For integer portion of a number,
  Divide by 2 and note remainder.
  Shifts right and reveals the next significant digit.
    works from least significant digit to most.

Converting fractional portion of a number to binary
  by multiplying by 2.
  Shifts left to reveal next significant digit.
    works from most signficant digit to least.

Representable precission determines when to stop.

Example :

  Assume 8 bits of data storage.




Decimal.Decimal to binary

 .431

. .431   .
0 .862   0
1 .724   1
1 .448   1
0 .896   0
1 .792   1
1 .584   1
1 .168   1
0 .336   0

.01101110b


  


Binary to Decimal.Decimal using shift and subtract
0.01101110

sum=                             0 
0 *        .5    + 0          =  0
1 *       .25    + 0          =  0.25
1 *      .125    + 0.25       =  0.375
0 *     .0625    + 0.375      =  0.375 
1 *    .03125    + 0.375      =  0.40625
1 *   .015625    + 0.40625    =  0.421875
1 *  .0078125    + 0.421875   =  0.4296875
0 * .00390625    + 0.4296875  =  0.4296875

sum=                             0.4296875




Note the difference between values 

0.431 - 0.4296875 = .0013125   (.3% difference)




Conversion by subtracting powers of 2.



.431
.431     - 0 * .5        =  .431
.431     - 1 * .25       =  .181
.181     - 1 * .125      =  .056
.056     - 0 * .0625     =  .056
.056     - 1 * .03125    =  .02475
.02475   - 1 * .015625   =  .009125
.009125  - 1 * .0078125  =  .0013125
.013125  - 0 * .00390625 =  .0013125