# Broken Bloom Filters

**Computer Science**Level 4

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.