $\sqrt{2} \times \sqrt{4}$ is $\sqrt{8}$ which is an irrational number. As $\sqrt{3}, \sqrt{2}, \sqrt{4}$ are irrational.

Hence, option D is correct.

4. (a) $\sqrt{7}$ is an irrational number.

5. (b) 

$\sqrt{4} \times \sqrt{81}$ $= \sqrt{2^2} \times \sqrt{9^2}$ $= 2 \times 9$ = 18

6. Fill in the blanks.

Any two integers are separated by a finite number of other integers .

There are an endless amount of rational numbers between 15 and 18 .

$\mathrm{X}+\mathrm{Y}$ is a rational number if $\mathrm{x}$ and $\mathrm{y}$ are both rational numbers .

Value of $\sqrt[3]{8}$ is $\underline{2}$

7. Match The Column:

Explanation:

8. Given an example of two irrational numbers whose;

Product is an irrational number $\sqrt{6} \times \sqrt{3}=\sqrt{6 \times 3}=\sqrt{18}=3 \sqrt{2}$

Difference is a irrational number $\sqrt{6}-\sqrt{3}$ = $\sqrt{3}$

Division is an irrational number $\dfrac{\sqrt{6}}{\sqrt{3}}=\sqrt{\dfrac{6}{3}}=\sqrt{2}$

9. Simplify; $(\sqrt{5}+\sqrt{6})(\sqrt{5}-\sqrt{6})$ 

We know that, $(a+b)(a-b)=a^2-b^2$

= $\left((\sqrt{5})^2-(\sqrt{6})^2\right)$

10. $\sqrt[3]{1331}-\sqrt{100}+\sqrt{81}$

= $\sqrt[3]{11^3}-\sqrt{10^2}+\sqrt{9^2}$

= $11-10+9$

11. $\dfrac{11^{\dfrac{1}{2}}}{11^{\dfrac{1}{4}}}$

$\dfrac{11^{\dfrac{1}{2}}}{11^{\dfrac{1}{4}}}=11^{\dfrac{1}{2}-\dfrac{1}{4}}$

$=11^{\dfrac{2-1}{4}}$

$=11^{\dfrac{1}{4}}$

12. Let, 

$p= 0.777…$ ....   (1)

Multiply both side in above equation 10

Then, 

$10p= 7.777…$ ….(2)

Subtracting equation (1) from (2), we get;

$10p-p= 7.777… - 0.777…$

$p= \dfrac{7}{9}$

13. Three rational number between $\dfrac{9}{11}$ and $\dfrac{5}{11}$

Rational number of $\dfrac{9}{11}$ and $\dfrac{5}{11}$ is denominator same

$= \dfrac{9}{11}, \dfrac{8}{11}, \dfrac{7}{11}, \dfrac{6}{11}, \dfrac{5}{11}$

14. $\dfrac{\sqrt{8}+\sqrt{12}}{\sqrt{32}+\sqrt{48}}$

$= \dfrac{\sqrt{2^3}+\sqrt{4 \times 3}}{\sqrt{8 \times 4}+\sqrt{8 \times 6}}$

$= \dfrac{2 \sqrt{2}+2 \sqrt{3}}{4 \sqrt{2}+4 \sqrt{3}}$

$= \dfrac{2(\sqrt{2}+\sqrt{3})}{4(\sqrt{2}+\sqrt{3})}$

$= \dfrac{(\sqrt{2}+\sqrt{3})}{2(\sqrt{2}+\sqrt{3})}$

$= \dfrac{1}{2}$

15. If $a=2$ and $b=3$

The value of $a^b+b^a$

$= 2^3+3^2$

16. $2^{\dfrac{2}{3}} \cdot 2^{\dfrac{1}{5}}$

$2^{\dfrac{2}{3}} \cdot 2^{\dfrac{1}{5}}=2^{\dfrac{2}{3}+\dfrac{1}{5}} \quad \because a^p \cdot a^q=a^{p+q}$

$=2^{\dfrac{10+3}{15}}$

$=2^{\dfrac{13}{15}}$

17. Value of $\dfrac{1}{a^b+b^a}$, where $a=5, b=2$

$= \dfrac{1}{5^2+2^5}$

$= \dfrac{1}{25+32}$

$= \dfrac{1}{57}$

18. Here we have : $\sqrt[3]{2}, \sqrt{3}, \sqrt[5]{5}$

We can also write the expression in simpler form as follows:

$2^{\dfrac{1}{3}}, 3^{\dfrac{1}{2}}, 5^{\dfrac{1}{6}}$

Now we can see that in the denominators of the exponents we have: $3,2,6$

We will now take the LCM of $3,2,6$, which is 6 .

