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Pascaline (also known as the arithmetic machine or Pascal's calculator) is a mechanical calculator invented by Blaise Pascal in 1642. Pascal was led to develop a calculator by the laborious arithmetical calculations required by his father's work as the supervisor of taxes in Rouen , France. [ 2 ]
On a single-step or immediate-execution calculator, the user presses a key for each operation, calculating all the intermediate results, before the final value is shown. [ 1 ] [ 2 ] [ 3 ] On an expression or formula calculator , one types in an expression and then presses a key, such as "=" or "Enter", to evaluate the expression.
The considerations above concern the recursion depth only. Either way of iterating leads to the same number of reduction steps, involving the same rules (when the rules r11 and r12 are considered "the same"). As the example shows the reduction of (,) converges in 9 steps: 1 X r7, 3 X r8, 1 X r9, 2 X r10, 2 X r11/r12. The modus iterandi only ...
Addition is commutative, meaning that one can change the order of the terms in a sum, but still get the same result. Symbolically, if a and b are any two numbers, then a + b = b + a. The fact that addition is commutative is known as the "commutative law of addition" or "commutative property of addition".
It uses a selection of full and half adders to sum the partial products in stages (the Dadda tree or Dadda reduction) until two numbers are left. The design is similar to the Wallace multiplier , but the different reduction tree reduces the required number of gates (for all but the smallest operand sizes) and makes it slightly faster (for all ...
The oxidative addition of an organic halide (RX) to L n M gives L n MR(X). Subsequently, the second partner undergoes transmetallation with a source of R' − . The final step is reductive elimination of the two coupling fragments to regenerate the catalyst and give the organic product.
A slide calculator, also known as an Addiator after the best-known brand, is a mechanical calculator capable of addition and subtraction, once made by Addiator Gesellschaft of Berlin, Germany. Variants of it were manufactured from 1920 until 1982. The devices were made obsolete by the electronic calculator.
In modular arithmetic, Barrett reduction is an algorithm designed to optimize the calculation of [1] without needing a fast division algorithm. It replaces divisions with multiplications, and can be used when n {\displaystyle n} is constant and a < n 2 {\displaystyle a<n^{2}} .
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