# Number Systems

In today’s world there has different number systems to perform different numerical work or we can say number representation .The most commonly used number systems are such as decimal, binary, octal, hexadecimal. And most familiar number system is the decimal number system. Now question is **what are the differences between different number systems?**

To finding the answer of this question we should know that those different number systems are classified by the value of their base of number systems. Now see how they classified

Decimal number systems :-The value of base is 10 so it is called decimal number system.

Hexadecimal number systems :-The value of base is 16 so it is called hexadecimal number system.

Octal number systems :– The value of base is 8 so it is called octal number system.

Binary number systems :-The value of base is 2 so it is called Binary number system.

Another important thing we should remember that the maximum value of any digit in any number system is** Base – 1**. So in

Decimal number systems :-The maximum value of single digit =base (10)-1 = 9. And the all 10 digits are 0, 1, 2,3, 4, 5, 6, 7, 8, 9.

Hexadecimal number systems :-The maximum value of single digit =base (16)-1 = 15. And the all 16 digits are 0, 1, 2,3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. Where the value of A, B, C, D, E, F are 10, 11, 12, 13, 14, 15 correspondingly.

Octal number systems :-The maximum value of single digit =base (8)-1 = 7. And the all 8 digits are 0, 1, 2,3, 4, 5, 6, 7, 8.

Binary number systems :-The maximum value of single digit =base (2)-1 = 1. And the all 2 digits are 0, 1.

In binary number systems if we want to express 9 (decimal number) in binary we may write 1001. The right most digit in this number system is called the ‘Least Significant Bit’ (LSB) . And the left most digit in this number system is called the ‘Most Significant Bit’ (MSB) .Now normally when we deal with different number systems we specify the base as the subscript to make it clear which number system is being used.

**Implementation of number systems in different area**

If we look on those number systems those all has specified filed of work. Like Hexadecimal number used in microprocessor and microcontroller, binary used in **digital systems**, decimal used in field of accountancy.