Question

Suppose a computer contained \(512 \mathrm{MB}\) (MiB) of main memory, and an operating system needed to create a virtual memory of twice that size using pages of \(2 \mathrm{~KB}\) (KiB). How many pages would be required?

Short answer

524288 pages are required.

Step-by-step solution

Determine Virtual Memory Size

The physical memory is given as \(512 \text{ MiB}\). The virtual memory needed is twice that size. Calculate the virtual memory size: \(512 \text{ MiB} \times 2 = 1024 \text{ MiB}\).

Convert Virtual Memory Size to Bytes

Convert the virtual memory size from MiB to bytes. Since 1 MiB = \(2^{20}\) bytes, 1024 MiB equals \(1024 \times 2^{20} = 2^{30}\) bytes.

Convert Page Size to Bytes

The page size is given as 2 KiB. Convert this page size to bytes: \(2 \text{ KiB} = 2 \times 2^{10} = 2^{11}\) bytes.

Calculate Number of Pages

Determine the number of pages by dividing the virtual memory size (in bytes) by the page size (in bytes). Using the previous conversions: \[\frac{2^{30}}{2^{11}} = 2^{19} = 524288 \text{ pages}.\]

Key concepts

Memory Management

Memory management is a crucial component of computer systems. It involves the handling and organization of memory in a way that allows an operating system to efficiently allocate resources to processes and applications. Effective memory management ensures that applications have access to adequate memory resources.
There are different approaches to memory management:

• Contiguous Memory Allocation: Allocates a single contiguous section of memory to a process.
• Segmentation: Memory is divided into varying-sized segments often aligned to different needs.
• Paging: Divides memory into fixed-sized pages to optimize space usage and manage virtual memory.

Memory management impacts system performance, ensuring programs run smoothly and efficiently without unnecessary delays.

Paging

Paging is a memory management scheme that eliminates the need for contiguous blocks of memory and thus reduces fragmentation. In paging, both physical memory and virtual memory are divided into fixed-sized pages.
The advantages of paging are numerous:

• Reduces the complexity of memory allocation by using pages of fixed size.
• Utilizes the virtual memory technique to give the illusion of infinite memory.
• Improves the management of memory by enabling non-contiguous storage.

With paging, when a process requests data that is not in physical memory, a page fault occurs. The system then retrieves the required page from secondary storage, ensuring efficient memory use across multiple processes.

Operating Systems

The operating system (OS) is the backbone of a computer system, managing hardware and software resources. It acts as an intermediary between users and the computer hardware. One key function of the OS is memory management, where it employs techniques like paging to manage virtual memory.
Key functions of an operating system include:

• Process Management: Handling active processes on the system by allocating CPU time.
• Memory Management: Utilizing techniques like paging for efficient memory use.
• File System Management: Organizing, storing, and tracking data in the file system.
• Device Management: Controlling the operation of hardware devices through drivers.

The OS ensures seamless operation of applications, optimal resource allocation, and user-friendly interaction with the computer system.

Binary Conversions

Binary conversions are essential in computer systems as computers operate using binary (base-2) numeral system. Understanding binary conversions helps in memory size calculations, such as converting between units used in memory (bytes, kilobytes, megabytes).
Here's how some binary conversions work:

• Kibibytes (KiB) to Bytes: 1 KiB = \(2^{10}\) bytes.
• Megibytes (MiB) to Bytes: 1 MiB = \(2^{20}\) bytes.
• Gibibytes (GiB) to Bytes: 1 GiB = \(2^{30}\) bytes.

By understanding these conversions, you can perform various calculations required in memory management, such as determining the number of pages in a virtual memory setup. These conversions ensure precision in calculations necessary in operating system functions.