10/05/2006

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It turns out there are a couple of emails in my backlog that I should
deal with.

But first, congratulations on surviving the first midterm.  Enjoy the weekend
and a little time away from 306.  See you in class on Monday when we will try
to take it to the next level.

Meanwhile, two messages that I want to respond to.

Dr. Patt,
My friend ****** and I were working on the 2004 exam and checked our
answers with the solutions...on question number 5, the dice game
question,
he noticed that there are two states for sums of two and three with back
lines to the start for all four states, as well as a back line for sum=1
(how can you get a sum of 1 after two die rolls, can't you only push the
button to go back to start after two rolls of the die?). We don't quite
understand why there are back lines on both Sum=2's and both Sum= 3's?
For example, considering the Sum=2's, we figured that one of the Sum=2
states would be for the first roll (when you roll a two) and the other
would be when you get a sum of 2 after two rolls (1+1)...wouldnt this
be the only case in which you would go back? Why would you go back
after just one roll? Could you please clarify this, thanks!

Much Appreciated,
<<name withheld to protect one who thinks everyone plays by the rules>>

You are correct: if you played the game according to the rules,
you would never hit B after one roll.  But not everyone plays the game
according to the specified rules, so we wanted to be sure if some idiot
pushes the button after the first roll, the finite state machine does
not go into some sort of coma.  It seemed to us that if someone did
that, the best solution would be to take the machine back to the
intial state.

If people played the game the way they are supposed to, the transitions
along the B lines you mentioned would never occur.

AND, a different kind of question:

I remember you telling me at Camp Texas this last Summer that the dual
processors work by splitting up the work.

True.  I did make my annual pilgrimage to Camp Texas in August and
I did tell you that.

processor1 does a little bit spits something out while
processor2 does the next part and spits it out right
after processor1's output to make it faster.

Not exactly.  Processors 1 and 2 can be working independently for awhile and
then converge at a relevant point in time.  If I remember correctly, at Camp
Texas I gave you the example of computing n! with two processors.  Say n=14.
You could have processor 1 compute 2 x 4 x 6 x 8 x 10 x 12 x 14 while
processor 2 is computing 3 x 5 x 7 x 9 x 11 x 13.  At the end of cycle 5,
processor 2 stores the result of its computation.  At the end of cycle 6,
processor 1 stores the result of its computation.  In cycle 7, both results
are multiplied, yielding the result 14!.  If we had one processor, it would
take 12 cycles.  You see the point?

If that is true then you could essentially double the speed.

BUT, only if the problem allowed you to break it down this way.
Not all problems are so accomodating.

But would there be 2 different clocks one for each processor or just one
that runs twice as fast?  I think it would be two, or maybe one with
a not
gate attached to it running to the other processor. ( Or else you could
have two values competing for the circuit.

Actually, you could have one clock at the same speed controlling both
processors.  With a symphony orchestra, do you have a separate conductor
controlling each instrument with his/her baton, or does one conductor
control all the processors (oops, I mean instruments!).

How close am I?

Define "close."

<<name withheld to protect the inquisitive one>>

Yale Patt

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