Saturday 21 January 2012

number system and conversion

Hello friends,Previously we have discussed about probability examples and today i am going to teach you Number system in mathematics which constitutes a large space in cbse text books. As we talk about computers it works on only two digits 0 and 1, called binary numbers. Computer can only capable of manipulating binary numbers. If we want to understand how computer works, we should be able to use binary number system. But in order to work well as a computer professional we should know all types of number systems and way to convert between each other, If anyone wants they can take help of online tutoring. Because many times we need to convert one number system into other.

Types of Numbers
1.      Decimal System
2.      Binary System
3.      Octal System
4.      Hexadecimal System

Decimal System
            Base 10
            Digits - 0 to 9

Also called the positional number system. In decimal number system each digit is multiplied by the power of 10 depending on the position of the digit, which increases as we move from right to left, where first right most digit has power 0.

Example: 78610
            786 = 7 * 102 + 8*101 + 6*100
                       = 700 + 70 + 6

Binary System
            Base 2
            Digit – 0 and 1
In Binary  number system there can be only two possible values 0 and 1, often called as “bit”. Number of bits used in binary number represents the number. Power of 2 is used rather than 10 as in decimal number.

Example: 100102 number of bits =5, 111011number of bits =6

Octal System
            Base 8
            Digits – o to 7
Power of 8 is used to represent or convert from any number system into octal.

Example : 2238, 4568,5578


Hexadecimal Number
            Base 16
            Digits – 0 to 9 and a to f

Power of 16 is used to represent number in this number system. Hexadecimal is the grouping of binary number that is hexamdecimal no can be broken into two parts of 4bits.

Example:  2AF416, 456AF16 (know more about numbers, here),


Conversion

We will see how to convert one number system into other number system.

          Example: 11101 = ?10
                Binary to Decimal

            1*25    +  1*24           +    1*23         +    1*22         +   0*21          +    1*20                             
            32        +   16            +      8               +        4          +      0           +      1
        
            61

9310 = ?2
Decimal to Binary

93/2 =  46  remainder  1                   (Least significant bit)
46/2 = 23   remainder  0
23/2 = 11   remainder  1
11/2 =  5    remainder  1
5/2    = 2    remainder  1
2/2    = 1    remainder  0
1/2    = 0    remainder  1                   ( most significant bit)

We write it from msb to lsb
Result = 1011101

 Octal to decimal
7548 into ?10

=7x82 +          7x81                    +          7x80
=448    +             56                          +             7
=511

Decimal to Octal
26410  = ?8
264/8 = 24 remainder 3
24/8   =  0 remainder 3
Result = 33

Hexa to Decimal
2CD16 = ?10
2x162  +          Cx16            +          Dx160
64        +          12x16             +          13x1
64        +          192                 +          13
26910

Decimal to hexa
19210 = ?16

192/16 = 57 remainder 9
57/16  = 3   remainder  9
  3/16  =  0  remainder 3
Result = 399

We can use a table to show the relation between all the number system we have.

Decimal Hexadecimal Octal binary
0 0 00000000000 0000
1 1 00100000001 0001
2 2 00200000010 0010
3 3 00300000011 0011
4 4 00400000100 0100
5 5 00500000101 0101
6 6 00600000110 0110
7 7 00700000111 0111
8 8 01000001000 1000
9 9 01100001001 1001
10 A 01200001010 1010
11 B 01300001011 1011
12 C 01400001100 1100
13 D 01500001101 1101
14 E 01600001110 1110
15 F 01700001111 1111
This table can be simply use to convert one number system into another .
This is all about number system and conversion and if anyone want to know about Properties of Irrational Numbers then they can refer to internet and text books for understanding it more precisely.Read more maths topics of different grades such as Rationalizing the Denominator  in the next session here.