Editing Embedded Programming Tips and Tricks for Beginners

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However care should be taken when using signed variables.<br>
 
However care should be taken when using signed variables.<br>
  
Rounding: With the method described above the result is effectively floored because the bits shifted out to the right are lost. These bits are the fraction of the result, and if the fraction is higher than 0.5, then the e MSB of the fraction equals 1.<br>
 
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Using the example above, but with Z=30 to illustrate the flooring:<br>
 
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On the calculator we see that 30*3/16 = 5.625 which is closer to 6<br>
 
In the binary world we see that (30*3)>>4 = 5 , why ? <br>
 
30*3 = 90 = 0101 1010 binary, where 1010 represents 10/16 > 0,5 and we get the rounding error.<br>
 
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fast divison with rounding: example Z / (16/3)
 
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  ''Z = Z * 3;''<br>
 
  ''Z = Z >> 4 + (Z >> 3) & 0x01;''<br>
 
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(the & 0x01 masks the bit we want to isolate and add to Z)<br>
 
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=Fast Multiplication=
 
=Fast Multiplication=

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