SMRTR Science & EngineeringJun 5, 2025John D. Cook

Binomial number system

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The binomial number system represents non-negative integers using a sum of three binomial coefficients. Every number can be uniquely expressed as C(c,3) + C(b,2) + C(a,1), where 0 ≤ a < b < c. This system has potential applications in signal processing. A Python implementation demonstrates how to find the coefficients a, b, and c for any given number, with an example using today's date. The system could be extended to use more than three binomial terms if desired.

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