• Ancient: Acharya Pingal

• Inventor: Acharya Pingal (Scholar of mathematics and Father of binary system)

• Time Period: 2nd century BCE

• Location: Bharatvarsh

• Evidence:  

Chandashastra

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अर्ध इत्यनुवर्तते । विषमसङ्ख्यायामेकमधिकं निक्षिप्य ततोऽर्धयेत । 
तत्रैको गकारो लभ्यते । तं पूर्वलब्धाल्लकारात् परं स्थापयेत् । 
ततो द्विसंख्यावशिष्यते । पुनस्तामर्थ- येत, ततश्चैकलकारं दद्यात् । 
ततश्चैकसंख्यावशिष्यते । तत्र तावत् सैके गिति लक्षण- मावर्तनीयं यावद्धृत्ताक्षराणि षट् पूर्यन्ते ।
 एवं सङ्ख्यान्तरेऽपि योज्यम्

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Meaning:
"In the case of an odd number, one should add one more and then halve it. In doing so, one obtains 'guru' as the remainder. That 'guru' should be added after the previous result. Then, divide the result by two. Again, following the same process, add 'laghu' after the result. Then divide the result by two. This process should continue until the syllables are exhausted. In this manner, even for other numbers, the same process should be followed."

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• In Pingala's system:

  • "Laghu" represents the digit 1.

  • "Guru" represents the digit 0.

 

• In contrast to modern binary numbers, which often rise to the left, Acharya Pingal's binary representation advances to the right. Acharya Pingal's system commences at number one, instead of zero. The initial pattern, "0000," has four short syllables and represents the number one. One is added to the total of the place values to obtain the numerical value.

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• Modern Connection: Leibniz's binary system finds inspiration in Acharya Pingal's Chandashastra, an ancient Indian mathematical text.