structural:reformatting, information:filtering, information:extraction, stylistic:tone
Leibniz

Leibniz wrote in excess of a hundred manuscripts on binary, most of them remaining unpublished. Before his first dedicated work in 1679, numerous manuscripts feature early attempts to explore binary concepts, including tables of numbers and basic calculations, often scribbled in the margins of works unrelated to mathematics.

His first known work on binary, “On the Binary Progression", in 1679, Leibniz introduced conversion between decimal and binary, along with algorithms for performing basic arithmetic operations such as addition, subtraction, multiplication, and division using binary numbers. He also developed a form of binary algebra to calculate the square of a six-digit number and to extract square roots..

His most well known work appears in his article Explication de l'Arithmétique Binaire (published in 1703).The full title of Leibniz's article is translated into English as the "Explanation of Binary Arithmetic, which uses only the characters 1 and 0, with some remarks on its usefulness, and on the light it throws on the ancient Chinese figures of Fu Xi ". Leibniz's system uses 0 and 1, like the modern binary numeral system. An example of Leibniz's binary numeral system is as follows:

While corresponding with the Jesuit priest Joachim Bouvet in 1700, who had made himself an expert on the I Ching while a missionary in China, Leibniz explained his binary notation, and Bouvet demonstrated in his 1701 letters that the I Ching was an independent, parallel invention of binary notation.Leibniz & Bouvet concluded that this mapping was evidence of major Chinese accomplishments in the sort of philosophical mathematics he admired. Of this parallel invention, Liebniz wrote in his "Explanation Of Binary Arithmetic" that "this restitution of their meaning, after such a great interval of time, will seem all the more curious."

The relation was a central idea to his universal concept of a language or characteristica universalis, a popular idea that would be followed closely by his successors such as Gottlob Frege and George Boole in forming modern symbolic logic. Leibniz was first introduced to the I Ching through his contact with the French Jesuit Joachim Bouvet, who visited China in 1685 as a missionary. Leibniz saw the I Ching hexagrams as an affirmation of the universality of his own religious beliefs as a Christian. Binary numerals were central to Leibniz's theology. He believed that binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing.

is not easy to impart to the pagans, is the creation ex nihilo through God's almighty power. Now one can say that nothing in the world can better present and demonstrate this power than the origin of numbers, as it is presented here through the simple and unadorned presentation of One and Zero or Nothing.