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Trachtenberg system. The Trachtenberg system is a system of rapid mental calculation. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly. It was developed by the Ukrainian engineer Jakow Trachtenberg in order to keep his mind occupied while being in a Nazi concentration ...
The calculation took only 13 minutes. In 1955, NORC was moved to the Naval Proving Ground [4] at Dahlgren, Virginia. It was their main computer until 1958, when more modern computers were acquired. It continued to be used until 1963. [5] [6] [self-published source] Its design influenced the IBM 701 and subsequent machines in the IBM 700 series ...
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
5 is halved (2.5) and 6 is doubled (12). The fractional portion is discarded (2.5 becomes 2). The figure in the left column (2) is even, so the figure in the right column (12) is discarded. 2 is halved (1) and 12 is doubled (24). All not-scratched-out values are summed: 3 + 6 + 24 = 33. The method works because multiplication is distributive, so:
For example, to multiply 7 and 15 modulo 17 in Montgomery form, again with R = 100, compute the product of 3 and 4 to get 12 as above. The extended Euclidean algorithm implies that 8⋅100 − 47⋅17 = 1, so R′ = 8. Multiply 12 by 8 to get 96 and reduce modulo 17 to get 11. This is the Montgomery form of 3, as expected.
A seven-inch reel of 1 ⁄ 4 in (6.4 mm) tape. The tape decks of the 1950s were mainly designed to use tape 1 ⁄ 4 inch (0.64 cm) wide and to accept one of two reel formats: 10 + 1 ⁄ 2 inches (27 cm) reels, almost always with metal flanges, which fit
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