Binary number double the number to be converted, record if the result is at least 1, and then throw away the integer part. For example, formula_10, in binary, is: Thus the repeating decimal fraction 0... is equivalent to the repeating binary fraction 0... . Or for example, 0.1, in binary, is: This is also a repeating binary fraction 0.0... . It may come as a surprise that terminating decimal fractions can have repeating expansions in binary. It is for this reason that many are surprised to discover that 0.1 + ... + 0.1, (10 additions) differs from 1 in floating point arithmetic.
Binary number as 0 hexagrams can be interpreted as sequence from 0 to 63. The Indian scholar Pingala (c. 2nd century BC) developed a binary system for describing prosody. He used binary numbers in the form of short and long syllables (the latter equal in length to two short syllables), making it similar to Morse code. Pingala's Hindu classic titled Chandaḥśāstra (8.23) describes the formation of a matrix in order to give a unique value to each meter. The binary representations in Pingala's system increases towards the right, and not to the left like in the binary numbers of the modern, Western