Learn about Number System – Definition, Types, Examples!

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Basic Concepts on Numbers & Number System:

What is a number?

A number system is a representation of numbers that are used for counting or measuring objects according.It is only the mathematical representation of numbers. Numbers are used to performing arithmetic calculations. We can represent various numbers such as natural numbers, complex numbers, whole numbers etc. in various forms.

Types of number system:- There are various types of number system as under:


Decimal number system:-

As the name indicates, decimal means 10. So a decimal system is a number system having base-10. It only uses 10 digits which are 0,1,2,3,4,5,6,7,8,9. These are a total 10 digits. In a decimal system the successive positions to the left of the decimal represents ones, tens, hundreds, thousands, one thousands, and so on. In the decimal number system, every position is represented as a power of the base 10. For example, 

In number system, 247 is represented as:-

  • 247 = (2×10^2)+(4×10^1)+(7×10^0)

              = 200+40+7


  • In number system 3838, can be represented as :-

           3838 = (3×10^3)+(8×10^2)+(3×10^1)+(8×10^0)

                     = 3000+800+30+8

                     = 3838

Binary number system:-

As the name indicates binary means 2. So a number is said to be represented in the binary number system if it has base 2. The figures represented using this number system are known as binary numbers. For example, in binary number system 14 is represented as:-



14 = (1110)^2


Octal number system:-

As the name indicates, octal means 8. So the octal number system is a system which has base 8 and it uses only 8 digits which are 0,1,2,3,4,5,6,7 i.e. 0 to 7. For example:

  • 235^8
  • 346^8 
  • 560^8

In these examples, all the digits are from 0 to 7 so these numbers are represented in the octal number system.


Hexadecimal number system:-

In the hexadecimal system, the numbers are represented with the base 16. The hexadecimal system uses 10 digits and 6 alphabets to represent a number with base 16. The 10 digits used in this system are 0,1,2,3,4,5,6,7,8,9 and the alphabets used are A,B,C,D,E,F. So in total these are 16.


Number System Questions & Answers - Sample

Que 1:- How 10 is represented in the binary number system?

  1. (1101)^2 

  2. (1010)^2

  3. (1111)^2

  4. (1100)^2

Ans Option 2 is the correct option


Que 2:- How can 340 be represented in the decimal number system?

  1. (3×10^2)+(0×10^1)+(4×10^0)

  2. (4×10^2)+(4×10^1)+(0×10^0)

  3. (3×10^2)+(4×10^1)+(0×10^0)

  4. (0×10^2)+(4×10^1)+(3×10^0)

Ans Option 3 is the correct option


Que 3 Convert (110)^2  into the decimal number system.

  1. 14

  2. 12

  3. 18

  4. 22

Ans Option 2 is the correct option.

Need Help in converting decimals to binary number systems?

Numbers and different number systems play a very important role in our  daily life. Everything we do from looking at the wall clock first thing in the morning to having only 2 toasts in the morning breakfast to writing complex computer software programs depends on the numbers. 

We learn the concepts of numbers starting with whole numbers and numerical operations with base ten as early as elementary school. Students typically in 3rd and 4th grade may learn fractions as part of their Math curriculum. Also middle school students start their journey with a number system and understand different types of numbers & their applications such as plotting a positive and negative number on a number line, and differentiating between a rational number and irrational numbers. As students advance their grades, they also continue to learn new concepts and by the time they reach high school, students start to deal with math problems related to imaginary numbers & complex numbers. 

Not only this binary system is used widely by college level students in their study of computer science and engineering. Therefore, it is crucial for one to have a strong understanding & clarity on the concept of number system.

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