1. The formula for maximum file size for the current UNIX BSD file system is given by:

    2¹⁰ * (10 + 2⁸ + 2¹⁶ + 2²⁴)

    Each pointer points at a 1KB (i.e., 2¹⁰ B) data block.  There are 10 pointers directly to data blocks, one pointer to an indirect block that contains 2⁸ (i.e., 256) pointers to data blocks, one    pointer to a doubly-indirect block that points to 2⁸ indirect blocks (each of which points to 2⁸ data blocks), and one pointer to a triply-indirect block (that points to 2⁸ doubly-indirect blocks, each of which points to a singly-indirect block, etc.).

1. If we add a quadruply indirect block pointer to the file header then the maximum size that a file could be (in bytes) is given by  the formula:


2¹⁰ * (10 + 2⁸ + 2¹⁶ + 2²⁴ + 2³²) =  2⁴² + 2³⁴ + ...

2. If we increase the block size to 4KB then the formula becomes:


    2¹² * (10 + 2¹⁰ + 2²⁰ + 2³⁰) =  2⁴² + 2³² + ...

Therefore adding a quadruply indirect block pointer to the file header will allow larger file sizes than increasing the block size to 4KB.
 

2. We need to update the following information on the disk:

• Contents of the bitmap that represents the free space on the disk,
• Contents of the current directory file (to add the new file "foo"),
• A new file header for the new file "foo",
• 16 data blocks for the contents of file "foo",
• One indirect block to point to the last 6 data blocks of "foo".

   Since UNIX employs metadata consistency, that means that all the disk blocks EXCEPT the 16 data blocks for file "foo" get written as soon as possible by the operating system.  Thus, the OS will immediately write the following disk blocks:
 
•  Contents of the free space bitmap,
• The disk block containing the newly allocated file header for "foo",
• One indirect block to point to the last 6 data blocks of "foo",
• The disk block of the file representing the current directory to which the new entry for file "foo" has been added (you may assume that new entry did not cause the directory's size to grow into another disk block).

   We accepted any order for the above disk write operations, as long as you said that they get written to the disk immediately instead of after 30 seconds.

   Since UNIX employs 30-second write-behind for user data, the 16 data blocks comprising the contents of "foo" get written to disk by the operating system at the next 30 second "write-flush" instance.