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Number System in Maths

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Number System in Maths

The fundamentals of Maths begins with the numbers that help us in counting objects. Apart from the counting numbers, we have learned other different types of numbers such as Whole numbers, Natural numbers, Integers, Even and Odd numbers, Rational and irrational numbers etc., used for mathematical calculations.

But these basic numbers are not useful for computer applications, since computers understand the language of 0’s and 1’s. The information is transmitted in the form of these two digits to the computers. After the computation is done by computer, the translator will again translate the computer language into human language. The bit is the smallest storage unit that uses only two digits (0’s and 1’s). And a collection of 8 bits is equal to one byte. 

Types of Number System

There are four types of number systems:

  1. Binary Number System
  2. Decimal Number System
  3. Hexadecimal Number System
  4. Octal Number System

Binary Number System

Binary numbers are the numbers that are represented with a base 2, using only two digits, i.e., 0’s and 1’s. Therefore, a binary number system is also called a base-2 number system. For example, 11102 is a binary number.

Decimal Number System

A decimal number system is a number system where the numbers are represented with a base 10. It uses digits from 0 to 9 (0,1,2,3,4,5,6,7,8,9). For example, 7410 is a decimal number, where 4 is in one unit place and 7 is in tens unit place, such that;

7 x 101 + 4 x 100 = 70 + 4 = 74

Octal Number System

In the octal number system, numbers are expressed with base-8. It uses digits from 0 to 7 only to represent a number.  For example, 458 is an octal number.

Each octal number is represented by three binary digits (0’s and 1’s).

0 2 3 4 5 6 7
000 001 010 011 100 101 110 111

Let us convert 678 into an equivalent binary number. 

From the table above, we can see 6 is equivalent to 110 and 7 is equivalent to 111. Therefore,

678 → 1101112 

The table given above is helpful to convert an octal number into its equivalent binary form. In the same way, it will be helpful to solve a variety of number system questions as well. A similar kind of table we can see the next number system as well. Let us proceed.

Hexadecimal Number System

In a hexadecimal number system, the numbers are expressed with a base-16. Example, 13116 is a hexadecimal number. In this number system, we use the digits from 0 to 9, similar to the decimal number system and later we use alphabets (A, B, C, D, E and F) to represent the hexadecimal numbers. Each hexadecimal number is equivalent to 4-bit binary numbers.

Base-10 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Base-16 0 2 3 4 5 6 7 8 9 A B D E F
Base-2 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111

For example, convert 8B16 into binary numbers. 

From the table, 

8 → 1000

B → 1011

Therefore, 8B16 = (10001011)2

The number system in Maths is one of the important topics to be learned so that students can use it for computer applications.