Past exam of the year 1 of the computer science course of the University of Oxford / 2014 / Digital systems, linear algebra, introduction to formal proof / 2 / f / Solution

With a resident inode, the deepest allowed path uses two address blocks and one file data block, so every byte through the end of the doubly indirect region meets the three-read bound. There are ten directly addressed file data blocks, 512 singly addressed ones and $512^2$ doubly addressed ones. Therefore the largest contiguous file satisfying this bound isThe next byte requires the triply indirect region, with three address-block reads and a fourth read for the file data block.

The resident-inode convention is essential. If the question's three reads must also include fetching a previously uncached inode, only two further reads remain; the maximum is thenNeither figure includes arbitrary pathname-resolution reads. These are worst-case counts in the traditional fully allocated multilevel inode indexing model; existing buffer cache entries can reduce them.