CSE 141 Homework # 1

To allow us to grade in parallel, please write up part A and part B on separate sheets of paper.

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Part A
1. Suppose that when Program A is run, the user CPU time is 3 seconds, the elapsed wallclock time is 4 seconds, and the system performance is 10 MFLOP/sec. Assume that there are no other processes taking any significant amount of time, and the computer is either doing calculations in the CPU, or doing I/O, but it can't do both at the same time. We now replace the processor with one that runs six times faster, but doesn't affect the I/O speed. What will the user CPU time, the wallclock time, and the MFLOP/sec performance be now?
2. You are on the design team for a new processor. The clock of the processor runs at 200 MHz. The following table gives instruction frequencies for Benchmark B, as well as how many cycles the instructions take, for the different classes of instructions. For this problem, we assume that (unlike many of today's computers) the processor only executes one instruction at a time.

   Instruction type	Frequency	Cycles
   Loads & Stores	30%	6 cycles
   Arithmetic instructions	50%	4 cycles
   All others	20%	3 cycles

   • Calculate the CPI for Benchmark B.
   • The CPU execution time on the benchmark is exactly 11 seconds. What is the ``native MIPS'' processor speed for the benchmark in millions of instructions per second?
   • The hardware expert says that if you double the number of registers, the cycle time must be increased by 20%. What would the new clock speed be (in MHz)?
   • The compiler expert says that if you double the number of registers, then the compiler will generate code that requires only half the number of Loads & Stores. What would the new CPI be on the benchmark?
   • How many CPU seconds will the benchmark take if we double the number of registers (taking into account both changes described above)?

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   Part B (please start a new sheet of paper here!)
3. Using the web, a catalog, or other source of up-to-date information, find the cost of memory (in dollars/MByte) for the three different storage technologies:
   • DRAM (just the chips or SIMMs, not the motherboard, power supply, and other stuff needed to make them useful.)
   • Hard disk drives.
   • Digital (DAT or DLT) tape drive plus tapes. Assume you'll spend half you budget on the tape drive and half on buying a bunch of tape cartridges or cassettes.
   For each technology, compute $/MByte using current product prices. You don't need to find the cheapest, but look for something reasonably economical. For price information, give name of the product and the source (i.e. the URL or name of the catalog or whatever) where you found the information.
4. How many bits can dance on the head of a pin? -- a back-of-the-envelope calculation (BotEC). Estimate how many bits can be stored in an area the size of a pin head on:
   • Semiconductor memory (using current DRAM technology).
   • Magnetic memory (using the technology of hard disk drives).
   The question is, how densely the bits can be packed on the silicon or iron oxide -- don't consider the space required by the chip's packaging or the disk's motors or head.

   Your BotEC estimate should use the BotEC format described in class: formulas, estimates, and calculations. Be sure to include the units (pin-heads per square millimeter, bits per Byte, square inches per disk platter, etc.) in your estimates and calculations. And remember, the overworked graders will have little patience for trying to make sense of a jumble of incomprehensible symbols.