CPSC 3300 - Spring 2017
Homework 2
Due at class time on Thursday, February 2
Each student must turn in a separate set of homework solutions,
but you may work together in study groups with other students
from the class. Include the names of your study group members on
the solution set you submit. (It is acceptable for the group to
prepare one document and then for each group member to turn in a
copy of that document with his or her name highlighted or circled.)
Also, please provide sufficient space on your homework solutions
so that your calculations and answers are easily readable and so
that grading will be easier. Furthermore, except for the simplest
of questions, giving only the answer without showing your work
is not acceptable. For the best chance at partial credit, show
the generic equation you are starting with and any derivations
needed to handle the information as given in the question, then
plug in the values from the question.
1. For a processor with 3 GHz clock frequency (a.k.a. clock rate),
what is the clock cycle time? (6 pts.)
2. Find the execution time for a program that executes 3 billion
instructions on a processor with an average CPI of 2.0 and a
clock frequency of 4 GHz. (10 pts.)
3. P1 has a 3.0 GHz clock frequency and an average CPI of 1.5 on
a given program. If the processor executes that program in 10
seconds, find: (6 pts. each)
(a) the number of cycles, and
(b) the number of instructions.
[This is question 1.5(b) for processor P1 from the textbook.]
4. What is the MIPS rate for processor P1 in question 2 above?
Use the MIPS formula that contains only the clock rate and CPI.
(6 pts.)
5. For the following workload and cycle values, find the average
CPI. [This is a weighted average that uses the instruction
frequencies as weights. You do not divide by three.] (6 pts.)
type | freq cycles
-------+--------------
alu | 0.4 1
ld/st | 0.4 4
branch | 0.2 2
6. If a new compiler for the computer in question 5 could reduce
the number of instructions to 80% of the original total and
alter the instruction frequencies in the following manner,
what would be the total speedup? (18 pts.)
type | freq cycles
-------+--------------
alu | 0.6 1
ld/st | 0.3 4
branch | 0.1 2
7. Consider a vector computer in which vector mode can provide a
speedup of 10. Using Amdahl's Law: (12 pts. each)
(a) What is the overall speedup for each incremental twentieth
in the fraction of vectorization (i.e., f = 0.05, 0.1, 0.15,
..., 0.95, 1.0)? You should express the speedup values with
two decimal places. (Hint: use a spreadsheet. You can also
chart the values.)
(b) What amount of vectorization is required for an overall
speedup of 2? Solve the problem algebraically and express
the answer as a reduced fraction rather than a decimal or
a percentage.
(c) What amount of vectorization is required for an overall
speedup of 5? Solve and express the answer as directed in
part (b).
8. Arithmetic/Harmonic/Geometric. Circle one of A, H, or G, as
applies. (2 pts. each)
A H G - Used for averaging normalized times or rates.
A H G - Used for averaging execution rates.
A H G - Used for averaging execution times.