Day 44: Discrete Math

The return of the section 7.3 homework (problems 18/20(a,b) and 19/21).

Some of you will need to bone up on Quine-McCluskey! Feel free to stop by for assistance during finals week, or to email me with questions.

A finite state machine cannot "self-flush": each input results in a single output, so if there is "padding" required it takes away from the "real" output.

Our machine is much more complex than hers, however - she beats us in minimization! What I didn't like about hers was the states' labels: for example, there is no state labelled as s₀. I was also confused by them, thinking that she was considering the input pairwise, when in fact it fairly reflected the role of each state. So now I like hers okay - but it still doesn't flush!

As an example of minimization, we'll show how our machine and her machine are equivalent.

A tad more about Finite-State Machines (minimization)

(As discussed last time, the homework for this section may be turned in for extra credit as late as Monday of next week. It will be graded by Wednesday of next week, for those who would like to have their papers in order to study for the final. Since this is extra credit, I will be a little tougher on the grading - do a nice job!)

Because we'll have a little more time for the final, expect a few more "in depth" problems.

1. Part I: we haven't covered that much material since your last hour exam, so look for detailed problems using the techniques we've considered from these chapters:
   • translating between logic networks, truth functions, and boolean expressions;
   • creating logic networks to solve tasks (e.g. the stairway light problem)
   • minimizing logic networks using
     • Karnough maps
     • Quine-McCluskey
   • creating finite state machines to solve tasks (especially recognition of regular sets)
   • create regular expressions which describe regular sets
   • minimize a finite state machine
   I've created a summary page, which you may wish to refer to.

2. Part II: the good news is that I'll allow you to skip one problem of your choice; the bad news is that I'll still expect you to remember how to do everything that we've studied to date! As I've already said, proofs are very much "on the table" - you should expect to do one or two.

   Overall, however, the problems you see will look like the homework, so a good strategy is to go over the sections and recall what we've done. Also look over the overviews I gave you for the last exams. I won't pull in any ringers not on those sheets.