A computer system implements a $$40$$-bit virtual address, page size of $$8$$ kilobytes, and a $$128$$-entry translation look-aside buffer $$(TLB)$$ organized into $$32$$ sets each having four ways. Assume that the $$TLB$$ tag does not store any process id. The minimum length of the $$TLB$$ tag in bits is ________________.

A computer system implements $$8$$ kilobyte pages and a $$32$$-bit physical address space. Each page table entry contains a valid bit, a dirty bit, three permission bits, and the translation. If the maximum size of the page table of a process is $$24$$ megabytes, the length of the virtual address supported by the system is _______________ bits.

Consider six memory partitions of sizes $$200$$ $$KB,$$ $$400$$ $$KB,$$ $$600$$ $$KB,$$ $$500$$ $$KB,$$ $$300$$ $$KB$$ and $$250$$ $$KB,$$ where $$KB$$ refers to kilobyte. These partitions need to be allotted to four processes of sizes $$357$$ $$KB,$$ $$210$$ $$KB,$$ $$468$$ $$KB$$ and $$491$$ $$KB$$ in that order. If the best fit algorithm is used, which partitions are NOT allotted to any process?

Consider the following C function.

int fun ( int n ) {

   int x = 1, k ;

   if ( n == 1) return x ;

   for( k = 1 ; k < n ; ++ k )

       x = x + fun( k ) * fun( n - k ) ;

   return x ;

}

The return value of fun (5) is ________.