The binary notation in the I Ching is used to interpret its quaternary divination technique. The I Ching dates from the 9th century BC in China. This method can be seen in use, for instance, in the Rhind Mathematical Papyrus, which dates to around 1650 BC. In this method, multiplying one number by a second is performed by a sequence of steps in which a value (initially the first of the two numbers) is either doubled or has the first number added back into it the order in which these steps are to be performed is given by the binary representation of the second number. The method used for ancient Egyptian multiplication is also closely related to binary numbers. Early forms of this system can be found in documents from the Fifth Dynasty of Egypt, approximately 2400 BC, and its fully developed hieroglyphic form dates to the Nineteenth Dynasty of Egypt, approximately 1200 BC. Horus-Eye fractions are a binary numbering system for fractional quantities of grain, liquids, or other measures, in which a fraction of a hekat is expressed as a sum of the binary fractions 1/2, 1/4, 1/8, 1/16, 1/32, and 1/64.
The scribes of ancient Egypt used two different systems for their fractions, Egyptian fractions (not related to the binary number system) and Horus-Eye fractions (so called because many historians of mathematics believe that the symbols used for this system could be arranged to form the eye of Horus, although this has been disputed). Leibniz was specifically inspired by the Chinese I Ching.Īrithmetic values thought to have been represented by parts of the Eye of Horus However, systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, and India.
The modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harriot, Juan Caramuel y Lobkowitz, and Gottfried Leibniz. 7 Conversion to and from other numeral systems.Signed-digit representation ( balanced ternary).