Why Base-20, Base-40, and Base-60 Number Systems?
نویسندگان
چکیده
Historically, to describe numbers, some cultures used bases much larger than our usual base 10, namely, 20, 40, and 60. There are explanations for 60, there is explanation but 40—used in medieval Russia—remains largely a mystery. In this paper, we provide possible all these three bases, an based on the natural need manage large groups of people. We also speculate why different bases.
منابع مشابه
Auto-similarity in Rational Base Number Systems
This work is a contribution to the study of set of the representations of integers in a rational base number system. This prefix-closed subset of the free monoid is naturally represented as a highly non regular tree whose nodes are the integers and whose subtrees are all distinct. With every node of that tree is then associated a minimal infinite word. The main result is that a sequential trans...
متن کاملPatterns in Rational Base Number Systems
Number systems with a rational number a/b > 1 as base have gained interest in recent years. In particular, relations to Mahler’s 32 -problem as well as the Josephus problem have been established. In the present paper we show that the patterns of digits in the representations of positive integers in such a number system are uniformly distributed. We study the sum-of-digits function of number sys...
متن کاملModular Multiplication and Base Extensions in Residue Number Systems
We present a new RNS modular multiplication for very large operands. The algorithm is based on Montgomery’s method adapted to residue arithmetic. By choosing the moduli of the RNS system reasonably large, an effect corresponding to a redundant high-radix implementation is achieved, due to the carry-free nature of residue arithmetic. The actual computation in the multiplication takes place in co...
متن کاملPowers of rationals modulo 1 and rational base number systems
A new method for representing positive integers and real numbers in a rational base is considered. It amounts to computing the digits from right to left, least significant first. Every integer has a unique such expansion. The set of expansions of the integers is not a regular language but nevertheless addition can be performed by a letter-to-letter finite right transducer. Every real number has...
متن کاملComplex base numeral systems
In this paper will be introduced large, probably complete family of complex base systems, which are ’proper’ for each point of the space there is a representation which is unique for all but some zero measure set. The condition defining this family is the periodicity we get periodic covering of the plane by fractals in hexagonal-type structure, what can be used for example in image compression....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Studies in systems, decision and control
سال: 2023
ISSN: ['2198-4182', '2198-4190']
DOI: https://doi.org/10.1007/978-3-031-16415-6_9