Now we will make all the denominators equal to 6 , so we have to multiply by the multiples in both numerator and denominator.

We can write the numbers as:

$2^{\dfrac{1}{3}} \times \dfrac{2}{2}=2^{\dfrac{2}{6}}$

For the second number we can write:

$3 \dfrac{1}{2} \times \dfrac{3}{3}=3 \dfrac{3}{6}$

Since in the third number we already have the desired denominator, so the third number is

$5^{\dfrac{1}{6}}$

Now we will again write the numbers in the root under, but we have to keep in mind that the numerator will turn as the exponential powers inside the root.

So we have the numbers as:

$\sqrt[6]{2^2}, \sqrt[5]{3^3}, \sqrt[5]{5}$

We will simplify the values inside the root, so we have:

$\sqrt[5]{4}, \sqrt[6]{27}, \sqrt[5]{5}$

From this we can write the smaller value in the front and then the larger value:

$\sqrt[5]{4}, \sqrt[6]{5}, \sqrt[5]{27}$

Hence the original numbers in ascending form are:

$\sqrt[3]{2}, \sqrt[6]{5}, \sqrt{3}$

19. $(4 \sqrt{5}+3 \sqrt{7})^2$

We know that,

$(a+b)^2=a^2+b^2+2 a b$

$=(4 \sqrt{5})^2+(3 \sqrt{7})^2+2 \times (4 \sqrt{5}) (3 \sqrt{7})$

$=80+63+24 \sqrt{5 \times 7}$

$=143+24 \sqrt{35}$

20. $\left(\dfrac{y}{x}\right)^{2 a-8}=\left(\dfrac{x}{y}\right)^{a-1}$

$\left(\dfrac{y}{x}\right)^{2 a-8}=\left(\dfrac{x}{y}\right)^{8-2 a}$   $ \because (x)^{-a}=\dfrac{1}{x^a}$

$\left(\dfrac{x}{y}\right)^{8-2 a}=\left(\dfrac{x}{y}\right)^{a-1}$

When the bases of both sides of an equation are the same, then their exponents are also equal.

$\Rightarrow 8-2 a=a-1$

$\Rightarrow 2 a+a=8+1$

$\Rightarrow 3 a=9$

$\Rightarrow a=\dfrac{9}{3}$

$\Rightarrow a=3$

21. $\dfrac{1}{\sqrt{7}}=\dfrac{1}{\sqrt{7}} \times \dfrac{\sqrt{7}}{\sqrt{7}}$

(Dividing and multiplying by $\sqrt{7}$ )

$=\dfrac{\sqrt{7}}{7}$

22. Writing $\pi$ as $\dfrac{22}{7}$ is only an approximate value and so we can't conclude that it is in the form of a rational. In fact, the value of $\pi$ is calculating as non-terminating, non-recurring decimal as $\pi=3.14159$ Whereas

If we calculate the value of $\dfrac{22}{7}$ it gives $3.142857$ and hence $\pi \neq \dfrac{22}{7}$

In conclusion $\pi$ is an irrational number.

23. Let $x=0.001001 \ldots \ldots$ (1)

Since 3 digits are repeated multiply both the sides of (1) by 1000

$1000 x=1.001001 \ldots$

$1000 x=1+0.001001 \ldots$

$1000 x=1+x$

$1000 x-x=1$

$x=\dfrac{1}{999}$

$\therefore 0 . \overline{001}=\dfrac{1}{999}$

24. Since we make the denominator the same first, then

$\dfrac{3}{4}=\dfrac{3 \times 5}{4 \times 5}=\dfrac{15}{20}$

$\dfrac{4}{5}=\dfrac{4 \times 4}{5 \times 4}=\dfrac{16}{20}$

Now we need to find 5 rational no.

$\dfrac{15}{20}  =\dfrac{15 \times 6}{20 \times 6}=\dfrac{90}{120}$

$\dfrac{16}{20}=\dfrac{16 \times 6}{20 \times 6}=\dfrac{96}{120}$

$\therefore$ Five rational numbers between $\dfrac{3}{4}$ and $\dfrac{4}{5}$ are $\dfrac{91}{120}, \dfrac{92}{120}, \dfrac{93}{120}, \dfrac{94}{120}$ and $\dfrac{95}{120}$

25. We can find any number of rational numbers between two rational numbers. First of all, we make the denominators same by multiplying or dividing the given rational numbers by a suitable number. If denominator is already same then depending on number of rational no. we need to find in question, we add one and multiply the result by numerator and denominator.

