Lecture 2 systems engineering
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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

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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


Lecture 2 systems engineering

CROSSING THE RIVER…


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.


Lecture 2 systems engineering

ALGORITHMS


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


Lecture 2 systems engineering

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


Negative numbers and real numbers are more complex

Negative numbers and real numbers are more complex…

We will cover those later…


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


Lecture 2 systems engineering

AND

  • X AND Y


Lecture 2 systems engineering

OR

  • X OR Y


Lecture 2 systems engineering

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)


Realization as electronic components

Realization as electronic components

AND

OR

NOT


Realization as electronic components1

Realization as electronic components

AND

OR

NOT


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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