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The binary number system expresses any number as a sum of powers of 2, and denotes it as a sequence of 0 and 1, separated by a binary point, where 1 indicates a power of 2 that appears in the sum; the exponent is determined by the place of this 1: the nonnegative exponents are the rank of the 1 on the left of the point (starting from 0), and ...
Namely, an attacker observing the sequence of squarings and multiplications can (partially) recover the exponent involved in the computation. This is a problem if the exponent should remain secret, as with many public-key cryptosystems. A technique called "Montgomery's ladder" [2] addresses this concern.
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, the power (+) expands into a polynomial with terms of the form , where the exponents and are nonnegative integers satisfying + = and the coefficient of each term is a specific positive integer ...
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To derive the value of the floating-point number, the significand is multiplied by the base raised to the power of the exponent, equivalent to shifting the radix point from its implied position by a number of places equal to the value of the exponent—to the right if the exponent is positive or to the left if the exponent is negative.
The running time of this algorithm is O(log exponent). When working with large values of exponent, this offers a substantial speed benefit over the previous two algorithms, whose time is O(exponent). For example, if the exponent was 2 20 = 1048576, this algorithm would have 20 steps instead of 1048576 steps.
The U.S. Commerce Department said Wednesday it has finalized a $1.5 billion government subsidy for GlobalFoundries to expand semiconductor production in Malta, New York and Vermont. The binding ...
9 Notes. 10 References. ... The exponent can be generalized to an arbitrary real number as follows: if >, then (+ ... Online e-book in PDF format.