$3=\dfrac{3 \times 7}{7} \text { and } \quad 4=\dfrac{4 \times 7}{7}$

$3=\dfrac{21}{7} \quad \text { and } \quad 4=\dfrac{28}{7}$

We can choose 6 rational numbers as: $\dfrac{22}{7}, \dfrac{23}{7}, \dfrac{24}{7}, \dfrac{25}{7}, \dfrac{26}{7}$ and $\dfrac{27}{7}$

Benefits of Learning Number System in Class 9 Chapter 1 Maths Worksheet The Class 9 Maths Chapter 1 worksheet pdf contains more than enough material to help students better understand what number systems are and how to solve them. The worksheets come with extensive questions, attempting to clear any doubts the students might have about the number system and their types.

The Maths assignment for Class 9 Number System list of questions and answers provide thorough insights on the topic’s resources and offers easy tricks to identify quicker ways to solve the questions faster while also being more aware and making sure students don’t go wrong or commit any silly mistakes in their solutions.

All of these worksheets have been developed by the best mathematicians and experienced arithmetic representatives who are very aware of the needs and requirements of the students of Class 9.

Examples of Usage of Number System for Class 9

These are a few examples of Maths assignments for Class 9 Number System exercises’ examples :

Answer the following.

Find two irrational numbers and two rational numbers between 0.7 and 0.77.

Every integer is not a whole number. True or false?

Find at least 7 rational numbers between 2 and 9.

Write down 4567 in the decimal and binary number systems.

Is 0 a rational number? State your reasons based on your answer.

Interesting Facts About Number System for Class 9

There are nine types of number systems in mathematics. They are :

Natural numbers

Whole numbers

Rational numbers

Irrational numbers

Real numbers

Imaginary numbers

Prime and composite numbers

Natural numbers are the root forms of numbers between 0 to infinity. They are also named “positive numbers” or “counting numbers” and are represented by the symbol N. (1, 2, 3, 4, 5 and so on)

Whole numbers are natural numbers, with the only difference being the inclusion of 0. They are represented by the symbol W. (0, 1, 2, 3, 4, 5 and so on)

Integers contain whole numbers and the negative values of natural numbers and don’t include fractions, so their numbers can’t be written in the “a/b” format. It ranges from infinity at the negative end to infinity at the positive end, including 0 and is represented by Z. (...-3, -2, -1, 0, 1, 2, 3… and so on)

Fractions are numbers written in the “a/b” format, where “a” (numerator) is a whole number, and “b” (denominator) is a natural number. Hence, the denominator can never be 0. (2/4, 0/10, 5/7, etc.)

Rational numbers can be written in fractions where “a” and “b” are both integers and b ≠ 0. All fractions are rational numbers, but all rational numbers are not fractions.(-5/9, 3/9, -8/14, etc)

Irrational numbers are numbers that can’t be written in fractional forms. (√8, √.127, √3.209, etc)

Real numbers can be written in decimals, including whole numbers, integers, fractions, etc. All integers belong to real numbers, but not all real numbers belong to integers. (1.25, 0.467, 8.9, etc.)

Imaginary numbers are not real numbers, resulting in negative numbers when squared or put together. They are also named complex numbers and are represented by the symbol i. (√-3, √-16, √-1, etc.)

Numbers that don’t have other factors except 1 are called prime numbers, and the rest of the numbers - except 0 - are called composite numbers, as 0 is neither a prime nor a composite number. ( 2, 3, 5… are prime numbers whereas 4, 6, 8… are composite numbers)

Other definitions and elaborated explanations will be provided in the operations on real numbers class 9 worksheet pdf and more .

Important Topics for Class 9 Number System

The important topics students will have to learn in the number system syllabus for Class 9 are as follows :

What are number systems, and how to solve them?

What are the four types of number systems?

How to convert one number system to another number system.

Solving the problems and choosing the correct answer.

Various other exercises in the Number System Class 9 worksheet

What does the PDF Consist of?

Most schools have syllabuses that don’t include just spoon-feeding the information to the students.

It only means that the students must learn by themselves, with the teachers guiding and aiding them throughout their learning process.

With technology being part of most school curriculums, a huge part of their assignments, tests, and worksheets are online, favoured as pdfs.

Vedantu’s pdf format is highly sought-after as it is used for creating, editing, highlighting, saving, and sharing content.

The worksheet for Class 9 Maths Chapter 1 with Solutions pdfs is free for download at Vedantu’s website.

Rest assured, all the worksheets adhere to the CBSE guidelines' strict, updated, and revised rules.

Many other Number Systems Class 9 worksheet pdfs are present at Vedantu’s platform, created by their own arithmetic subject matter experts, ensuring that the students receive the best training and exercises needed to test their skills and excel in their examinations.

FAQs on CBSE Class 9 Maths Worksheet Chapter 1 Number System

1. Which number system is frequently used?

The decimal number system is the most widely used.

