Question

If a logical address in a paged memory management system is \(\langle 2,133\rangle\), what do the values mean?

Short answer

Page number is 2, offset is 133.

Step-by-step solution

Understanding the Logical Address

A logical address in a paged memory system has two parts: the page number and the offset. In this exercise, the address is given in the form \((p,o)\) where \(p\) is the page number, and \(o\) is the offset within that page.

Identifying the Page Number

In the given logical address \((2,133)\), the first value \(2\) represents the page number. This means the address refers to the second page within the memory space.

Identifying the Offset

The second value \(133\) in the logical address \((2,133)\) is the offset. This indicates the specific location, 133 units from the start, within page number 2.

Conclusion

Thus, the logical address \(\langle 2,133 \rangle\) represents the address 133 units into page 2 within the memory in a paged memory management system.

Key concepts

Logical Address

In a paged memory management system, the concept of a logical address is crucial for efficiently organizing and accessing data. A logical address is a reference to a memory location that is used by programs to access memory content.

It consists of two parts: the page number and the offset. This system allows operating systems to manage data without worrying about the actual physical location in memory, providing an abstraction.

• The page number indicates which page in memory should be accessed.
• The offset tells you the exact position within the specified page.

By separating the address into two segments, it simplifies memory management and increases the efficiency of accessing memory resources.

Page Number

The page number is an essential part of paged memory management systems. It denotes which specific page in the memory should be accessed by the system.

Imagine the memory as a book, with each page holding different pieces of data. The page number in a logical address acts much like the page number in a book, pointing out which section to look at next.

By having a page number:

• Memory is divided into equal-sized blocks, called pages.
• Pages help in efficient utilization of memory by eliminating fragmentation.
• The system can quickly identify and access large blocks of memory.

In our exercise, a logical address of \((2,133)\), for example, indicates page number 2 should be accessed.

Memory Management System

A memory management system is pivotal in any modern computer architecture. It organizes and coordinates how data is stored and retrieved in memory.

The system ensures that a computer’s memory resources are used efficiently. Paged memory management, specifically, breaks memory into fixed-size pages. This allows quick access and flexible management.

• Prevents memory leakage by recycling memory that is no longer needed.
• Optimizes performance by minimizing delays when accessing frequently used data.
• Facilitates multiple processes to utilize memory space simultaneously.

This system provides protection, ensuring that processes do not interfere with each other's memory space, thus improving overall stability and reliability.

Offset

The offset within a logical address specifies the exact location within a page. After identifying which page to access using the page number, the system needs to pinpoint the precise position to be read or written on that page.

The offset is these coordinates, measured in units, such as bytes, from the start of the page.

• It can be thought of as the line number on a particular page in a book.
• Combines with the page number to give the complete logical address.
• Allows programs to efficiently and accurately access small chunks of data within larger blocks.

For instance, an offset of 133 in the logical address \((2,133)\) directs the system to the 134th position (considering the count starts at 0) on page 2.