Russian Multiplication

Also called "Ethiopian multiplication." To multiply two numbers a and b, write a_0=a and b_0=b in two columns. Under a_0, write |_a_0/2_|, where |_x_| is the floor function, and under b_0, write 2b_0. Continue until a_i=1. Then cross out any entries in the b column which are opposite an even number in the a column and add the b column. The result is the desired product. For example, for a=27,b=35

  27;  13;  6;  3;  1;  35;  70;  140-----;  280;  560__;  945

Russian multiplication works because it implements binary multiplication:

1. If a=1 (mod 2), accumulate b.

2. Right-shift a one bit.

3. If a=0, exit.

4. Left-shift b one bit.

5. Loop.

See also

Binary, Multiplication

Portions of this entry contributed by Dave Zobel

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Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, p. 44, 1986.

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Russian Multiplication

Cite this as:

Weisstein, Eric W. and Zobel, Dave. "Russian Multiplication." From MathWorld--A Wolfram Web Resource.

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