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Arithmetic
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  The dream of creating an automatic (mechanic or electronic) device to perform arithmetic calculation very old and the creation of the first "low cost" CPU (the 4004) started the IT-revolution, which made it possible to study these lines from any computer around the world, connected to the internet.

Read about the old dream here:   http://en.wikipedia.org/wiki/Mechanical_calculator

   
  In a CPU will the Arithmetic and Logic calculations performed by the ALU (Arithmetic Logic Unit)

Read more about ALU's here:  http://en.wikipedia.org/wiki/Arithmetic_logic_unit

 
 
  In my search for Adders on the net I found this:  OpAr Version 1

Very informative indeed - thanks for sharing