3) Number system conversions

I)How to convert any radix number to decimal number system ?

Any radix number to  Decimal number system    

                                                               



where
     p-> No of digits to the left of the radix.
     n->No of digits to the right of the radix.
     d->value of the number.
     r->radix of the number.

1)Binary to Decimal conversion
       Example
             10111₂ = 1*2⁴  + 0*2³ + 1*2² + 1*2¹ + 1*2⁰ = 23₁₀
        

2)Octal number system to Decimal number system

        Example

              27₈ = 2*8¹ + 7*8⁰  = 23₁₀

3)Hexadecimal number system to Decimal number system

        Example

              17₁₆ = 1*16¹ +7*16⁰  = 23₁₀

II)How to convert decimal to any radix number?

   1)Decimal to Binary conversion

        Example

              23₁₀ = 10111₂

             

2)23      Remainder

2)11   ----1

2)5 --------1

2)2---------1

2)1----------0

  2)Decimal to  Octal conversion

          Example

                23₁₀ = 27₈

8)23   Remainder

8)2  -----7

    3)Decimal to hexadecimal conversion

            Example

                  23₁₀ = 17₁₆

16)23     Remainder

16)1  -----7

More examples

1)Binary to octal

Example

11011.011₂   = 011 011 . 011 = 33.3₈( group of 3s)

2)Binary  to hexadecimal

Example

11011.011₂ = 0001 1011 . 0110 = 1B.6₁₆(group of 4s)

3)Decimal to binary conversion

Example

0.7₁₀ = ?₂

0.7*2=1.4

0.4*2=0.8

0.8*2=1.6

0.6*2=1.2

Ans

 0.7₁₀ = 0.1011₂

4)Octal to binary conversions

Example

(123.4567)₈ = (001 010 011 . 100 101 110 111)₂

5)Hexadecimal to binary conversions

Example

(123A.58C)₁₆  = (0001 0010 0011 1010 . 0101 1000 1100)₂

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