Normalize the number 277.431 using the the real IEEE float vlaues 
    1 bit sign, 8 bit exponent, 23 bit significand
 

Convert integer portion to binary (see last example) : 
   277 = 100010101b

Convert fractional portion to binary (1st example) :
   
   .431 = .011011100101100000b
 
Combine the two :

   100010101.011011100101100000b
   
Represent in the equivalent of scientific notation,.

   1.0001 0101 0110 1110b * 2^8
   (Truncated to 16 decimal points)

Generating a IEEE 754 bias.

  Use formula 2^(n-1) - 1 where n is the size of the exponent.
    2^(8-1)-1 = 127 bias

Biasing this exponent give :

  63 + 8 = 71 = 100 0111


Sign bit 0 (positive)
Biased Exponent 100 0111
Signficand : 0001 0101 0110 1110
  Remember, when normalizing, we don't record the most signicant bit. 

Floating point 0 1000111 0001010101101110