What Is The Difference Between External And Internal Fragmen

What Is The Difference Betweenexternalandinternal Fragmentationgiven

What is the difference between external and internal fragmentation? Given five memory partitions of 100 KB, 400 KB, 200 KB, 300 KB, and 700 KB in order, how would each of the first-fit, best-fit, and worst-fit algorithms place processes of 312 KB, 217 KB, 112 KB, and 426 KB? Consider a computer system with a 32-bit logical address and 2-KB page size. The system supports up to 256 MB of physical memory. How many entries are there in a conventional page table? Explain your answer. Consider a paging system with the page table stored in memory. If a memory reference takes 120 nanoseconds, how long does a paged memory reference take? Explain your answer. If we add TLBs, and 70% of all page-table references are found in the TLBs, what is the effective memory reference time? Assume that finding a page-table entry in the TLBs takes zero time if the entry is there.

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What Is The Difference Betweenexternalandinternal Fragmentationgiven

The concepts of external and internal fragmentation are fundamental in understanding memory management within operating systems. External fragmentation occurs when free memory is divided into small, noncontiguous blocks scattered throughout the system, making it difficult to allocate large contiguous memory segments despite having enough total free space. Internal fragmentation, on the other hand, arises when allocated memory blocks contain unused space within them, often because of fixed partition sizes that are larger than the actual memory required by processes. This leads to inefficient utilization of memory resources.

External fragmentation is characterized by the fragmentation of free memory space, which cannot be used efficiently for process allocation. This situation often results from dynamic memory allocation and deallocation, where free spaces are broken into smaller pieces over time. Compaction techniques can sometimes mitigate external fragmentation by reorganizing memory to create larger contiguous free blocks. Conversely, internal fragmentation results from the mismatch between allocated memory and process needs—when, for example, fixed-size partitions are used, and a process’s memory requirement is less than the partition size, leaving unused memory within the allocated segment. Internal fragmentation can be reduced by adopting variable-sized partitions or paging.

Memory Allocation Algorithms and Process Placement

Given five memory partitions of 100 KB, 400 KB, 200 KB, 300 KB, and 700 KB, and processes of 312 KB, 217 KB, 112 KB, and 426 KB, different placement strategies can be employed:

First-Fit Algorithm

First-fit places each process in the first available partition large enough. For process 312 KB, the first suitable partition is 400 KB. After placement, the remaining free space is 88 KB in this partition. Next, process 217 KB is placed in 400 KB, but since 400 KB has already been partly occupied, the subsequent free space will be evaluated. Continuing with process 112 KB, it will be allocated to the 400 KB partition (remaining 171 KB). Process 426 KB cannot be placed because no large enough partition is available.

Best-Fit Algorithm

Best-fit searches for the smallest partition that can accommodate each process. It seeks to minimize wasted space. For process 312 KB, the best fit is the 400 KB partition, leaving 88 KB unused. Process 217 KB is allocated to the 300 KB partition, which is the best fit for its size, leaving 83 KB free. Process 112 KB fits into the remaining small partitions appropriately, but since 100 KB is too small, it is allocated to 200 KB. Process 426 KB cannot fit into any remaining partition.

Worst-Fit Algorithm

Worst-fit assigns processes to the largest available partition. The 700 KB partition is chosen for process 312 KB, leaving 388 KB free. Then, process 217 KB is allocated in the 700 KB partition, leaving 171 KB free. Next, process 112 KB fits into the remaining large partitions, and finally, process 426 KB is too large for remaining partitions.

Page Table Entries Calculation

With a 32-bit logical address and a 2 KB page size, the number of pages is determined by dividing the total address space by page size. Since the maximum physical memory supported is 256 MB, or 268,435,456 bytes, the total number of pages can be calculated as:

Number of pages = Total physical memory / Page size = 268,435,456 bytes / 2,048 bytes = 131,072 pages.

Thus, the page table contains 131,072 entries, each mapping a virtual page to a physical frame.

Memory Reference and TLB Impact

In a paging system, a memory reference involves two steps: accessing the page table and then accessing the actual memory location. If each reference takes 120 nanoseconds without a TLB, the total time for a paged memory reference is typically the sum of the page table lookup and the memory access. When the page table is stored in memory, an additional delay is introduced for the page table reference itself during the first access, leading to a best-case total of around 2 × 120 ns (one for the page table access and one for the data).

The introduction of a Translation Lookaside Buffer (TLB) significantly reduces the effective memory access time. With 70% of page table references found in the TLB, only 30% require access to the page table in memory. Assuming immediate access for TLB hits (zero time), the effective memory time can be calculated as:

Effective access time = (TLB hit rate × memory access time) + (TLB miss rate × (page table access + memory access))

= 0.70 × 120 ns + 0.30 × (120 ns + 120 ns) = 0.70 × 120 ns + 0.30 × 240 ns = 84 ns + 72 ns = 156 ns.

Hence, the use of TLBs reduces the average memory access time considerably, demonstrating their importance in efficient memory management.

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