### Numeral systems in antiquity and modernity

V. I. Tikhvinsky, V.V. Kholmogorov

#### Abstract

Mankind has long sought to simplify the computational process. Having divided counting units into digits, it came up with a number system [1]. The number system is a way of writing numbers with special characters. The number in such a record shows the number of ones in the digit of the number. A number is a set of one or more digits that determines the total number of units calculated. A unit is a measure for counting something.

A number system can have one or more bases. The base shows how many times the unit of the next digit is greater than the unit of the previous one. In a system with more than one base, several digits can play the role of one, as will be shown later. The digit of the number has a weight that determines how many times the number of units of the current digit is greater than the units from which the counting began.

There are non-positional number systems in which the digit determines both the number of units in the digit of the number and the weight of this digit. In positional number systems, the weight of the digit depends on the position of the digit in the numerical set.

Initially, the number systems were non-positional, writing their numbers was associated with a counting board. The counting board was a field divided into stripes, in other words, recesses. Counting stamps moved in the stripes [2]. The stamps were deposited on the left side of the counting board and discarded on the right side. The number of stamps set aside determined the number of calculated units. To record set aside units by a scribe on papyrus or other medium for a particular brand of counting board discharge, a specific symbol was used to indicate both the counted unit on the counting board and the weight of the discharge. The digit could consist of a set of symbols of the same type that determine the number of units in the digit [3], which will be shown in the examples below.

PDF (Russian)

#### References

R.S. Guter, Yu.L. Polunov, From the abacus to the computer, - M .: “Knowledge”, 1982. -208 p.

Tikhvinsky V.I., Prehistory of computing automation in the pre-computer era, -M .: Management and business administration, No. 3, 2015 -199-202 p.

Vygodsky M.Ya., Arithmetic and algebra in the ancient world, -M.: Nauka, 1967. -367 p.

Depman I.Ya., History of arithmetic, -M.: Ministry of Education, 1959. -405 p.

V. Kuzmishchev, Mystery of the Maya Priests, 1968, -357 p.

Ershova G. G., Maya: secrets of ancient writing, - M .: Aleteya, 2004. -296 p.

Bergman G. A. A number system with an irrational base. Mathematics Magazine, 1957, no. 31, 98-119.

Stakhov A.P., Bergman number system and new properties of natural numbers, Institute of the Golden Section - Mathematics of Harmony (http://www.trinitas.ru/rus/doc/0232/004a/02321068.htm)

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