CSCI 4320 (Principles of Operating Systems), Fall 2010:
Homework 4

Credit:
20 points.

Reading

Be sure you have read Chapter 3, sections 3.1 through 3.3.

Problems

Answer the following questions. You may write out your answers by hand or using a word processor or other program, but please submit hard copy, either in class or in my mailbox in the department office.

  1. (5 points) Consider a computer system with 10,000 bytes of memory whose MMU uses the simple base register / limit register scheme described in section 3.2 of the textbook, and suppose memory is currently allocated as follows:

    Answer the following questions about this system.

    1. What value would need to be loaded into the base register if we performed a context switch to restart process $ A$ ?

    2. What memory locations would correspond to the following virtual (program) addresses in process $ A$ ?

      • 100

      • 4000

  2. (5 points) Consider a computer system using paging to manage memory; suppose it has 64K ($ 2^{16}$ ) bytes of memory and a page size of 4K bytes, and suppose the page table for some process (call it process $ A$ ) looks like the following.

    Page number Present/absent bit Page frame number
    0 1 5
    1 1 6
    2 1 2
    3 0 ?
    4 0 ?
    5 1 7
    6 0 ?
    ... 0 ?
    15 0 ?

    Answer the following questions about this system.

    1. How many bits are required to represent a physical address (memory location) on this system? If each process has a maximum address space of 64K bytes, how many bits are required to represent a virtual (program) address?

    2. What memory locations would correspond to the following virtual (program) addresses for process $ A$ ? (Here, the addresses will be given in hexadecimal, i.e., base 16, to make the needed calculations simpler. Your answers should also be in hexadecimal. Notice that if you find yourself converting between decimal and hexadecimal, you are doing the problem the hard way. Stop and think whether there is an easier way!)

      • 0x1420

      • 0x2ff0

      • 0x4008

      • 0x0010

    3. If we want to guarantee that this system could support 16 concurrent processes and give each an address space of 64K bytes, how much disk space would be required for storing out-of-memory pages? Explain your answer (i.e., show/explain how you calculated it). Assume that the first page frame is always in use by the operating system and will never be paged out. You may want to make additional assumptions; if you do, say what they are.

  3. (5 points) Now consider a bigger computer system, one in which addresses (both physical and virtual) are 32 bits and the system has $ 2^{32}$ bytes of memory. Answer the following questions about this system. (You can express your answers in terms of powers of 2, if that is convenient.)

    1. What is the maximum size in bytes of a process's address space on this system?

    2. Is there a logical limit to how much main memory this system can make use of? That is, could we buy and install as much more memory as we like, assuming no hardware constraints? (Assume that the sizes of physical and virtual addresses don't change.)

    3. If page size is 4K ($ 2^{12}$ ) and each page table entry consists of a page frame number and four additional bits (present/absent, referenced, modified, and read-only), how much space is required for each process's page table? (You should express the size of each page table entry in bytes, not bits, assuming 8 bits per byte and rounding up if necessary.)

    4. Suppose instead the system uses a single inverted page table (as described in section 3.3.4 of the textbook), in which each entry consists of a page number, a process ID, and four additional bits (free/in-use, referenced, modified, and read-only), and at most 64 processes are allowed. How much space is needed for this inverted page table? (You should express the size of each page table entry in bytes, not bits, assuming 8 bits per byte and rounding up if necessary.) How does this compare to the amount of space needed for 64 regular page tables?

  4. (5 points) Tanenbaum says, in one of the questions at the end of the chapter, that although the 8086 processor provided no support for virtual memory, there were companies that sold computer systems that used an unmodified 8086 processor and did paging. How do you think they managed this? (Hint: Think about the logical location of the MMU.)


Berna Massingill
2010-10-29