CS439: Principles of Computer Systems

Discussion Section 6 Problem Set Solutions

Due in Section on Friday, March 6, 2026

The problem set must be completed before section and brought to section. To ensure that your problem set is turned in correctly and that you receive credit for discussion section, you must follow these guidelines exactly.

Include the following header at the top of your file:

Discussion Section Problem Set #:
Student Name:
EID:

You may either type your answers or write them by hand, but you must have a copy with you in discussion section.

In discussion section, your TA will check that you made a good effort on the problem set, you are participating in the discussions in section, and you are ready and able to answer when called upon. If all of those are true, you will receive credit for discussion section that day. Note that a "good effort" on the problem set includes that all answers are in words unique to you and not copied from anywhere else, including the slide deck.

Draw a picture that shows how to translate a logical address into a physical address in a single-level forward-mapped paging system that includes a TLB.

Assume you have a virtual memory system that uses paging. Is the system vulnerable to internal and/or external fragmentation? Explain.

Consider a two-level paging system with 128 pages and a page size of 256 bytes. The system has 2048 bytes of physical memory and is byte addressable. Assume the first-level page table holds 8 entries.
1. How many bits are in a physical address?
2. How many bits of the virtual address represent the first-level page table?
3. How many bits of the virtual address represent the second-level page table?
4. How many bits are in the complete virtual address?
5. What size are the page frames?

Name two advantages of using small pages and two advantages of using large pages in a paging mechanism. Why are page sizes growing in paging memory systems?

Belady's anomaly: Intuitively, it seems that the more frames the memory has, the fewer page faults a program will get. Surprisingly enough, this is not always true. Belady (1969) discovered an example in which FIFO page replacement causes more faults with four page frames than with three. This strange situation has become known as Belady's anomaly. To illustrate, a program with five virtual pages numbered from 0 to 4 references its pages in the order: 0 1 2 3 0 1 4 0 1 2 3 4
1. Using FIFO replacement and assuming demand paging, compute the number of page faults with 3 frames. Repeat for 4 frames.
2. Compute the number of page faults under LRU, the clock algorithm, and the optimal algorithm. What do you notice?
Consider a program with seven virtual pages numbered from 0 to 6 references its pages in the order:

0 1 3 6 2 4 5 2 5 0 3 1 2 5 4 1 0

Using clock page replacement algorithm with 4 frames and assuming demand paging, compute the number of page faults and show the state of frames (pages in frames and value of clock bit) after each page access.