Fri, 16 Sep 2011, 18:40

One of the study groups is confused about truth tables and muxes.  If you 
are not confused about truth tables and muxes, feel free to delete and 
move on.  If you are still confused about muxes, please continue to read.

A student writes:

> Dr. Patt,
> 
> My study group and I were looking over number six and the more we think
> about it, the more we feel that we are not understanding the question.
> 
> When the question is asking for the output for the truth table, are you
> asking for the binary bit or for the input that will be outputted by the
> mux?

What is a truth table?  Answer: a table that shows what the output will be
for every combination of input variables.  In this case, there are 6 input
variables (four sources A,B,C,D and two control signals S1,S0 which will 
select which of the sources will be at the output).

What is the output of a truth table?  Answer: the binary value that will be
present at the output for each of the input combinations.  ...otherwise known
as the column of binary values labeled OUT.  In this case, since there are
6 input variables, there must be 2^6 input combinations.  That means the output
of the truth table is the 2^6 outputs you would get for the 2^6 input
combinations.  ...in other words, "Please fill in the output column of the
truth table."

> When we draw out the diagram using the "2 to 1" mux's, we started out by
> needing to have 8 mux's. 

You do not need 8 muxes.  Did you ask the TA about this in discussion section?

> By doing this, we are getting if both S0 and S1
> (Control Signals) are 0, then the output is 0 (16 out of the 64 cases)
> whereas every other case is a 1 ( 48 out of the 64 cases).
> We are wondering if we are using the right approach or are missing the
> purpose and intent of the question completely.
> 
> Thanks in Advance,
> <<name withheld to protect the student who needs to re-read Section 3.3.2.>> 

I think you need to start over.

Question 1: What does a 2-to-1 mux do?  Answer: It selects one of two
sources to put at the output.

Question 2: How does it do it?  <<I will let you answer this>>

Question 3: What does a 4-to-1 mux do?  <<I leave that for you also>>

Question 4: What must it have to be able to do that?  

Hopefully, going through this sequence of questions will provide the
"Aha!" to enable you to design the four-input mux with two-input muxes.
If not (after an acceptable amount of thinking) ask one of the TAs or me.

Good luck finishing the problem set!
Yale Patt