Past exam of the mathematics course of the University of Cambridge / 2007 / ia / Paper 5 / 8 / d / Solution

An inode is a filesystem object record, identified by its inode number. It contains file type and mode bits, owner/group identifiers, link count, file size, timestamps and the information locating data blocks. It normally does not contain the filename: directory entries map names to inode numbers, allowing several names to refer to one inode. In the traditional Unix layout, there are direct block pointers and single-, double- and triple-indirect pointers. A single-indirect block points to data blocks; a double-indirect block points to single-indirect blocks; the triple-indirect level adds one further pointer layer.

Let $D$ be the number of direct pointers. Before triple indirection is needed, the file can use $D$ directly addressed data blocks, 512 singly addressed data blocks and $512^2$ doubly addressed data blocks. Indirection blocks consume disk space but are not part of the file's logical byte contents. HenceThe PDF does not specify $D$. With the common twelve-direct-pointer convention, this is $4096(12+512+512^2)=1,075,888,128$ bytes; with ten direct pointers, substitute $D=10$. The formula, rather than an unstated choice of direct-pointer count, determines the answer for the given inode layout. Actual filesystems can use other pointer organizations such as extents.