O algoritmo do par binário: um estudo da representação decimal do quociente a/2 n , a ∈ R e n ∈ N*

Abstract

In the traditional context, the unequivocal determination of the quotient and the remainder of the Euclidean division takes place by means of algorithms based approaches in determining the ma- ximum dividend by the product of the divisor and quotient candidate number, then the difference between the approach and the dividend paid original, a process permeated by obtaining partial quo- tients obtained considering convenient groups of digits of the dividend taken in order from largest to smallest order. In the specific case of the divider 2, you can bypass the process of calculating this recurrence classic, by defining a function that relates each digit of the dividend to its coun- terpart of the same order in the quotient. In this paper we prove the existence of such a function defined on Z2 ×{0,1,2,3,4,5,6,7,8,9}, we use to call "function binary pair"to time we offer an additional contribution to the study of the regularities of the decimal representation in the context of the division by integers of the form 2n, with n ∈ N and, extensively, 2n · 10m with m ∈ Z. Additi- onally, we expose arithmetic applications of the binary pair algorithm, among which highlight the relationship between binary and decimal bases, and propose, as a product of this work, a didactic sequence about the binary numbering system on Z in playful way with the known mathematical game "Matemágica dos cartões numerados", whose operation is based on the conversion of binary decimal expressions of integers.