Consider a file system on a disk that has both logical and physical block sizes of $512$ bytes. Assume that the information about each file is already in memory. For each of the three allocation strategies $($contiguous$,$ linked, and indexed$),$ answer these questions:

a$.$ How is the logical$-$to$-$physical address mapping accomplished in this system? $($For the indexed allocation, assume that a file is always less than $512$ blocks long.$)$

b$.$ If we are currently at logical block $12($the last block accessed was block $12)$ and want to access logical block $5,$ how many physical blocks must be read from the disk?