Past exam of the year 1 of the computer science course of the University of Oxford / 2013 / Digital systems, linear algebra, introduction to formal proof / 3 / e

A traditional UNIX-like file system identifies a computer file by an inode number. Its inode records file metadata, such as byte length, ownership and permissions, and contains direct file data block addresses plus indirect block pointers. A file-system directory maps a name to the inode number; the filename need not be stored inside the inode.

In the familiar direct/single/double/triple scheme, a single indirect block pointer reaches a block of data-block addresses, a double indirect block pointer reaches blocks of those addresses, and a triple indirect block pointer adds one more level. If there are $d$ direct pointers, one pointer of each indirect level, block size $B$ bytes and pointer width $h$ bytes, put $q=\lfloor B/h\rfloor$. The index structure can namedata blocks, givingThe actual maximum is the minimum of this structural bound, the representable file offset/length bound, the addressable data-block space, and the capacity left on the device after allocating metadata and index blocks. For an unsigned $\ell$-bit byte-length field, its bound is $2^{\ell }-1$ bytes. An empty computer file is permitted and needs no data blocks in this scheme. Exact numerical limits cannot be given without the inode layout and field widths; different UNIX-like implementations choose different layouts, and some use extent trees rather than this traditional scheme.