The size of the physical address space of a processor is $2^{32}$ bytes. The capacity of a cache memory unit is $2^{23}$ bytes. The cache block size is 128 bytes. The cache memory unit can be built as a direct mapped cache or as a $K$-way set-associative cache, where $K=2^L$ and $L \in\{1,2,3\}$. Let the length of the TAG field be $M$ bits for the direct mapped cache, and $N$ bits for the set-associative cache.

Which one of the following options is true?

The EX stage of a pipelined processor performs the memory read operations for LOAD instructions, and the operations for the arithmetic and logic instructions. Let $t_{E X}$ denote the time taken by the EX stage to perform the operation for an instruction. For each instruction type, the values of $t_{E X}$ and $M$ (the number of instructions of that type in a sequence of 100 instructions for a program $P$ ), are given in the table below. The duration of the pipeline clock cycle is 1 nanosecond. Assume that the latch time for the interstage buffers in the pipeline is negligible.

When program $P$ is executed, the number of clock cycles for which the pipeline is stalled due to structural hazards in the EX stage is $\_\_\_\_$ . (answer in integer)

Let $n$ be an odd number greater than 100 . Consider a binary minheap with $n$ elements stored in an array $P$ whose index starts from 1. Which of the following indices of $P$ do/does NOT correspond to any leaf node of the minheap?

Consider a hash table $P[0,1, \ldots, 10]$ that is initially empty. The hash table is maintained using open addressing with linear probing. The hash function used is $h(x)=(x+7) \bmod 11$. Consider the following sequence of insertions performed on $P$ :

$$ 1,13,22,15,11,24 $$

Which of the following positions in the hash table is/are empty after these insertions are performed?