Mixed float

Normalize the number 277.431
    1 bit sign, 8 bit exponent, 15 bit significand
    (Different size exponent and significand from previous examples). 

Start with the most significant digits.

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

Convert fractional portion to binary (1st example) :
   
   .431 = .011011100101011000b
 
Combine the two :

   100010101.011011100101011000b
   
Represent in the equivalent of scientific notation,.

   (1).0001 0101 0110 111b * 2^8
   (Truncated to 15 decimal points)

Generating the 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 :

  8 + 127 = 135 = 1000 0111b


Sign bit 0 (positive)
Biased Exponent 1000 0111
Significand : 0001 0101 0110 111
  Remember, when normalizing, we don't record the most significant bit. 
    of the mantissa.

Floating point 0 10000111 000101010110111

Conversion back