Broken Bloom Filters

Computer Science Level 3

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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