Number System

 Introduction:- 

Ten numerals we already are familiar with i.e, 0,1,2,3,4,5,6,7,8,9 are used for expressing any arbitrary number, popularly known as the decimal number system. Decimal numbers are used to represent numbers.Some other commonly used number systems are : binary, octal and hexadecimal number system. Decimal numbers having base 10 , Binary have base 2 , octal with base 8 and hexadecimal with base 16. 

Decimal Number system

The decimal number system has a base 10 and is a position-value system. Here the base 10 means that it contains ten unique symbols or digits i.e, 0,1,2,3,4,5,6,7,8,9. For expressing quantities exceeding nine, two or more digits are used. The placement of the digits is in the sequence from right to left which carry a specific meaning. 

For example: 4287 (four thousand two hundred eighty seven) more formally, we can write it as 

4287 = 4 × 10³ + 2 × 10² + 8 × 10¹ + 7 × 10⁰

Here 10 plays the role of a base or also called radix, hence the name decimal number system. Here 7 is the least significant digit whereas 6 is the most significant digit. 

9’s complements : It is determined by subtracting each digit in the number from nine. For example we have 25 , so the 9’s complement of 25 is 99-25 = 74 , 9’s complement of 2435 is 9999-2435 = 7564. 

9’s complement subtraction : The process is simple here, first of all we find 9’s complement of the given number and add carry to the result. For example:

Subtraction by using the 9’s complement method:- 08 from 14 

Regular subtraction will be 14-8 = 6                                 Using 9’s complement :     14+ 91 = 105    Where 91 is the 9’s complement of 08. i.e, 99-08 = 91.                                           Here in 105 1 is the carry that will be added in the result like 05+1 = 6 

One more example of 9’s complement subtraction: 235 from 572 

Regular subtraction: 572- 235 = 337                                 Using 9’s complement :   572 + 764 = 1336    Where 764 is 9’s complement of 235 like 999-235=764                          Here in result 1336 = 1 is the carry and that will be added in the result like   336+1= 337.