Топ-100 ★ Non-adjacent form - non-standard positional numeral syste
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★ Non-adjacent form - non-standard positional numeral systems ..



Non-adjacent form
                                     

★ Non-adjacent form

The non-adjacent form of a number is a unique signed-digit representation. Like the name suggests, non-zero values cannot be adjacent. For example:

0 1 2 = 4 + 2 + 1 = 7 1 0 −1 2 = 8 − 2 + 1 = 7 −1 2 = 8 − 4 + 2 + 1 = 7 1 0 −1 2 = 8 − 1 = 7

All right signed-digit representations of 7, but only in the final representation, 1 0 -1 2, NAF.

                                     

1. Properties. (Свойства)

NAF provides a unique view of the whole, but the main advantage of it is that Hamming weight of value will be minimal. For regular binary representations of values, half of all bits will not be zero, on average, but with NAF this drops to only a third of all numbers.

It is obvious that more than half of the numbers, different from zero, which was the reason it was introduced by V. G. Reitweisner to accelerate algorithms in the beginning of the multiplication, as well as coding Booth.

Because each non-zero digit must be adjacent to two 0 C, NAF representation can be implemented so that it only accepts a maximum of M 1 bits per value, which must be represented in binary with m bits.

NAF properties make it useful in various algorithms, especially in cryptography, for example, to reduce the number of multiplications required to perform exponentiation. In the algorithm of fast exponentiation, the number of multiplication depends on the number of nonzero bits. If the exponent here is given in NAF form, a digit value of 1 means multiplying by the base, and a digital value of -1 for its return.

Other ways of coding integers that are not consecutive 1S includes coding the stand and encode Fibonacci.

                                     

2. Converting to NAF. (Преобразование в НВС)

There are several algorithms for obtaining the NAF representation of the value of this in binary. One such is the following method using repeated division, it works by selecting non-zero coefficients so that the resulting quotient is divisible by 2 and therefore, the next coefficient is zero.

Input E = e m − 1 e m − 2 e 1 e 0 2 Output Z = z m z m − 1 z 1 z 0 NAF i ← 0 while E >, 0 do if E is odd then z i ← 2 − E mod 4 E ← E − z i else z i ← 0 E ← E /2 i ← i + 1 return z
                                     
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  • series of non - stoichiometric compounds. The coordination polymer Prussian blue, nominally Fe7 CN 18 and their analogs are well known to form in non - stoichiometric
  • 90 or π 2 radians If the two complementary angles are adjacent their non - shared sides form a right angle. In Euclidean geometry, the two acute angles
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  • Theory. Discontinuous expressions are permitted in Warlpiri because non - adjacent nominals are able to correspond to a single verbal AUX argument. This
  • the triangle and one of the two sides adjacent to angle A. The adjacent leg is the other side that is adjacent to angle A. The opposite side is the side
  • particular topics, see the articles listed in the adjacent box. For non - standard dialect forms and antique forms see individual dialect articles and the article
  • cannot be shown to be true is considered false rather than unknown Non - adjacent form a signed - digit representation of numbers in mathematics and cryptography


                                     
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  • usual adjacency matrix but with 1 for adjacency 1 for nonadjacency 0 on the diagonal. Skew - adjacency matrix - an adjacency matrix in which each non - zero
  • takes place between p orbitals that are adjacent by virtue of a σ bond joining the atoms and takes the form of side - to - side overlap of the two equally
  • England covering London and adjacent counties. Established in 1907, it merged with the South Midlands League in 1997 to form the Spartan South Midlands
  • voiceless in others the cords are lax, so that it may take on the voicing of adjacent sounds. It is an oral consonant, which means air is allowed to escape through
  • affected by the child support legislation. The Non - Custodial Parents Party Equal Parenting was formed in Australia in 1998 by Andrew Thompson and other
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  • which contains codons, while the non - coding strand contains anticodons. During transcription, RNA Pol II binds to the non - coding strand, reads the anti - codons
                                     
  • reason is that if one of the end numbers remains non - black this would result in either two adjacent black cells or two cells with the same number in the
  • using optimized cold form shapes that are outside of the scope of the main specification and are not pre - qualified for DSM use. These non - pre - qualified sections
  • tooth height. Such deposits form bulbous enlargements on the roots and may interfere with extractions, especially if adjacent teeth become fused concrescence
  • the vector cross product of two adjacent sides. Any line through the midpoint of a parallelogram bisects the area. Any non - degenerate affine transformation
  • imāla led to the raising of a and aː adjacent to a sequence i ː C or Ci ː where C was a non - emphatic, non - uvular consonant, e.g. al - kēfirīna al - kāfirīna
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  • fitting a free - form line to a sequence of observations under the following constraints: the fitted free - form line has to be non - decreasing or non - increasing
  • required to file Form 1040 or one of its variants Form 1040A or Form 1040EZ Non - residents for tax purposes are generally required to file Form 1040NR or

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