2. How are the values of various figures calculated?

All these figures carry their values, and these values can be determined by: 

looking at the digit 

the position in the number 

the base of the number. 

3. Can rational numbers be whole numbers?

No, since rational numbers may be fractional and whole numbers are not.

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When we type some letters or words, the computer translates them in numbers as computers can understand only numbers. A computer can understand the positional number system where there are only a few symbols called digits and these symbols represent different values depending on the position they occupy in the number.

The value of each digit in a number can be determined using −

The position of the digit in the number

The base of the number system (where the base is defined as the total number of digits available in the number system)

Decimal Number System

The number system that we use in our day-to-day life is the decimal number system. Decimal number system has base 10 as it uses 10 digits from 0 to 9. In decimal number system, the successive positions to the left of the decimal point represent units, tens, hundreds, thousands, and so on.

Each position represents a specific power of the base (10). For example, the decimal number 1234 consists of the digit 4 in the units position, 3 in the tens position, 2 in the hundreds position, and 1 in the thousands position. Its value can be written as

As a computer programmer or an IT professional, you should understand the following number systems which are frequently used in computers.

Binary Number System

Characteristics of the binary number system are as follows −

Uses two digits, 0 and 1

Also called as base 2 number system

Each position in a binary number represents a 0 power of the base (2). Example 2 0

Last position in a binary number represents a x power of the base (2). Example 2 x where x represents the last position - 1.

Binary Number: 10101 2

Calculating Decimal Equivalent −

Note − 10101 2 is normally written as 10101.

Octal Number System

Characteristics of the octal number system are as follows −

Uses eight digits, 0,1,2,3,4,5,6,7

Also called as base 8 number system

Each position in an octal number represents a 0 power of the base (8). Example 8 0

Last position in an octal number represents a x power of the base (8). Example 8 x where x represents the last position - 1

Octal Number: 12570 8

Note − 12570 8 is normally written as 12570.

Hexadecimal Number System

Characteristics of hexadecimal number system are as follows −

Uses 10 digits and 6 letters, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

Letters represent the numbers starting from 10. A = 10. B = 11, C = 12, D = 13, E = 14, F = 15

Also called as base 16 number system

Each position in a hexadecimal number represents a 0 power of the base (16). Example, 16 0

Last position in a hexadecimal number represents a x power of the base (16). Example 16 x where x represents the last position - 1

Hexadecimal Number: 19FDE 16

Note − 19FDE 16 is normally written as 19FDE.

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Electronic and Digital systems may use a variety of different number systems, (e.g. Decimal, Hexadecimal, Octal, Binary), or even Duodecimal or less well known but better named Uncial. All the other bases other than Decimal result from computer usage. Uncial (named from Latin for 1/12 “uncia” the base twelve analogue of Decimal from the Latin word for 1/10 “decima”). 

A number N in base or radix b can be written as: 

In the above, d n-1 to d 0 is the integer part, then follows a radix point, and then d -1 to d -m is the fractional part. 

d n-1 = Most significant bit (MSB)  d -m = Least significant bit (LSB)

How to convert a number from one base to another?

Follow the example illustrations: 

1. Decimal to Binary

(10.25) 10  

Note: Keep multiplying the fractional part with 2 until decimal part 0.00 is obtained.  (0.25) 10 = (0.01) 2  

Answer: (10.25) 10 = (1010.01) 2   

2. Binary to Decimal

3. decimal to octal.

Note: Keep multiplying the fractional part with 8 until decimal part .00 is obtained.  (.25) 10 = (.2) 8

Answer: (10.25) 10 = (12.2) 8    

4. Octal to Decimal

5. hexadecimal to binary.

To convert from Hexadecimal to Binary, write the 4-bit binary equivalent of hexadecimal.

(3A) 16 = (00111010) 2  

6. Binary to Hexadecimal

To convert from Binary to Hexadecimal, start grouping the bits in groups of 4 from the right-end and write the equivalent hexadecimal for the 4-bit binary. Add extra 0’s on the left to adjust the groups. 

7. Binary to Octal

To convert from binary to octal, start grouping the bits in groups of 3 from the right end and write the equivalent octal for the 3-bit 

binary. Add 0’s on the left to adjust the groups.

111 101 101

(111101101) 2 = (755) 8  

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Important Questions and Notes

Chapter 2 Number System Class 11 Computer Science NCERT Solution

Encoding scheme & number system class 11 computer science ncert solution, q1. write base values of binary, octal and hexadecimal number system..

Show Answer Ans. Base value of binary – 2

Base value of Octal – 8

Base value of Hexadecimal – 16

Q2. Give full form of ASCII and ISCII.

