Construction of algorithms for parallel addition in expanding bases via Extending Window Method

Legerský, Jan; Svobodová, Milena

doi:10.1016/j.tcs.2019.08.010

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Example 11 Consider the Matrix Numeration System With Base M...1

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2023

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“…Consider the numeration system in C with base β = ı − 1. In [19], a 7-local function of parallel addition in system (β, A) is found for the digit set A = {0, ±1, ±ı}. Let us denote the 7-local function as φ : (A + A) 7 → A, acting on a 7-tuple (w j , .…”

Section: Example 11 Consider the Matrix Numeration System With Base M...mentioning

confidence: 99%

From positional representation of numbers to positional representation of vectors

2023

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To represent real m-dimensional vectors, a positional vector system given by a non-singular matrix M ∈ ℤm×m and a digit set Ɗ ⊂ ℤm is used. If m = 1, the system coincides with the well known numeration system used to represent real numbers. We study some properties of the vector systems which are transformable from the case m = 1 to higher dimensions. We focus on an algorithm for parallel addition and on systems allowing an eventually periodic representation of vectors with rational coordinates.

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Section: Example 11 Consider the Matrix Numeration System With Base M...mentioning

confidence: 99%

From positional representation of numbers to positional representation of vectors

2023

View full text Add to dashboard Cite

show abstract

Construction of algorithms for parallel addition in expanding bases via Extending Window Method

Cited by 1 publication

References 10 publications

From positional representation of numbers to positional representation of vectors

From positional representation of numbers to positional representation of vectors

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