Ethiopian Multiplication

The Ethiopians have used a quite interesting way to multiplicate two big numbers.

First of all they wrote the two numbers (which should be multiplicated) side by side, e.g.:

  5468   *   72 .

So this is still the same as we do it today. But the following is quite different. For every following line the left number is divided by 2 (digits behind the comma are omitted), and the right number is doubled for each line. This sequence goes on until the left number is 1.

  5468   *   72
  -------------
  2734      144
  1367      288
   683      576
   341     1152
   170     2304
    85     4608
    42     9216
    21    18432
    10    38864
     5    73728
     2   147456
     1   294912

Now all lines with the left number being not an odd number are crossed out.

  xxxx---*---xx
  -------------
  xxxx------xxx
  1367      288
   683      576
   341     1152
  -xxx-----xxxx
    85     4608
  --xx-----xxxx
    21    18432
  --xx----xxxxx
     5    73728
  ---x---xxxxxx
     1   294912

The remaining right numbers are added.

       288
  +    576
  +   1152
  +   4608
  +  18432
  +  73728
  + 294912
  --------
  = 393696

And the sum 393696 is - voila! - the result of the multiplication (5468*72).

Thanks to Anja S. who told me of this!


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