Misil teledirigido antitanques

The Technique of multiplication known as Russian consists in dividing by 2 the multiplier (and then quotients obtained), until a null quotient, and noting the remainders; and to multiply the multiplicand by 2 in parallel. One then adds the multiples obtained with the multiplicand corresponding to the nonnull remainders.

That returns in fact to write the multiplier bases 2 of them and to then make multiplications by 2 and of the additions. It is thus an alternative of the Technique of the multiplication in ancient Egypt, although it could be rédécouverte independently.

Example

13 X 238 one writes

13 = 1101 base 2 of them (obtained by reading the remainders upwards in the table, and written according to the usual convention of right-hand side -- units -- on the left -- high powers -- )

To limit the number of operations, it is generally necessary to choose like the smallest multiplier of the two numbers to multiply. However, if one of them is a power of 2, it is rather him which it is necessary to prefer (there is no addition). It will be noted that the remainders become inevitably null, and thus the result becomes stable, as from the moment when the quotient is him even null. Formally, the condition of stop (to stop when the quotient is null) is thus only one convenience.

Graphic algorithm

Graphically, one can say that a multiplication transforms a rectangle multiplying X multiplicand into a line by preserving the number of elements.

The graphic algorithm consists for the Russian multiplication with:

a) if the multiplier is even, to take the lower half of the rectangle and to stick it on a side (one thus transforms a rectangle 2n X p into a rectangle N X 2p);
b) if the multiplier is odd, to remove the last line initially and to put it aside, which brings back to the preceding case 1.a);
to start again until obtaining only one line;
to add all the lines put aside.

See too

Technical of multiplication

Random links: