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[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.
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).
Trachtenberg defined this algorithm with a kind of pairwise multiplication where two digits are multiplied by one digit, essentially only keeping the middle digit of the result. By performing the above algorithm with this pairwise multiplication, even fewer temporary results need to be held. Example:
Operation Input Output Algorithm Complexity Addition: Two -digit numbers : One +-digit number : Schoolbook addition with carry ()Subtraction: Two -digit numbers : One +-digit number
Lattice multiplication, also known as the Italian method, Chinese method, Chinese lattice, gelosia multiplication, [1] sieve multiplication, shabakh, diagonally or Venetian squares, is a method of multiplication that uses a lattice to multiply two multi-digit numbers.
The integer X is the repeating digits of the fraction 1 ⁄ F, say d p d p-1...d 3 d 2 d 1, where d p, d p-1, ..., d 3, d 2 and d 1 each represents a digit and p is the number of digits. The multiple n X is thus the repeating digits of the fraction n ⁄ F, say d k d k-1...d 3 d 2 d 1 d p d p-1...d k+2 d k+1, representing the results after ...
Area of a cloth 4.5m × 2.5m = 11.25m 2; 4 1 / 2 × 2 1 / 2 = 11 1 / 4 Multiplication (often denoted by the cross symbol × , by the mid-line dot operator ⋅ , by juxtaposition, or, on computers, by an asterisk * ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition ...
A binary computer does exactly the same multiplication as decimal numbers do, but with binary numbers. 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.
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