COMPUTER DATA REPRESENTATION AND NUMBER SYSTEM

                                      

             Number are two types 

                            Non positional number are  those symbols which we uses instead of the decimal number like(i=1,ii=2,iii=3,iv=4)etc. those symbols represents the same value regardless of its position in a number.

Positional number:-positional number there are only a few symbols called digits.these symbols represent different values depending on the position they occupy in number.

Some positional number are

1 decimal number system

2 binary number system

3 octal number system

4 Hexadecimal number system

Decimal number system:- in this system base in equal to 10 .because there are altogether ten symbols or digits( 0,1,2,3,4,5,6,7,8  and 9)

Binary number system:-in binary number ststem ,the value of base is two  because it has only two symbols or digits(0,1)

Octal number system:- in octal number system the base value is 8(eight) ,hence there are only eight symbols or digits(0,1,2,3,4,5,6 and 7)

Hexadecimal number system:-In hexadecimal number system  base is 16 (sixteen) ,hence there are 16 symbols or digits ,the first 10 digits are the same digits of decimal 0 to 9 and other six are (A,B,C,D,E and F)

How to convert  binary number decimal number ?

                                                For example

1.       10101010= 1*2⁷+0*2⁶+1*2⁵+0*2⁴+1*2³+0*2²+1*2¹+0*2⁰

128+0+32+0+8+0+2+0

=170

Then binary number 10101010 means 170 decimal number.

2.       110111=1*2⁵+1*2⁴+0*2³+1*2²+1*2¹+1*2⁰

=32+16+0+4+2+0

=54

There for binary number 110111 means 54decimal number.

how to convert decimal to binary number

 

1                      542=542/2

=(271-0)/2

=(135-1)/2

=(67-1)/2

=(33-1)/2

=(16-1)/2

=(8-0)/2

=(4-0)/2

=(2-0)/2

=1-0

THEN THE DECIMAL NUMBER 542 MEANS 1000011110 BINARY NUMBER

3.       45=45/2

=(22-1)/2

=(11-0)/2

=(5-1)/2

=(2-1)/2

=1-0

Then the decimal number 45 means 101101 binary number.

How to convert binary number to octal number

1.       1101= 1*8³+1*8²+0*8¹+1*8⁰

        =512+64+0+1

        =577

2.       110011=1*8⁵+1*8⁴+0*8³+0*8²+1*8¹+1*8⁰

=32768+4096+0+0+8+1

=36873

How to convert decimal to octal number

1.       45₁₀=

Divided		Remainder
45/8=5		5
5/8=0		5

The octal number is remainder buttom to up.that means 45₁₀=55₈

2.       230₁₀=

divided	Reminder
230/8=28	6
28/8=3	4
3/8=0	3

That means 230₁₀=346₈

How to convert decimal number to hexadecimal  number

1.       85₁₀=

Divide		Reminder
85/16=5.3125	5
.3125*16	5

Then the decimal number 85₁₀=55₁₆

divide	reminder
456/16=28.5
28.5/16=1.78125	1
.78125*16=12.5	12
.5*16=8.0	8

 

 

 

 2.456=

 

that means 456₁₀=1C8₁₆