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a) Assuming a 1 KB page size, what are the page numbers and offsets for the following logical addresses references (provided as decimal numbers). Show all calculations steps. : • 21112 5500050 b) Consider a 1 KB page size and a process size 66800, calculate the internal fragmentation. Show all calculations steps.

a) Assuming a 1 KB page size, what are the page numbers and offsets for the following logical addresses references (provided as decimal numbers). Show all calculations steps. : • 21112 5500050 b) Consider a 1 KB page size and a process size 66800, calculate the internal fragmentation. Show all calculations steps.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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## Operating System ### Problem Set a) Assuming a 1 KB page size, what are the page numbers and offsets for the following logical addresses references (provided as decimal numbers). Show all calculation steps. - 21112 - 5500050 b) Consider a 1 KB page size and a process size of 66800, calculate the internal fragmentation. Show all calculation steps. --- ### Solution **a) Calculation of Page Numbers and Offsets:** To find the page number and offset for a given logical address, follow these steps: 1. **Convert the page size to bytes:** 1 KB = 1024 bytes. 2. **Page Number:** Divide the logical address by the page size. 3. **Offset:** The remainder of the logical address divided by the page size. **For the logical address 21112:** 1. Page Number \( = \left\lfloor \frac{21112}{1024} \right\rfloor = \left\lfloor 20.625 \right\rfloor = 20 \) 2. Offset \( = 21112 \mod 1024 = 21112 - (20 \times 1024) = 21112 - 20480 = 632 \) **Result:** - Page Number: 20 - Offset: 632 **For the logical address 5500050:** 1. Page Number \( = \left\lfloor \frac{5500050}{1024} \right\rfloor = \left\lfloor 5371.0458984375 \right\rfloor = 5371 \) 2. Offset \( = 5500050 \mod 1024 = 5500050 - (5371 \times 1024) = 5500050 - 5500032 = 18 \) **Result:** - Page Number: 5371 - Offset: 18 --- **b) Calculation of Internal Fragmentation:** To calculate internal fragmentation: 1. **Convert the page size to bytes:** 1 KB = 1024 bytes. 2. **Total Pages Required:** Divide the process size by the page size and round up to the next whole number. 3. **Internal Fragmentation:** Calculate the number of unused bytes in the last page. **For a process size of 66800:** 1. Total Pages
Transcribed Image Text:## Operating System ### Problem Set a) Assuming a 1 KB page size, what are the page numbers and offsets for the following logical addresses references (provided as decimal numbers). Show all calculation steps. - 21112 - 5500050 b) Consider a 1 KB page size and a process size of 66800, calculate the internal fragmentation. Show all calculation steps. --- ### Solution **a) Calculation of Page Numbers and Offsets:** To find the page number and offset for a given logical address, follow these steps: 1. **Convert the page size to bytes:** 1 KB = 1024 bytes. 2. **Page Number:** Divide the logical address by the page size. 3. **Offset:** The remainder of the logical address divided by the page size. **For the logical address 21112:** 1. Page Number \( = \left\lfloor \frac{21112}{1024} \right\rfloor = \left\lfloor 20.625 \right\rfloor = 20 \) 2. Offset \( = 21112 \mod 1024 = 21112 - (20 \times 1024) = 21112 - 20480 = 632 \) **Result:** - Page Number: 20 - Offset: 632 **For the logical address 5500050:** 1. Page Number \( = \left\lfloor \frac{5500050}{1024} \right\rfloor = \left\lfloor 5371.0458984375 \right\rfloor = 5371 \) 2. Offset \( = 5500050 \mod 1024 = 5500050 - (5371 \times 1024) = 5500050 - 5500032 = 18 \) **Result:** - Page Number: 5371 - Offset: 18 --- **b) Calculation of Internal Fragmentation:** To calculate internal fragmentation: 1. **Convert the page size to bytes:** 1 KB = 1024 bytes. 2. **Total Pages Required:** Divide the process size by the page size and round up to the next whole number. 3. **Internal Fragmentation:** Calculate the number of unused bytes in the last page. **For a process size of 66800:** 1. Total Pages
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