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SCIENCE OF
BINARY ENCODING
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CombinatoricsThe
Chandaḥ-śāstra
presents the first known description of a binary numeral system in
connection with the systematic enumeration of
all possible modifications of the syllabic
meters.[4]
The
commentary of Halayudha discloses some
important concepts of Vedic combinatorics such
as binomial theorem
and Pascal's triangle
(called Meru-prastāra,
Space of Meru ).
Pingala's work also contains the basic ideas of Fibonacci number, called Mātrā-meru, and now known as the Gopala–Hemachandra number.[5] The first clear literary definition and extensive use of zero is ascribed to Pingala who defined and represented 0 and 1 as short and long syllables. As Pingala's system ranks binary patterns starting at zero (three long syllables—binary "000"—is the first pattern), the n-th decimal pattern corresponds to the binary representation of n-1, written backwards.  
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