Normalize the number .431. using a IEEE style float format but using 24 bits.
  1 bit sign, 7 bit exponent, 16 bit significand
  (real 1,8,23 format makes example difficult) 
 
First convert to binary.  We need to go at least 16 places past the most 
significant 1

  . .431
  0 .862 (.431 x 2)
  1 .724 (.862 x 2) # start counting from here - this will be the hidden bit.
  1 .448 (.724 x 2)
  0 .896 (.448 x 2)

  1 .792 (.896 x 2)
  1 .584
  1 .168
  0 .336

  0 .672
  1 .344
  0 .688
  1 .376

  0 .752
  1 .516
  1 .032
  0 .064

  0 .128
  0 .256 # we have 16 digits past the most significant 1.
  ...

  .0110 1110 0101 0110 00 

Represent in the equivalent of scientific notation,.

  1.10 1110 0101 0110 00 * 2^-2

 * We left the exponent in decimal format because we haven't added the bias yet.

Since, only 1 can be to the left of the decimal point, we don't need to store
  it (hidden bit). 

  (1).1011100101011000

   .1011100101011000

  This is called the significand and allows for 1 extra digit of precision.

  If our conversion had does not produce enough digits, 
    right pad with zeros to fill significand.
 
  0.5
  1.0 (.5 x 2)
   .0 (.0 x 2)
   etc.

   (1).0000000000000000


With 16 bit precision, a very close approximation can be found.

Biasing