The correct answer is B) power of 2.

Why Page Size is Typically a Power of 2:

In computer systems and operating systems, the size of a page in virtual memory is typically chosen to be a power of 2. This design choice offers several advantages and is rooted in the underlying hardware and software considerations. Here’s a detailed explanation of why page size is typically a power of 2:

Binary Representation:

Computer systems use binary representation at the hardware level. In binary, numbers are expressed using only two digits: 0 and 1. This binary representation aligns well with powers of 2, making calculations and addressing more efficient.

When the page size is a power of 2, it aligns perfectly with the binary representation, simplifying memory addressing and manipulation. For example, with a page size of 2^10 (1024 bytes), each page can be addressed using a 10-bit binary number.

Memory Addressing:

Memory addressing in computer systems is done using binary addresses. Each binary digit (bit) in an address corresponds to a power of 2. When the page size is also a power of 2, it matches this addressing scheme seamlessly.

For example, with a page size of 2^12 (4096 bytes), each address can be expressed using 12 bits, allowing for direct and efficient memory access within pages.

Efficient Division and Multiplication:

Binary powers of 2 allow for highly efficient division and multiplication operations. Shifting bits left or right in binary, which is equivalent to multiplying or dividing by powers of 2, is much faster and simpler in hardware than arbitrary divisions or multiplications.

This efficiency is essential for various memory management operations, including page table lookups and address translation.

Memory Hierarchy:

Modern computer systems often feature memory hierarchies with multiple levels of cache. These cache levels frequently use block sizes that are powers of 2 to align with memory pages.

Using page sizes that are powers of 2 ensures that cache lines and memory pages are of compatible sizes, optimizing data transfer between levels of the memory hierarchy.

Why the Other Options Are Not Correct:

A. Varied:

Having page sizes that vary arbitrarily would introduce complexity and inefficiency in memory management. It would require custom addressing and handling for each page size, leading to more complex page tables and translation mechanisms.

Uniformity in page size simplifies memory management and allows for consistent addressing and calculations.

C. Power of 4:

While power of 4 page sizes are a possibility, they are less common and less aligned with binary representation and memory addressing. Using powers of 2 offers greater simplicity and compatibility with binary systems.

Powers of 4 may be used in specific contexts, but they are not the typical choice for page sizes in most general-purpose computer systems.

D. None of the Mentioned:

This option is not correct because, as explained above, page sizes are typically chosen to be powers of 2 in computer systems and operating systems. It is a well-established and widely followed convention due to the advantages it offers in terms of efficiency and simplicity.

In conclusion, the practice of using page sizes that are powers of 2 in computer systems is based on the inherent characteristics of binary representation, memory addressing, and hardware efficiency.

It simplifies memory management, enhances addressability, and aligns well with the binary nature of computing systems. This convention has been widely adopted to optimize memory utilization and access in modern computer architectures.