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Lecture 2: Systems Engineering. EEN 112: Introduction to Electrical and Computer Engineering. Professor Eric Rozier, 1 / 23 / 2013. CROSSING THE RIVER…. Farmer, Wolf, Goat, Cabbage. A farmer needs to transport a wolf, a goat, and a cabbage across the river. F. G. Boat has two seats

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lecture 2 systems engineering

Lecture 2: Systems Engineering

EEN 112: Introduction to Electrical and Computer Engineering

Professor Eric Rozier, 1/23/2013

farmer wolf goat cabbage
Farmer, Wolf, Goat, Cabbage

A farmer needs to transport a wolf, a goat, and a cabbage across the river.

F

G

  • Boat has two seats
    • Farmer must drive…
  • If left alone…
    • The wolf will eat the goat.
    • The goat will eat the cabbage.

W

C

farmer wolf goat cabbage1
Farmer, Wolf, Goat, Cabbage

As a group, formulate a solution to transport everything across the river, without anything being eaten.

F

G

W

C

what do we learn from this exercise
What do we learn from this exercise?
  • Sometimes we have to move backwards to move forwards.
  • Even simple systems need thought to formulate a plan for accomplishing their goals.

We call this plan, an algorithm.

algorithms
Algorithms
  • al-Khwarizmi
    • Persian mathematician, astronomer, and geographer born780 A.D.
    • Invented a few things…
      • Decimal system
      • Algebra
      • Trigonometry
algorithms1
Algorithms
  • al-Khwarizmi also introduced the idea of solving problems using step-by-step procedures for calculations.
  • Algorithms – A method of solving a problem or accomplishing a task expressed as a finite list of well defined instructions.
    • Starting from an initial state and an initial input, the instructions describe a computation that, when executed will proceed through a finite number of well defined successive states, eventually producing output, and terminating at a final ending state.
states inputs and outputs
States, Inputs, and Outputs
  • States are a way of measuring the condition of a system, and it’s environment.
  • Inputs are a way of getting information to a system.
  • Outputs are a way of getting information from a system.
algorithms2
Algorithms
  • Algorithms let us define, formally, what we want machines and automated systems to do.
  • Algorithms are written to have precise meanings, and to be generally applicable.
systems engineering and cyberphysical systems
Systems Engineering and Cyberphysical Systems
  • We build systems to do jobs, solve problems, and accomplish tasks.
  • Often these systems are cyberphysical systems, i.e. they combine computational components with the real world.
  • An algorithm is a way of telling the components how to do their job, and how to work together.
example system thermostat
Example System: Thermostat
  • Thermostat
    • What is the goal?
    • What problem does it solve?
    • How would we characterize the state?
    • What would the inputs and outputs be?
example system thermostat1
Example System: Thermostat
  • Thermostat
    • What is the goal?
    • What problem does it solve?
    • How would we characterize the state?
    • What would the inputs and outputs be?
    • Break into groups
      • Define the problem
      • Define what the thermostat needs to do
example system thermostat2
Example System: Thermostat
  • Thermostat
    • Regulate temperature
    • Specification
      • Must be able to sense temperature
      • Based on the temperature must be able to signal cooling or warming the room, or to do nothing.
      • State: temperature, heating state, cooling state
example system thermostat3
Example System: Thermostat
  • Thermostat
    • Pseudocode algorithm
      • tempLow = L
      • tempHigh = H
      • loop()
        • Test temperature, store the value in T
        • If (T < L) send a heating signal
        • If (T > H) send a cooling signal
example system thermostat4
Example System: Thermostat

Thermostat

Signal: Heat

Signal: Cool

Heater

Air Conditioner

Sensor

slide17
Thermostat
  • Some important points…
    • Four systems here, each with their implementations…
    • Need to communicate with each other…

Signal: Heat

Signal: Cool

Heater

Air Conditioner

Sensor

networking and communication
Networking and Communication
  • Systems communicate via signals, over wires, or wirelessly via electromagnetic radiation.
  • In our thermostat system, the heater and cooler can be switched on or off by a pure signal on the wire. I.e., if electrons are flowing, turn on, if not, turn off!
networking and communication1
Networking and Communication
  • But how do we get information from the sensor?
  • It needs to send a number… how do we do that?
networking and communication2
Networking and Communication
  • What if we encode the signal into pulses?
  • Detect if the value is above or below some threshold, and decide it represents a 1, or a 0.
  • Strings of 1’s and 0’s can be interpreted as a number.
some simple things we can represent with 1 s and 0 s
Some simple things we can represent with 1’s and 0’s
  • True or false…
    • 1 – true
    • 0 – false
    • We already were doing this with pure signals.
some simple things we can represent with 1 s and 0 s1
Some simple things we can represent with 1’s and 0’s
  • Integers
  • Examples
    • 00000000 – 0 - 00000010 - 2
    • 00000001 – 1 - 00001010 – 10
    • 00000011 – 3 - 10010011 – 147
boolean algebra
Boolean Algebra
  • Using true/false values in complicated ways
  • Thermostat system
    • Let’s make a change to the basic system
    • Add a switch with values “Heat” and “Cool”
    • Cool the room if T > H and Switch is set to “Heat”
    • Heat the room if T < L and Switch is set to “Cool”
boolean algebra1
Boolean Algebra
  • Gets back to gators and grades…
  • Represent truth as 1, and false as 0
    • We can operate on values using the following basic operators:
      • AND
      • OR
      • NOT
slide26
AND
  • X AND Y
slide27
OR
  • X OR Y
slide28
NOT
  • NOT X
abbreviations
Abbreviations
  • ^ - And
  • v – Or
  • ! – Not
  • !X ^ Y
commutative laws
Commutative laws
  • X ^ Y = Y ^ X
  • X v Y = Y v X
associative laws
Associative laws
  • X ^ (Y ^ Z) = (X ^ Y) ^ Z
  • X v (Y v Z) = (X v Y) v Z
distributive laws
Distributive laws
  • X ^ (Y v Z) = (X ^ Y) v (X ^ Z)
  • X v (Y ^ Z) = (X v Y) ^ (X v Z)
some exercises
Some exercises
  • !x ^ !y
  • !(x ^ y)
  • !x ^ x
  • (x v y) ^ !(x ^ y)
derived operators
Derived operators
  • X XOR Y
    • (x v y) ^ !(x ^ y)
    • Exclusive Or
  • X  Y
    • (!X v Y)
    • Implication
  • X = Y
    • (!X XOR Y)
de m organ s laws
De Morgan’s Laws
  • The negation of a conjunction, is the disjunction of the negations
    • !(X ^ Y) <-> (!X) v (!Y)
    • !(X v Y) <-> (!X) ^ (!Y)
homework
Homework
  • Prove the equivalence of the expressions in De Morgan’s Laws with truth tables (show they are the same!)
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