Hexadecimal fraction representation

We will discuss in detail about how we can represent the fractional numbers in hexadecimal number system.

The hexadecimal point or the radix point plays the same role as that of decimal point in decimal number system and octal point in the octal number system i.e. the point that separates the integer part of the hexadecimal digits and fractional hexadecimal number digits.

The procedure is similar to the steps that we followed to represent a decimal fraction and binary fractions.

Example 1: (4 1 A . E F 9 )₁₆ is the Hexadecimal equivalent of ( 1050 . 883049 ) in decimal number system.

Step 1:

Write down the sequence of hexadecimal positional weights based on the number of digits present in the given hexadecimal number separated by the hexadecimal point as shown below

   16²     16¹      16⁰                     16 ^-1      16 ^-2      16 ^-3                ← Weights in hexadecimal

.

    ↑                                                            ↑
MSD                                                        LSD

Step 2: Assign the values for each of the weights starting from LSD till the hexadecimal point and again beginning from the hexadecimal point assign the integer hexadecimal values up to the MSD towards far left as done below.



   16²       16¹      16⁰                       16 ^-1     16 ^-2    16 ^-3                ← Weights in hexadecimal

4

1

A

.

E

F

9

    ↑                                                               ↑
MSD                                                          LSD

Step 3: Compute the product of individual hexadecimal digits and its associated individual weights to get the products which looks like the following

9 x 16 ^-1   ← LSD             

F x 16 ^-2                               

E x 16 ^-3

    ^.                                

A x 16 ⁰                               

1 x 16 ¹

4 x 16 ²   ← MSD             

Step 4: Determine the sum of the individual products separated by the hexadecimal point as illustrated below

       4 x 16 ² + 1 x 16 ¹ + A x 16 ⁰  .  E x 16 ^-1 + F x 16 ^-2 + 9 x 16 ^-3

 =    4 x 16 ² + 1 x 16 ¹ + A x 16 ⁰  .  E x 16 ^-1 + F x 16 ^-2 + 9 x 16 ^-3 

        ↑                                                                     ↑
      MSD                                                                LSD

=    4 x 256     + 1 x 16     + 10 x 1     .  14 x ( 1 / 16 ) + 15 x ( 1 / 256 ) + 9 x ( 1 / 4096 )  

=    1024         +       16      +    10        .  ( 0 . 875 )       +  ( 0 . 005859 )   + ( 0 . 00219 )

=    ( 1050   .  883049 )₁₆ 

NOTE:

Here the alphabets in the hexadecimal number system have the following decimal values and we use these values for representing the hexadecimal numbers in the decimal number system

A   → 10


B   → 11


C   → 12


D   → 13


E   → 14


F   → 15