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[ Option B ]

[ Option B ]

Paging is a memory management technique that divides physical memory into fixed-size blocks called frames and logical memory into blocks of the same size called pages. Pages are mapped to frames using a page table, allowing non-contiguous allocation of memory.

[ Option A ]

In a paging system, the logical address space is divided into fixed-size pages, and a page table maps each logical page to a physical frame in memory. In this problem, the system has a 32-bit logical address space, which means it can address 2³² bytes.
The page size is given as 4 KB, which is 2¹² bytes. To find the number of pages, we divide the total logical address space by the page size: 2³²/ 2¹²=2²⁰.
Since each page requires one entry in the page table, the page table will contain 2²⁰ entries.

[ Option C ]

In Cache Memory, a main memory address is divided into tag, index, and block offset fields if using Direct Mapping.

• The index field identifies the specific cache line where the memory block is stored.
• The tag field identifies which block from main memory is stored in that cache line.

If main memory has 2ⁿ words and cache has 2^K words, then:
Index field = K bits (To select one of 2^K cache lines)
Tag field = n−K bits (Remaining bits to identify the memory block)

[ Option A ]

In a virtual memory system that uses paging, the virtual address space can be larger than the available physical memory, because only the required pages of a program are loaded into main memory at any given time, while the rest remain on secondary storage. Hence, statement I is true. 
Statement II is false because a program does not need to be completely resident in main memory throughout its execution, only the currently needed pages are brought into memory on demand. 
Statement III is false because pages are fixed-size blocks determined by the system, not based on the semantic or logical structure of the program.

[ Option C ]

Memory Interleaving is a technique used to improve memory performance by dividing memory into multiple banks so that they can be accessed simultaneously.
In two-way memory interleaving, memory is organized into two banks, allowing:

• 8-bit operations from one bank.
• 16-bit operations using both banks together.

This increases data transfer speed and improves overall system performance.

[ Option B ]

A Read Only Memory (ROM) is a type of non-volatile memory used to store data permanently. The notation “m × n” in memory terminology means that the ROM contains m words, and each word consists of n bits.

• The first number (32) represents the number of memory locations (words).
• The second number (8) represents the number of bits stored per word (i.e., output lines).

In a 32 × 8 ROM, there are 32 memory locations, and each location can store 8 bits of data. This means the ROM can store a total of 32×8=256 bits of information. Hence, a 32 × 8 ROM is best described as “32 words of 8 bits each.”

[ Option B ]

[ Option C ]

The virtual address is 38 bits long, where 10 bits are for the page directory and 16 bits for the page table. Each page table entry is 4 bytes. So, the number of entries in a page table is 2¹⁶. Multiplying by 4 bytes gives 2¹⁸ bytes, which is equal to 256 KB. Hence, the maximum size of a page table is 256 KB.

[ Option D ]

The Valid-Invalid bit in a page table entry is used to check whether a page belongs to a process’s logical address space. If the bit is valid (1), the page is part of the process and can be accessed. If it is invalid (0), the page does not belong to the process, and any access attempt will cause a memory protection error. This mechanism helps the operating system prevent illegal memory access and ensures safe process isolation.

[ Option A ]

[ Option B ]

Cache memory is a small, high-speed memory placed between the CPU and main memory to reduce access time. Average Memory Access Time (AMAT) is calculated using the formula:
AMAT = (Hit Ratio × Cache Access Time) + (Miss Ratio × Main Memory Access Time)

• Hit Ratio is the fraction of memory accesses found in the cache.
• Miss Ratio = 1 − Hit Ratio.

Given:
Cache access time = 100 ns
Main memory access time = 1000 ns
Hit ratio = 0.9
Miss Ratio=1−0.9=0.1
AMAT = (0.9×100) + (0.1×1000) = 90 + 100 = 190 ns
Approximating to the closest option gives 200 ns.

[ Option D ]

In Operating Systems (OS), page replacement algorithms are used when a page fault occurs and physical memory is full. The system must decide which existing page should be removed to make space for the new page.

[ Option A ]

In an Operating System (OS) that uses paging, both logical memory and physical memory are divided into fixed-size blocks.

When a program is executed:

• Its logical memory is divided into pages.
• Physical Memory (RAM) is divided into frames.
• Each page is loaded into a frame.

[ Option B ]

Thrashing occurs in a paging system when a process spends more time swapping pages in and out of memory than executing instructions.
It typically happens when the system does not have enough physical memory to hold the working set of all active processes. Thrashing leads to severe performance degradation, as the CPU is mostly idle waiting for page transfers.

[ Option D ]

In an Operating System (OS) that uses virtual memory, physical memory (RAM) is divided into fixed-size blocks called frames, and logical memory is divided into pages. When a program tries to access a page that is not currently in memory, a page fault occurs.
At this time, the OS needs to bring the required page from the disk into main memory. To do this efficiently, the OS maintains a Free-Frame List, which is a list of all the empty frames available in physical memory.
When a page fault happens, the OS selects a free frame from this list, loads the required page into it, and updates the page table.

So, the free-frame list helps the operating system know which parts of memory are empty so it can quickly allocate space whenever a new page needs to be loaded due to a page fault.

[ Option D ]

In Paging Systems, when a page fault occurs and memory is full, the OS must decide which page to replace.
LRU (Least Recently Used) algorithm evicts the page that has been unused for the longest time, under the assumption that pages used recently are more likely to be used again soon. This is based on temporal locality of reference, a key principle in memory access patterns.
So, LRU page replacement algorithm uses the principle of evicting the page that has not been used for the longest period of time.

[ Option D ]

The Optimal Page Replacement Algorithm replaces the page that will not be used for the longest period in the future. This algorithm gives the minimum possible number of page faults.
Given Reference String : 6, 0, 5, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 5, 2

Total Page Faults = 8