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For 8-bit integers the table of quarter squares will have 2 9 −1=511 entries (one entry for the full range 0..510 of possible sums, the differences using only the first 256 entries in range 0..255) or 2 9 −1=511 entries (using for negative differences the technique of 2-complements and 9-bit masking, which avoids testing the sign of ...
The standard procedure for multiplication of two n-digit numbers requires a number of elementary operations proportional to , or () in big-O notation. Andrey Kolmogorov conjectured that the traditional algorithm was asymptotically optimal, meaning that any algorithm for that task would require () elementary operations.
The method for general multiplication is a method to achieve multiplications with low space complexity, i.e. as few temporary results as possible to be kept in memory. This is achieved by noting that the final digit is completely determined by multiplying the last digit of the multiplicands .
Here, complexity refers to the time complexity of performing computations on a multitape Turing machine. [1] See big O notation for an explanation of the notation used. Note: Due to the variety of multiplication algorithms, () below stands in for the complexity of the chosen multiplication algorithm.
Napier's bones is a manually operated calculating device created by John Napier of Merchiston, Scotland for the calculation of products and quotients of numbers. The method was based on lattice multiplication, and also called rabdology, a word invented by Napier.
The Chisanbop system. When a finger is touching the table, it contributes its corresponding number to a total. Chisanbop or chisenbop (from Korean chi (ji) finger + sanpŏp (sanbeop) calculation [1] 지산법/指算法), sometimes called Fingermath, [2] is a finger counting method used to perform basic mathematical operations.
The basic algorithm, as best exemplified in a 2 • 2 multiplication problem, is as follows (where t represent a tens digit, u represent a units digit, and T symbolizes the tens digit multiplied by its respective power): Step 1 = (t 1 - u 1) • u 2 = A Step 2 = u 1 • t 2 = B Step 3 = (u 1 • u 2) + t (u 1 • u 2) = C
The grid method (also known as the box method) of multiplication is an introductory approach to multi-digit multiplication calculations that involve numbers larger than ten. Because it is often taught in mathematics education at the level of primary school or elementary school, this algorithm is sometimes called the grammar school method. [1]