Carry-Free Multiplication

Using the meaning of a number we show three novel and simpler ways to do ordinary or carry type multiplication. It is assumed that one knows the multiplication table by heart. Let p = ab where a and b are positive integers. Write a = a1 + a2 where a1 contain a’s even powers of ten and a2 contains a’s odd powers of ten. Form p1 = a1b, p2 = a2b via ordinary multiplication. Then p = p1+p2. The subproducts of p1, p2 will not have any carries and can be written down by rote. Alternatively, each row of p1 and p2 can be paired as two rows and then p can be computed directly. This second way is another way to do box multiplication. Furthermore, if one now adds each pair of rows together producing a single row again one would obtain carry type multiplication done another way. We also expand our approach to handle doing these new algorithms in base 100 and base 1000.

By: Fred G. Gustavson

Published in: RC24726 in 2009


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