Show Answer Ans. Full forms are :

ASCII : American Standard Code for Information Interchange

ISCII : Indian Script Code for Information Interchange

Q3. Try the following conversions. (Number after bracket is showing the base)

(i) (514) 8  = (?) 10

(ii) (220) 8 = (?) 2

(iii) (76F) 16  = (?) 10

(iv) (4D9) 16  = (?) 10

(v) (11001010) 2  = (?) 10

(vi) (1010111) 2  = (?) 10

Show Answer Ans. i) (514) 8  = (332) 10

ii) (220) 8 = (10010000) 2

iii) (76F) 16  = (1903) 10

iv) (4D9) 16  = (1241) 10

v) (11001010) 2  = (202) 10

vi) (1010111) 2  = (87) 10

Q4. Do the following conversions from decimal number to other number systems.

(i) (54) 10  = (?) 2

(ii) (120) 10  = (?) 2

(iii) (76) 10  = (?) 8

(iv) (889) 10  = (?) 8

(v) (789) 10  = (?) 16

(vi) (108) 10   = (?) 16

Show Answer Ans. (i) (54) 10  = (110110) 2

(ii) (120) 10  = (1111000) 2

(iii) (76) 10  = (114 )8

(iv) (889) 10  = (1571) 8

(v) (789) 10  = (315) 16

(vi) (108) 10   = (6C) 16

Q5. Express the following octal numbers into their equivalent decimal numbers.

Show Answer Ans. (i) (145) 8  = (101) 10

(ii) (6760) 8  = (3568) 10

(iii) (455) 8  = (301) 10

(iv) (10.75) 8  = (8.953125) 10

Q6. Express the following decimal numbers into hexadecimal numbers.

(iv) 100.25

Show Answer Ans. (548) 10  = (224) 16

(ii) (4052) 10  = (FD4) 16

(iii) (58) 10  = (3A) 16

(iv) (100.25) 10  = (64.4) 16

Q7. Express the following hexadecimal numbers into equivalent decimal numbers.

Show Answer Ans. (i) (4A2) 16 = (1186) 10

(ii) (9E1A) 16  = (40474) 10

(iii) (6BD) 16  = (1725) 10

(iv) (6C.34) 16  = (108.203125) 10

Q8. Convert the following binary numbers into octal and hexadecimal numbers.

(i) 1110001000

(ii) 110110101

(iii) 1010100

(iv) 1010.1001

Show Answer Ans. (i) (1110001000) 2  = (1610) 8 = (388) 16

(ii) (110110101) 2  = (665) 8 = (1B5) 16

(iii) (1010100) 2  = (124) 8 = (54) 16

(iv) (1010.1001) 2  = (12.44) 8 = (A.9) 16

Q9. Write binary equivalent of the following octal numbers.

(iv) 65.203

Show Answer Ans. (i) (2306) 8  = (10011000110) 2

(ii) (5610) 8  = (101110001000) 2

(iii) (742) 8  = (111100010) 2

(iv) (65.203) 8  = (110101.010000011) 2

Q10. Write binary representation of the following hexadecimal numbers.

(iv) 132.45

Show Answer Ans. (i) (4026) 16  = (100000000100110) 2

(ii) (BCA1) 16  = (1011110010100001) 2

(iii) (98E) 16  = (100110001110) 2

(iv) (132.45) 16  = (100110010.01000101 2 )

Q11. How does computer understand the following text? (hint: 7 bit ASCII code).

Show Answer Ans.

ASCII value of H is 72 and its equivalent 7-bit binary code = 1001000

ASCII value of O is 79 and its equivalent 7-bit binary code = 1001111

ASCII value of T is 84 and its equivalent 7-bit binary code = 1010100

ASCII value of S is 83 and its equivalent 7-bit binary code = 1010011

Binary equivalent of complete word “HOTS” is given below :

HOTS = 1001000100111110101001010011

ASCII value of ‘M’ is 77 and its equivalent 7-bit binary code = 1001101

ASCII value of ‘a’ is 97 and its equivalent 7-bit binary code = 1100001

ASCII value of ‘i’ is 105 and its equivalent 7-bit binary code = 1101001

ASCII value of ‘n’ is 110 and its equivalent 7-bit binary code = 1101110

Binary equivalent of complete word “Main” is given below :

Main = 1 001101110000111010011101110

ASCII value of ‘C’ is 67 and its equivalent 7-bit binary code = 1000011

ASCII value of ‘S’ is 83 and its equivalent 7-bit binary code = 1010011

ASCII value of ‘e’ is 101 and its equivalent 7-bit binary code = 1101110

Binary equivalent of complete word “CaSe” is given below :

CaSe = 1000011 110000110100111100101

Q12. The hexadecimal number system uses 16 literals(0–9, A–F). Write down its base value.

