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The Binary Overflow Theorem | Synapse

February 21, 20260 citationsOpen Access

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The Binary Overflow Theorem

BWBrian Wooldridge

Puntos clave

To establish a universal theorem that defines the overflow of powers of real numbers relative to their nearest smaller power of two.
Mathematical derivation of the theorem
Analysis of real numbers greater than one
Examination of positive integers as exponents
The exact relationship between a power of a real number and the nearest smaller power of two is defined
Overflow is quantified as the difference between the power and the largest power of two not exceeding it

Resumen

We establish a universal, exact theorem governing the overflow of any power of any real base relative to its nearest smaller power of two. For any real number p > 1 and positive integer m, let N = pᵐ. The overflow of N — defined as the difference between N and the largest power of two not exceeding N

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Cite This Study

Brian Wooldridge (Thu,) studied this question.

synapsesocial.com/papers/69994cdf873532290d021b25 https://doi.org/https://doi.org/10.5281/zenodo.18699395

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