# Broken Bloom Filters

A bloom filter is composed of a bit array of $$2^{16}$$ bits. We are told that the filter is designed to be optimally performing when there are $$2^8$$ entries.

Given that the filter is filled with $$2^8$$ entries, what is the expected number of queries one has to perform to perform to get a false positive?

If your answer is $$x$$, enter the value of $$\lfloor \log_{10} x \rfloor$$.

Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

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