NUMBER SYSTEM

     

               NUMBER SYSTEM

We learn numbers from 1to 100 and so on in our school days.Number is a part of our day- to- day life. We solve many mathematical problems by using these numbers.

 DIFFERENT TYPES OF NUMBER SYSTEM ARE:- 1)Decimal Number System

          2)Binary Number System                 

          3)Hexadecimal Number System

          4)Octal Number System 

 Now we learn the different types of number systems in detail:- 

1) Decimal Number System:- 

 i) Decimal number system is start from 0 to 9.

 ii) It uses base 10. 

iii) Hence the ten possible values are :-0,1,2,3,4,5,6,7,8,9.

 2) Binary Number System:- 

 i) Most modern computer systems use the binary logic for their operation.

 ii)A binary number system uses only two digits namely 0 and 1.

 iii)Binary number system uses the base 2. iv)The largest value of a digit is 1. 

 v)The binary digits (0&1) are also called as bits.Thus binary number system is a two bit system. 

 vi)The leftmost bit in a binary number with the highest weight is called as Most Significant Bit(MSB) whereas the rightmost bit in a number with the lowest weight is called as Least Significant Bit(LSB).

 3) Hexadecimal Number System:- 

 i)The base of hexadecimal number system is 16. 

 ii) Number of a values assumed by eaxh digit is 16. The values include digits 0 through 9 and letters A,B,C,D,E,F. 

 iii)The sixteen possible values are: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. iv)0 represents the least significant digit whereas F represents the most significant digit.

 v)The largest value of a digit in the hexadecimal number system is 15 and it is represented by F. 

 vi)The hexadecimal number higher than F will be 10.

vii)0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F10,11,12,13,14,15,16,17,18,19,1A,1B,1C,1D,1E,1F,......................FF.

 4)Octal Number System:-

 i)The base used for octal number system is 8.

   ii)Each digit in the octal system will assume 8  diffferent values from 1 to 7 (0,1,2,3,4,5,6,7).

  iii)The largest value of a digit in the octal number higher than 7 will not be 8,instead of that it will be 10.

By using, this table we can easily understand the different number system.

Decimal Number	Binary number	Hexadecimal Number	Octal Number
0	0000	0	0
1	0001	1	1
2	0010	2	2
3	0011	3	3
4	0100	4	4
5	0101	5	5
6	0110	6	6
7	0111	7	7
8	1000	8	10
9	1001	9	11
10	1010	A	12
11	1011	B	13
12	1100	C	14
13	1101	D	15
14	1110	E	16
15	1111	F	17
16	10000	10	20
17	10001	11	21
18	10010	12	22
19	10011	13	23
20	10100	14	24