Determine the number of page table entries (PTES) that are needed for the following combinations of virtual address size (n) and page size (P): n P=2P Number of PTES 16 4K 16 BK 32 4K 32 BK

Computer Networking: A Top-Down Approach (7th Edition)
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ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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The answers are NOT 1048576(2^20) and 524288(2^19)

### Educational Website Content

#### Page Table Entries Calculation

To understand and implement efficient memory management systems, it is essential to determine the number of page table entries (PTEs) required for various combinations of virtual address size (n) and page size (P).

#### Example Problem

**Question: Determine the number of page table entries (PTEs) that are needed for the given combinations of virtual address size (n) and page size (P):**

\[ n = P = 2^p \]

| Virtual Address Size (n) | Page Size (P) | Number of PTEs |
| ------------------------ | ------------- | -------------- |
| 16                       | 4K            |                |
| 16                       | 8K            |                |
| 32                       | 4K            |                |
| 32                       | 8K            |                |

#### Steps to Calculate PTEs

1. **Identify the Virtual Address Size (n)**: This is typically a power of 2 (e.g., 16, 32).
2. **Select the Page Size (P)**: This is also typically a power of 2 (e.g., 4K, 8K).
3. **Calculate the Number of PTEs**:
   \[
   \text{Number of PTEs} = \frac{\text{Virtual Address Size}}{\text{Page Size}}
   \]

#### Practical Task

To better understand this concept, let's work through an example.

**Example Calculation for a 16-bit Virtual Address and a 4K Page Size:**

- **Virtual Address Size (n)**: 16 bits
- **Page Size (P)**: 4K

\[ \text{Number of PTEs} = \frac{2^{16}}{4K} = 2^{16-12} = 2^4 = 16 \]

#### Interactive Section

**Part C:** Determine the number of page table entries (PTEs) in the third line. Express your answer as an integer.

```
Input: 8192
Incorrect; Try Again
```

**Part D:** Determine the number of page table entries (PTEs) in the fourth line. Express your answer as an integer.

```
Input: 8192
Incorrect; Try Again
```

---

#### Conclusion

Understanding the calculation of page table entries is crucial for
Transcribed Image Text:### Educational Website Content #### Page Table Entries Calculation To understand and implement efficient memory management systems, it is essential to determine the number of page table entries (PTEs) required for various combinations of virtual address size (n) and page size (P). #### Example Problem **Question: Determine the number of page table entries (PTEs) that are needed for the given combinations of virtual address size (n) and page size (P):** \[ n = P = 2^p \] | Virtual Address Size (n) | Page Size (P) | Number of PTEs | | ------------------------ | ------------- | -------------- | | 16 | 4K | | | 16 | 8K | | | 32 | 4K | | | 32 | 8K | | #### Steps to Calculate PTEs 1. **Identify the Virtual Address Size (n)**: This is typically a power of 2 (e.g., 16, 32). 2. **Select the Page Size (P)**: This is also typically a power of 2 (e.g., 4K, 8K). 3. **Calculate the Number of PTEs**: \[ \text{Number of PTEs} = \frac{\text{Virtual Address Size}}{\text{Page Size}} \] #### Practical Task To better understand this concept, let's work through an example. **Example Calculation for a 16-bit Virtual Address and a 4K Page Size:** - **Virtual Address Size (n)**: 16 bits - **Page Size (P)**: 4K \[ \text{Number of PTEs} = \frac{2^{16}}{4K} = 2^{16-12} = 2^4 = 16 \] #### Interactive Section **Part C:** Determine the number of page table entries (PTEs) in the third line. Express your answer as an integer. ``` Input: 8192 Incorrect; Try Again ``` **Part D:** Determine the number of page table entries (PTEs) in the fourth line. Express your answer as an integer. ``` Input: 8192 Incorrect; Try Again ``` --- #### Conclusion Understanding the calculation of page table entries is crucial for
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