From the history of the binary number system. Francesco Brunetti

Abstract

The article describes the book of the Italian mathematician Francesco Brunetti "Arimmetica binomica...", published in 1746. Examples of numbers from the book, examples of addition, subtraction, multiplication, division and extraction of the square root in the binary system, as well as binary values of the logarithms of a number of numbers are given. The book also presents operations on fractions and mixed binary numbers. Attention is drawn to the original way of writing binary numbers proposed by Brunetti. According to this method, instead of the entire binary number, only the numbers (in the form of decimal digits) of those digits in which units are represented (with numbering starting from the right) are recorded. Ordinal numbers of digits greater than 9, Brunetti proposes to designate as their last digit (0, 1, ..., 9), writing a comma (prime) to the right of all such digits, and numbers greater than 19 — similarly with two commas, etc. With such a notation, four arithmetic operations on binary numbers are greatly facilitated (the article provides an example of adding the numbers written accordingly).