Show Answer Ans. 16

Q13. Let X be a number system having B symbols only. Write down the base value of this number system.

Show Answer Ans. Base value of this number system is B.

As we know the number of symbols is equal to base number like in binary there are two symbols so base value is two similarly in Octal, Decimal and Hexadecimal

Q14. Write the equivalent hexadecimal and binary values for each character of the phrase given below. ‘‘ हम सब एक”

Show Answer Ans .

Q15. What is the advantage of preparing a digital content in Indian language using UNICODE font?

Show Answer Ans. The most important advantage of UNICODE is that we need not to add/install these fonts in our system . These are rendered automatically in the system.

Q17. Encode the word ‘COMPUTER’ using ASCII and convert the encode value into binary values.

Binary code of ‘COMPUTER’ is :

10000111001111100110110100001010101101010010001011010010

Number System Class 11 Computer Science

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Class 9 Mathematics Number System Assignments

We have provided below free printable Class 9 Mathematics Number System Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 9 Mathematics Number System . These Assignments for Grade 9 Mathematics Number System cover all important topics which can come in your standard 9 tests and examinations. Free printable Assignments for CBSE Class 9 Mathematics Number System , school and class assignments, and practice test papers have been designed by our highly experienced class 9 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Number System Class 9 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Number System Class 9. Students can click on the links below and download all Pdf Assignments for Mathematics Number System class 9 for free. All latest Kendriya Vidyalaya Class 9 Mathematics Number System Assignments with Answers and test papers are given below.

Mathematics Number System Class 9 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 9 Mathematics Number System . Students and teachers can download and save all free Mathematics Number System assignments in Pdf for grade 9th. Our expert faculty have covered Class 9 important questions and answers for Mathematics Number System as per the latest syllabus for the current academic year. All test papers and question banks for Class 9 Mathematics Number System and CBSE Assignments for Mathematics Number System Class 9 will be really helpful for standard 9th students to prepare for the class tests and school examinations. Class 9th students can easily free download in Pdf all printable practice worksheets given below.

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Number System Conversion

As we know, the number system is a form of expressing the numbers. In number system conversion , we will study to convert a number of one base, to a number of another base. There are a variety of number systems such as binary numbers, decimal numbers, hexadecimal numbers, octal numbers, which can be exercised.

In this article, you will learn the conversion of one base number to another base number considering all the base numbers such as decimal, binary, octal and hexadecimal with the help of examples. Here, the following number system conversion methods are explained.

• Binary to Decimal Number System
• Decimal to Binary Number System
• Octal to Binary Number System
• Binary to Octal Number System
• Binary to Hexadecimal Number System
• Hexadecimal to Binary Number System

Get the pdf of number system with a brief description in it. The general representation of number systems are;

Decimal Number – Base 10 – N 10

Binary Number – Base 2 – N 2

Octal Number – Base 8 – N 8

Hexadecimal Number – Base 16 – N 16

Number System Conversion Table

Number system conversion methods.

Number system conversions deal with the operations to change the base of the numbers. For example, to change a decimal number with base 10 to binary number with base 2. We can also perform the arithmetic operations like addition, subtraction, multiplication on the number system. Here, we will learn the methods to convert the number of one base to the number of another base starting with the decimal number system. The representation of number system base conversion in general form for any base number is;

(Number) b = d n-1 d n-2 —– . d 1 d 0 . d -1 d -2 —- d -m

In the above expression, d n-1 d n-2 —– . d 1 d 0 represents the value of integer part and d -1 d -2 —- d -m represents the fractional part.

Also, d n-1 is the Most significant bit (MSB) and d -m is the Least significant bit (LSB).

Now let us learn, conversion from one base to another.

Decimal to Other Bases

Converting a decimal number to other base numbers is easy. We have to divide the decimal number by the converted value of the new base.

Decimal to Binary Number:

Suppose if we have to convert  decimal to binary , then divide the decimal number by 2.

Example  1.  Convert (25) 10 to binary number.

Solution: Let us create a table based on this question.

Therefore, from the above table, we can write,

(25) 10 = (11001) 2

Decimal to Octal Number:

To convert decimal to octal number we have to divide the given original number by 8 such that base 10 changes to base 8. Let us understand with the help of an example.

Example 2: Convert 128 10 to octal number.

Solution: Let us represent the conversion in tabular form.

Therefore, the equivalent octal number = 200 8

Decimal to Hexadecimal:

Again in decimal to hex conversion , we have to divide the given decimal number by 16.

Example 3: Convert  128 10 to hex.

