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Multiply each digit by 2 (with carrying). Example: ... If the answer is greater than a single digit, simply carry over the extra digit (which will be a 1 or 2) to the ...
To multiply two numbers with n digits using this method, one needs about n 2 operations. More formally, multiplying two n-digit numbers using long multiplication requires Θ(n 2) single-digit operations (additions and multiplications).
[1] [2] [3] It is a divide-and-conquer algorithm that reduces the multiplication of two n-digit numbers to three multiplications of n/2-digit numbers and, by repeating this reduction, to at most single-digit multiplications.
(A blank space or zero to the upper left of each digit, separated by a diagonal line, should be understood, since 1 × 1 = 01, 1 × 2 = 02, 1 x 3 = 03, etc.) A small number is chosen, usually 2 through 9, by which to multiply the large number.
As an example, consider the multiplication of 58 with 213. After writing the multiplicands on the sides, consider each cell, beginning with the top left cell. In this case, the column digit is 5 and the row digit is 2. Write their product, 10, in the cell, with the digit 1 above the diagonal and the digit 0 below the diagonal (see picture for ...
For any 2-digit by 2-digit multiplication problem, if both numbers end in five, the following algorithm can be used to quickly multiply them together: [1] E x : 35 × 75 {\displaystyle \mathrm {Ex} :35\times 75}
In binary encoding each long number is multiplied by one digit (either 0 or 1), and that is much easier than in decimal, as the product by 0 or 1 is just 0 or the same number. Therefore, the multiplication of two binary numbers comes down to calculating partial products (which are 0 or the first number), shifting them left, and then adding them ...
Multiplication can also be thought of as scaling. Here, 2 is being multiplied by 3 using scaling, giving 6 as a result. Animation for the multiplication 2 × 3 = 6 4 × 5 = 20. The large rectangle is made up of 20 squares, each 1 unit by 1 unit. Area of a cloth 4.5m × 2.5m = 11.25m 2; 4 1 / 2 × 2 1 / 2 = 11 1 / 4
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