Lecture 4: Networking and Information Flow

Lecture 4: Networking and Information Flow

EEN 112: Introduction to Electrical and Computer Engineering

Professor Eric Rozier, 2/4/2013

COMMUNICATION

Where we are

• We can give simple instructions to machines in the form of algorithms.– These algorithms can be implemented in

hardware, or software• So what about working with other systems?• Need a way to communicate.

Communication

• Allows the sharing of information• Sharing of resources (printers, monitors,

message servers)• Linking of systems to increase power• Redundancy of information and resources

(protects against failures and threats)• Simplify administration and access

Limitations and Standards

• Often limited by the connective framework• Need standards to pass information in these

cases• Lab this week

– Learning a bit about TCP/IP standard

MUDDY CHILDREN

The Muddy Children PuzzleSeveral children are playing outside.

After playing they come inside, and their mother says to them, “At least one of you has mud on your head!”

She then asks the following question, over and over:

“Can you tell for sure whether you have mud on your head?”

1. Each child can see the mud on others, but cannot see his or her own forehead.

2. The children make no direct communications to one another, they can only chose to step forward to get clean, or not.

Let’s try to solve this as a whole class of muddy children

It’s pretty hard to solve a problem this large…

What can we do to get a better grip on it?

Inductive Reasoning

• What if we want to solve a very large problem?

• Sort a deck of cards…– We could just sort two cards to start…– Then we could sort a third card in…– Then we could sort a fourth card in…– And so on until we sorted 52 cards.

Inductive Reasoning

• “Bottom-up” logic1. Start with a basis, or base case.

– Solve the problem for this base case.2. Come up with an inductive step.

– Show that if something holds for one step, it holds for the next higher step.

Inductive Reasoning

• Show if we push down one domino, it falls over.

• Show we can place a second domino in the path, and knock it over as the consequence of a domino falling…

• Line up our dominos and watch them fall!

Let’s get back to Muddy Children

Maybe if we start with the right base cases we can figure this

out…

Let’s do the simplest case

One child…

(this is what we call a degenerate case)

“At least one of you children has mud on their head!

Something less trivial, but still easy…

Two children…

“At least one of you children has mud on their head!

Two Children

• What are the possibilities?

• How could each child react logically for these possibilities?

A much harder one…

Three children…

“At least one of you children has mud on their head!

Three Children

• What are the possibilities?

• How could each child react logically for these possibilities?

More children

• What about four children?

• What about five children?

• What about N+1 children… for arbitrary values of N? Does our solution generalize?

• What can we take away from this puzzle about communication?

WRAP UP

Upcoming Items of Interest

• Lab this week, networking• Next week: Midterm I on

Wednesday 2/13– Boolean Algebra– Logic Gates– Networking