Solution: As per the method, we can create a table;

Therefore, the equivalent hexadecimal number is 80 16

Here MSB stands for a Most significant bit and LSB stands for a least significant bit.

Other Base System to Decimal Conversion

Binary to Decimal:

In this conversion, binary number to a decimal number, we use multiplication method, in such a way that, if a number with base n has to be converted into a number with base 10, then each digit of the given number is multiplied from MSB to LSB with reducing the power of the base. Let us understand this conversion with the help of an example.

Example 1 . Convert (1101) 2 into a decimal number.

Solution: Given a binary number (1101) 2 .

Now, multiplying each digit from MSB to LSB with reducing the power of the base number 2.

1 × 2 3 + 1 × 2 2 + 0 × 2 1 + 1 × 2 0

= 8 + 4 + 0 + 1

Therefore, (1101) 2 = (13) 10

Octal to Decimal:

To convert octal to decimal, we multiply the digits of octal number with decreasing power of the base number 8, starting from MSB to LSB and then add them all together.

Example 2: Convert 22 8 to decimal number.

Solution: Given, 22 8

2 x 8 1 + 2 x 8 0

Therefore, 22 8  = 18 10

Hexadecimal to Decimal:

Example 3: Convert 121 16 to decimal number.

Solution: 1 x 16 2 + 2 x 16 1  + 1 x 16 0

= 16 x 16 + 2 x 16 + 1 x 1

Therefore, 121 16 = 289 10

Hexadecimal to Binary Shortcut Method

To convert hexadecimal numbers to binary and vice versa is easy, you just have to memorize the table given below.

You can easily solve the problems based on hexadecimal and binary conversions with the help of this table. Let us take an example.

Example:  Convert (89) 16 into a binary number.

Solution: From the table, we can get the binary value of 8 and 9, hexadecimal base numbers.

8 = 1000 and 9 = 1001

Therefore, (89) 16 = (10001001) 2

Octal to Binary Shortcut Method

To convert octal to binary number, we can simply use the table. Just like having a table for hexadecimal and its equivalent binary, in the same way, we have a table for octal and its equivalent binary number.

Example:  Convert (214) 8 into a binary number.

Solution: From the table, we know,

Therefore,(214) 8 = (010001100) 2

Practice Problems on Number System Conversion

• Convert 146 10 into a binary number system
• Convert  1A7 16 into the decimal number system
• Convert (110010) 2 into octal number system
• Convert DA2 16 into the binary number system
• Convert 4652 8  into the binary number system

Frequently Asked Question on the Number System Conversion

Why do we need the number system conversion.

One of the most important applications of the number system is in computer technology. Generally, a computer uses the binary number system, but humans will use the hexadecimal number system, as it is easier to understand. For this reason, the number system conversion is required.

What is meant by the base 2 number system?

The base 2 number system is called the binary number system. It uses only two digits, such as 0, 1. For example, the number 6 is represented by 0110 (or) 110.

Write down the conversion procedure from decimal to binary number system?

The steps to convert the decimal number system to binary number system are: Divide the given number by 2 Now, use the obtained quotient for the next iteration Obtain the remainder for the binary number Repeat the steps until the quotient is equal to 0

What is meant by the base 8 number system?

The base 8 number system is called the octal number system. It uses the digits such as 0, 1, 2, 3, 4, 5, 6, 7.

What is meant by the hexadecimal number system?

The hexadecimal number system is called the base 16 number system. It uses the digits from 0 to 9, and A, B, C, D, E, F

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Class 7 Computer Chapter 1: Number System

• 1 What is Number System?
• 2.1 1.Decimal number system
• 2.2 2. Binary number system
• 2.3 3. Octal number system
• 2.4 4. Hexadecimal number system
• 3 Table of Number Systems
• 4 Number System Conversions
• 5.1 Number System – Fill in the Blanks
• 5.2 Number System – True or False
• 5.3 Number System- Application based Questions
• 5.4 Number System- Multiple Choice Questions
• 5.5 Number System- Answer the Following Questions
• 5.6 Number System – Lab Session Activity
• 5.7 Find the Difference between the following:
• 5.8 Multiply the following Binary numbers:

What is Number System?

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.

Type of Number system :

There are 4 types of number system:

• Decimal number system.
• Binary number system.
• Octal number system.
• Hexadecimal number system.

1.Decimal number system

Decimal number system has only ten 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.

2. Binary number system

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

Also See: Binary to Text converter

3. Octal number system

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 octal number system is 8, because it has only 8 digits.

4. Hexadecimal number system

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 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.

Table of Number Systems

Number system conversions.

