Fri, 22nd Sept 2017, 00:01 Re: Problem Set 2 Clarifications

A student writes:

> Hello Dr. Patt,
> I had some questions about what some of the questions and terms on the
> problem set meant exactly. 

The student had questions about three problems.  Problem 3:

> For question 3, what does the term "identity" mean? Is it asking what value
> should replace "X" so that the output will be the same as the given input?

No!  "Identity" means what it has always meant, at least since high school.
An equation has a left side and a right side.  On each side we have
independent variables, in this case logical variables that can each take on
the value 0 or 1.

You have an identify if for all input combinations, the left side and the
right side evaluate to the same logical value.

To be sure you understood, we worked "part a" for you.  "0 OR X" is identical
to "what"?  The answer is "0 OR X is identical to X" because the one logical
variable X can take on one of two values, 0 or 1.  In both cases, the value
of the left side is identical to the value of the right side.

> For example, in a., should a value replace "X" so that the output will
> equal 0, the given input? If so, then what is e. asking for?

Second question: Problem 5.

> For question 5, does "4-to-1" and "2-to-1" muxes mean 4 or 2 inputs and 1
> output?

This one I am disappointed that you are asking.  Did you see Fig 3.12 on
page 61, where we discuss muxes?  What is the caption of the figure?
What do you suppose a 4-to-1 mux is?

> Also, what does B) mean? What is the "F"? The output?

You are given a logic equation F = A XOR B and asked to implement it with
"only" two 2-to-1 muxes.  That is, if you had a box, with inputs A,B and
output F, and the box was to implement F = A XOR B, how would you connect
two 2-to-1 muxes inside that box so that the output would in fact produce
the result A XOR B.

This problem is very tricky, and so I need to tell you something: I would
never put a problem like this on an exam because it is too tricky, and you
could spend hours looking at the two muxes and not figure it out.  However,
from time to time, I will put problems like this on the homework to challenge

Having said that, you should also know that I will put on exams problems that
will test how well you understand the concepts in the course.  They will not
be trick problems, but they will require you to really understand the concepts
in the course in order to solve them.  Those problems I will expect you to
solve in the time you have to take the exam.

Bottom line: there are so many problems I can give you that test your deep
understanding that I will never have to waste your time on an exam with any
trick problems.

Finally, Problem 11.

> For question 11, what is a "comparator"?

The statement of the problem directed you to page 92 of the textbook.  Did
you look at page 92?  Is it not clear that a "comparator" COMPARES two values
and provides the output, A is greater than B, A is less than B, or they are

> I'm sorry if I'm asking you while already having figured out what the
> question is actually asking. I know you said you get frustrated whenever
> students don't figure out something that, for the most part, is obvious.
> The questions/terms just weren't that clear to me, so figured it would be
> better to be safe than sorry and ask for clarification.

Actually, this brings up an important point.  You say you figured it out, but
needed clarification.  Are you in a study group?  Did you check with other
members of your study group?  Doing so should be enough to clarify?

> Thank you,
> <<name withheld to protect the student who just needs to clarify>>