Brojevni sustavi

Abstract

Prvi brojevni sustavi razvili su se oko 3500. g. pr. Kr. kada su i prvi puta uvedene brojke. Stare civilizacije koristile su brojevne sustave s bazama 10, 12, 20 i 60. Nas u ovom radu zanimaju općeniti brojevni sustavi s bazom koja je proizvoljan prirodni broj veći od 1. Za njih proučavamo funkciju sume znamenaka definiranu na prirodnim brojevima te općenitije brojanje blokova znamenki. U drugom dijelu rada promatramo prikaz u bazi $k$ s drugim skupom znamenki te neke nestandardne prikaze poput Fibonaccijevog, Ostrovskijevog ili prikaza u negativnoj ili kompleksnoj bazi.The first numeration systems evolved around 3500 BC. when the numbers were introduced for the first time. Old civilizations used numeration systems with bases 10, 12, 20, and 60. In this work, we are interested in general numeration systems with a base that is an arbitrary positive integer greater than one. We study the sum of digits function defined on positive integers and, more generally, functions counting blocks of digits. In the second part of this work, we examine representations in base $k$ with alternative set of digits and some non-standard representations such as Fibonacci's, Ostrowsky's and also representations in negative or complex bases