Question
Explain how
logical addresses are translated into physical addresses in a paged system, mentioning
the role of the page table.
logical addresses are translated into physical addresses in a paged system, mentioning
the role of the page table.
Answers
GPT-4o mini
In a paged memory management system, logical addresses used by a process (also referred to as virtual addresses) are translated into physical addresses used by the hardware (main memory). This translation is critical for the efficient and secure use of memory in modern operating systems. Here's how the translation works, including the role of the page table:
### 1. **Logical Address Structure:**
A logical address typically consists of two components:
- **Page Number (p)**: Identifies which page within the logical address space the address belongs to.
- **Offset (d)**: Identifies a specific location within that page.
For example, in a system with a page size of 4 KB (2^12 bytes), a logical address might look like this:
- Logical Address = Logical Page Number (p) | Offset (d)
### 2. **Page Table:**
The page table is a crucial data structure that maps the logical page numbers to physical frame numbers in the main memory. Each process has its own page table which is maintained by the operating system.
The entries in the page table contain:
- **Frame Number (f)**: The physical location (or frame) in memory where the data for that page is stored.
- **Status Bits**: Information such as whether the page is in memory or on disk, access permissions, etc.
### 3. **Address Translation Process:**
When a process attempts to access a memory address, the following steps occur:
1. **Extracting Page Number and Offset**: The logical address is divided into the page number (p) and the offset (d) based on the page size.
2. **Page Table Lookup**:
- The operating system uses the page number (p) to index into the page table.
- It retrieves the frame number (f) corresponding to the page.
3. **Generating Physical Address**:
- The physical address is then constructed by combining the frame number (f) with the offset (d).
- Since the offset remains the same in both logical and physical addresses (it refers to the same position within the page), the physical address is given by:
\[
\text{Physical Address} = (\text{Frame Number} \times \text{Page Size}) + \text{Offset}
\]
### 4. **Example:**
Assume we have:
- Page Size = 4 KB (thus, offset size = 12 bits)
- Logical Address = 0x12345 (or decimal 74565)
1. Split the logical address:
- Calculate page number (p) and offset (d):
- p = \( \frac{74565}{4096} \) = 18 (in decimal) (Page size is 4096 bytes)
- d = \( 74565 \mod 4096 \) = 221 (in decimal)
2. Look up page table:
- Assume the page table entry for page 18 gives frame number 5.
3. Compute the physical address:
- Physical Address = \( (5 \times 4096) + 221 \)
- Physical Address = 20480 + 221 = 20701
### Summary:
The page table is essential for converting logical addresses to physical addresses by maintaining mappings from logical page numbers to physical frame numbers. The translation ensures that processes can operate in their own memory spaces while still allowing for efficient and secure memory management.
### 1. **Logical Address Structure:**
A logical address typically consists of two components:
- **Page Number (p)**: Identifies which page within the logical address space the address belongs to.
- **Offset (d)**: Identifies a specific location within that page.
For example, in a system with a page size of 4 KB (2^12 bytes), a logical address might look like this:
- Logical Address = Logical Page Number (p) | Offset (d)
### 2. **Page Table:**
The page table is a crucial data structure that maps the logical page numbers to physical frame numbers in the main memory. Each process has its own page table which is maintained by the operating system.
The entries in the page table contain:
- **Frame Number (f)**: The physical location (or frame) in memory where the data for that page is stored.
- **Status Bits**: Information such as whether the page is in memory or on disk, access permissions, etc.
### 3. **Address Translation Process:**
When a process attempts to access a memory address, the following steps occur:
1. **Extracting Page Number and Offset**: The logical address is divided into the page number (p) and the offset (d) based on the page size.
2. **Page Table Lookup**:
- The operating system uses the page number (p) to index into the page table.
- It retrieves the frame number (f) corresponding to the page.
3. **Generating Physical Address**:
- The physical address is then constructed by combining the frame number (f) with the offset (d).
- Since the offset remains the same in both logical and physical addresses (it refers to the same position within the page), the physical address is given by:
\[
\text{Physical Address} = (\text{Frame Number} \times \text{Page Size}) + \text{Offset}
\]
### 4. **Example:**
Assume we have:
- Page Size = 4 KB (thus, offset size = 12 bits)
- Logical Address = 0x12345 (or decimal 74565)
1. Split the logical address:
- Calculate page number (p) and offset (d):
- p = \( \frac{74565}{4096} \) = 18 (in decimal) (Page size is 4096 bytes)
- d = \( 74565 \mod 4096 \) = 221 (in decimal)
2. Look up page table:
- Assume the page table entry for page 18 gives frame number 5.
3. Compute the physical address:
- Physical Address = \( (5 \times 4096) + 221 \)
- Physical Address = 20480 + 221 = 20701
### Summary:
The page table is essential for converting logical addresses to physical addresses by maintaining mappings from logical page numbers to physical frame numbers. The translation ensures that processes can operate in their own memory spaces while still allowing for efficient and secure memory management.