Skew binary number system non-zero digits, a form called the sparse representations of numbers by Okasaki, incrementation and decrementation can be performed in constant time. Other arithmetic operations are performed by switching between the skew binary representation and the binary representation. Given a skew binary number, its value can be computed by a loop, computing the successive values of formula_4 and adding it once or twice for each formula_5 such that the formula_5th digit is 1 or 2 respectively. A more efficient method is now given, with only bit representation and one substraction. The skew binary number of the form formula_7 without 2 and
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