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Follow up to algebraically tracing carries in base 2 multiplication

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  • Kermit Rose
    I now have found a way to simplify the calculations somewhat. Setting z = x y where z = 1 + 2 z1 + 4 z2 + . . . x = 1 + 2 x1 + 4 x2 + . . . y = 1 + 2 y1 + 4 y2
    Message 1 of 1 , Oct 10, 2007
      I now have found a way to simplify the calculations somewhat.

      Setting z = x y
      where z = 1 + 2 z1 + 4 z2 + . . .
      x = 1 + 2 x1 + 4 x2 + . . .
      y = 1 + 2 y1 + 4 y2 + . . .


      If w = a1 s1 + a2 s2
      then
      parity(w) = parity( parity(a1) s1 + parity(a2) s2 )

      Applying this results in y1, y2, etc having the forms

      y1 = t10 + t11 x1
      y2 = t20 + t21 x1 + t22 x2 + t23 x2 x1
      y3 = t30 + t31 x1 + t32 x2 + t33 x2 x1 + t34 x3 + t35 x3 x1 + t36 x3 x2
      + t37 x3 x2 x1
      etc
      where all the t parameters depend only on the z's.



      Kermit < kermit@... >
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