Notes

 Number System in brief:

There are four numbers system, which are use in Digital System.

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

        1)         Decimal Number System :-

    Decimal Number System contains 10 digits  i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 . In decimal system, there is no symbol for the number ten (10). But the number ten (10) and the number about it can be expressed as a combination of these digits. Decimal number system any number can be express by positional weighting. Decimal Number System base is 10.

For Example number 3439, it can be written as,

                                    3439 =3000 + 400 +30 + 9

                                    3439 = 3 x 10³ + 4 x 10² +3 x 10¹ + 9 x 10⁰

In above Number (3439) , 3 number coming two time , but first 3 number (from left side) value is 30 and second 3 number value is 3000 because both number position is different.

            2)                Binary Number System :-

    The binary system has only two digits ‘ 0 ’ and ‘ 1 ’.Generally, 0 (Zero) represent LOW state and 1 (one) represent HIGH state. Counting is similar to decimal counting, it is start from 0 and next is 1. In binary system 0 is lowest and 1 is highest value. Binary number system any number can be express by positional weighting. Binary Number System base is 2.

For Example number 1010, it can be written as,

                        111 = 100 + 10 + 1                      

            111 = 1 x 2² + 1 x 2¹  + 1 x  2⁰

Below table shows how Binary Numbers 0 to 15

                                                                                                 Binary

Number (Decimal)	23 = 8	22 = 4	21 =2	20 =1
0				0
1				1
2			1	0
3			1	1
4		1	0	0
5		1	0	1
6		1	1	0
7		1	1	1
8	1	0	0	0
9	1	0	0	1
10	1	0	1	0
11	1	0	1	1
12	1	1	0	0
13	1	1	0	1
14	1	1	1	0
15	1	1	1	1

                     3)      Hexadecimal Number System :- The Binary number are longer to represent binary equivalent for given decimal number. Hexadecimal number system are one forth of binary word length and yet provides the same binary information. The Hexadecimal number formed from a binary number by grouping bits in group of four bit each ( Bit means either ‘0’ or ‘1’). The Hexadecimal number system uses 16 digits to represent all the numbers. Thus, its base is 16. The digits are :

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F.

 

Below table shows how Hexadecimal Numbers 0 to 15

 

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

 

Hexadecimal number system any number can be express by positional weighting.

For Example number 8E, it can be written as,

            8E = 80 + E

            8E = 80 + 14

            8E = 8 x 16¹ + 14 x 16⁰