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Course Name – Number System and its Conversions

Course Description (Short) - Number system is the base for studying digital electronics which is a part of physics

Course Description (Long) – 

Electronics circuits and systems are divided into two categories analog and digital. 

Analog system 

An analog circuit uses continuous time voltages and currents. These circuits operate on continuous-valued signals (commonly referred to as analog signals).

Digital system 

The name 'digital' indicates that these systems work on 'digit' or 'digits'. The 'digit' means a single symbol of a number system and digital is the method of representing a number by discrete units. Thus Digital system works only on the digital signal that is they operate on signals that exist only at two levels - 0's and 1's.

Features of digital system

Digital electronics is one of the important branches as it is related to computer circuits, digital systems, digital communications, etc. Some important features of a digital system are

Information can be processed in digital systems. 

They have the memory to store the information.

They are relatively much easier to design and have higher accuracy.

They are less affected by noise, temperature, and aging.

They have a small size, low cost, low power, and high speed.

It is easy to communicate between digital systems. 


A number is a mathematical value used for counting or measuring or labeling objects. Numbers are used to perform 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. 

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. A number system is defined as the set of values used to represent a quantity for example number of students attending a particular lecture, the number of lectures per day, or marks obtained by a student. The study of the number system is not just limited to computers but is used in everyday life. By studying the number system we can get insight into how a computer processes and saves information. 

Number System, any of numerous sets of symbols and the rules for using them to denote numbers, which are used to state how many objects are there in a given set. Thus, the idea of “oneness” can be denoted by the Roman numeral I, by the Greek letter alpha α which was the first letter used as a numeral, by the Hebrew letter aleph which is the first letter used as a numeral, or by the modern number 1, which is nothing but a Hindu-Arabic in origin

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, and division.

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

The digit

Its position in the number

The base of the number system

 Base or Radix of a number system is the number of digits or basic symbols used in that system. Commonly used number systems are

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)

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.

Numbers can be represented in any of the number system categories like binary, decimal, hex, etc. Also, any number which is represented in any of the number system types can be easily converted to other. A number can be converted from one number system to another number system. 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. 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.

This course covers the entire concepts of the number system with their types, conversions, and questions. This topic is included in plain BSc, BSc Computer science, BScIT BCA, MCA, MSc, MSc Physics, MSc Statistics, MSc Mathematics, and Engineering. It is also included in various competitive examinations such as CET, Gate, NET, SET, etc

Course Category – Teaching & Academics – Science – Physics – Digital Electronics

Course Eligibility – HSC

Course Take away – 1) Introduction to number system

 2) Types of the Number system

 3) Conversion of numbers from 1 system to another

Course Structure – 

Introduction to Digital Electronics

Decimal Number system Conversion

Decimal to binary conversion

Decimal to octal conversion

Decimal to hexadecimal conversion

Decimal to any other number system conversion

Binary Number system conversion

Binary to Decimal conversion

Binary to octal conversion

Binary to hexadecimal conversion

Octal Number system conversion

Octal to Decimal Conversion

Octal to Binary Conversion

Octal to Hexadecimal Conversion

Hexadecimal Number system conversion

Hexadecimal to Decimal Conversion

Hexadecimal to Binary Conversion

Hexadecimal to Octal Conversion

Basic Requirement

  • HSC

Skills Covered

  • Introduction to number system

  • Types of Number system

  • Conversion of numbers from 1 system to another

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Course creator

                                 Dipti Parab