 Solution

Let a disk block number and a file number each occupy $h$ bytes. System B spends about $3h$ bytes per physical block on successor/count, predecessor and owner, leaving $B-3h$ payload bytes. It also needs its per-file header. In the traditional inode scheme, file data blocks are entirely payload; indexing occupies the fixed inode and separate indirect blocks.

For $N$ data blocks in a large densely occupied indirect tree, about $N/q$ lowest-level index blocks, $N/q^2$ next-level blocks and so on are needed. With $q=B/h$, the asymptotic indexing space is approximatelyor about $Nh$ bytes when $q$ is large. ThusThis is a comparison of typical densely used structures. For a small file, the fixed inode dominates; near an indirect-level boundary, partly empty index blocks add overhead. Both schemes can waste part of the last block through internal fragmentation.

The main performance advantage is indexed access to an arbitrary file offset: the inode finds the required data block with at most three indirect levels, whereas System B may need to follow a long chain from one end. Index blocks can be cached and scanned in batches, leaving complete data blocks for transfers. The inode scheme also naturally supports sparse files, where absent data-block pointers represent zero-filled holes without allocating every intervening block.

There are additional costs. A cold lookup can require separate index-block reads, allocation near a boundary can require allocating and updating several index blocks, and small files can pay more fixed metadata cost. System B already has a tail pointer and can append with local chain updates, while its owner and predecessor fields can help recovery from surviving blocks. Losing a UNIX indirect block can disconnect many data blocks, and those blocks do not automatically carry System B's owner information. Thus the space and file offset access advantages do not imply uniformly cheaper updates or uniformly better recovery.