• Decimal to Binary
• Binary to Decimal
• Decimal to Octal
• Octal to Decimal
• Octal to Binary
• Binary to Octal
• Decimal to Hexadecimal
• Hexadecimal to decimal

Class 7 Computer Chapter 1-Number System Solutions

Number system – fill in the blanks.

Q1: The base of binary number system is __________.

Ans: The base of binary number system is __ 2 ___.

Q2 : The base of ___________ number system is 10.

Ans: The base of Decimal number system is 10.

Q3: Octal number system consists of ___________ digits.

Ans: Octal number system consists of 8 digits

Q4: In Binary addition, 1+1 equals to ____________.

Ans: In Binary addition, 1+1 equals to 0 with 1 carry .

Q5: ____________ number system is understood by computer system.

Ans: Binary number system is understood by computer system.

Q6: ___________ number system uses 16 digits, from 0 to 9 and letters A to F.

Ans: Hexadecimal number system uses 16 digits, from 0 to 9 and letters A to F.

Q7: In Binary subtraction, 1-1 equals to __________.

Ans: In Binary subtraction, 1-1 equals to 0 .

Number System – True or False

Q1: You cannot perform arithmetic operations on binary numbers.

Ans: False.

Q2: Decimal number system consists of 10 digits, i.e. 0 to 9.

Q3: Method to perform division of two binary numbers is not hte same as decimal numbers.

Q4: 1 multiplied by 0 equal to 0.

Q5: Charles Babbage introduce the concept of 0(zero).

Q6: The numbers used in octal number system are 1 to 7.

Number System- Application based Questions

Q1: Sonam’s computer teacher has asked her to convert an octal number to decimal. Suggest the method which she should use to convert octal number.

Ans: To convert an octal number to decimal number, start multiplying the digits of the number from the right hand side with increasing power of 8 starting from 0 and then calculating the sum of all the products.

Q2: The teacher has given assignment to Shubham on binary subtraction. Shubham is confused about how to subtract 1 from 0. Help him solving the problem.

Ans: The number is borrowed when 1 is subtracted from 0 (10-1=1).

Number System- Multiple Choice Questions

Q1: ____________ introduced the concept of 0(zero).

a) Ada lovelace b) Aryabhat c) Charles Babbage

Ans: Aryabhat .

Q2: A ___________ converts the decimal format into its binary equivalent.

a) Digital computer b) Cell phone c) Abacus

Ans: Digital computer

Q3: A computer understand only the ________ code.

a) English b) French c) Binary

Ans: Binary

Q4: In Binary multiplication, 1 X 1 equals to _____________.

a) 0 b) 1 c) 2

Q5: To convert a decimal number into a binary number, divide the number by _______.

a) 2 b) 8 c) 10

Number System- Answer the Following Questions

Q1: What are the rules to convert a decimal number into a binary number?

Ans: To convert a decimal number into a binary number, follow the below given steps:

• Divide the given decimal number with base 2.
• Write down the remainder and divide the quotient again by 2.
• Repeat the step 2 till the quotient is 0.
• Wtite the remainders obtained in each step in the reverse order to form the binary equivalent of the given decimal number, i.e., placing the least significant digit at the top and most significant digit at the bottom.

Q2: What are the rules to multiply two binary numbers?

Ans: The rules for performing multiplication using binary numbers is same as that of decimal numbers. The given table illustrate the multiplication of two binary digits.

Number System – Lab Session Activity

Q1: Convert the following decimal numbers into binary.

Ans: 1000100

Ans: 1111011011

Ans: 1010010001

Q2: Convert the following binary number into decimal.

Q3) Perform the binary addition on the following numbers

a) 10101+00111

Ans: Binary value: 10101+00111= 011100 , Decimal value: 21+7= 28 .

b) 1000101101+1001101

Ans: Ans: Binary value: 1000101101+1001101= 01001111010 , Decimal value: 557+77= 634 .

c) 1101+1001

Ans: Ans: Binary value: 1101+1001= 010110 , Decimal value: 13+9= 22 .

Find the Difference between the following:

a) 10011-01010

Ans: Binary value: 10011-01010= 01001

Decimal value: 19-10= 9

b) 11001001-01100110= 01100011

Ans: Binary value: 11001001-01100110= 01100011

Decimal value: 201-102= 99

Ans: Binary value: 111-001= 0110

Decimal value: 7-1= 6

Multiply the following Binary numbers:

a) 101 X 011

Ans: Binary value: 101 X 011= 01111

Decimal value: 5 X 3= 15

b) 1011 X 101

Ans: Binary value: 1011 X 101= 0110111

Decimal value: 11 X 5= 55

c) 101010 X 1011

Ans: Binary value: 101010 X 1011= 0111001110

Decimal value: 42 X11= 462

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