Float  1 bit sign, 11 bit exponent, 10 bit significand

Bias   2^(11-1) - 1 = 1024 - 1 = 1023

Convert the value 912.730 to float.
Integer 912
                 check
  912            1  1  1   0   0   1    0    0    0    0
  456  0         1  2
  228  0            3  6 
  114  0               7  14
   57  0                  14  28
   28  1                      28  56
   14  0                          57  114
    7  0                              114  228
    3  1                                   228  456 
    1  1                                        456  912
    0  1                                             912 

   10 digits  

Decimal .730  

   . .730        
   1 .460      1  * .5                .5
   0 .920      0  * .25               .5
   1 .840      1  * .125              .625
   1 .680      1  * .0625             .6875
   1 .360      1  * .03125            .71875
   0 .720      0  * .015625
  
We can only store 10 digits so we should have plenty.


So, 912.730  ~   1110010000.101110 b 

Scientific       1. 1100100001 01110 * 2^9

 Bias  1023 + exponent 9 = 1032
 
  1032          1  0  0  0   0   0   0    1    0    0     0
   516  0       1  2
   258  0          2  4
   129  0             4  8
    64  1                8  16
    32  0                   16  32
    16  0                       32  64
     8  0                           64  128
     4  0                               129  258
     2  0                                    258  516
     1  0                                         516  1032
     0  1                                              1032


Float  sign + = 0
sign  biased exponent  significand
  0   100 0000 1000    1100 1000 01 


If you look, you can see that we only preserved 1 digit to the right of the
original real value, so the stored value is :

  912.5