Unit 1: Fundamentals Analog and Digital Logic:

dehisceforkElectronics - Devices

Nov 2, 2013 (3 years and 7 months ago)

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Binary Clock, Wired on Breadboard

Unit 1:

Fundamentals Analog and Digital Logic
:

Unit 1 is focused upon
how electricity flows in circuits. Definitions of voltage, current
and resistance and series and parallel circuits are defined.

The Board Game Counter is used to
illustrate a circuit which includes an analog section,
a combinational logic section (gates) and a sequential logic section. (flip flops)
.

Different
packaging types and data sheets for IC’s are introduced.

Unit 2: Combin
a
tional Logic
:

Unit 2 is about logic gates and how to apply them to problems. NAND and NOR gates
are introduced as the universal gates which can replace any of the other gates.
Converting between binary, hexadecimal and decimal number systems is covered.

Also,
using 2’s complement arithmetic to subtract binary numbers, use binary adders and
multiplexors is covered. Programmable logic chips can be used to provide customized
logic that would otherwise need several logic gates. Driving 7 segment displays i
s
covered.

Unit 3: Sequential Logic
:

Sequential logic involves memory devices, namely flip flops. The D Flip Flop is
introduced as a way to store when something has happened. Students breadboarded a
circuit with a phototransistor that sounds an alarm whe
n a beam of light is broken. The
alarm is latched on the Q output of a D flip flop. Ripple counters can be built from D
or J/K ff’s and they are introduced as well as synchronous counters
. Synchronous
counters have ff’s with clocks wired together so the

ff’s change at same time. Finite
state machines

are logical designs that move from one state to the next. FF’s are used
to represent the different states and logic gates are used to transition from one state to
the next. An elevator door circuit is giv
en as an example.

Unit 4: Microcontrollers
:

Microcontrollers like the basic STAMP can be used to execute logic written in PBASIC. A
microcontroller can store information in variables and can loop and branch as needed to
implement a particular algorithm.
The BOE Bot line navigation project was used
as an
example project.



Match the definitions with the terms by putting in the letter at the left.


1.

Capacitor

T
Coding system of colored stripes on a resistor to indicate the resistor's value and
tolerance

2.

Cold
Solder Joint

U
A two terminal device that conducts in only one direction.

3.

Digital Multimeter

O
Electronic test equipment that can perform multiple tasks. Typically one capable of
measuring voltage, current, and resistance. More sophisticated modern digital

multimeters also measure capacitance, inductance, current gain of transistors, and/or
anything else that can be measured electronically.

4.

Diode

S
The unwanted formation of a conductive path of solder between conductors


5.

Dual In
-
Line
Package (DIP)

V
Light
-
emitting diode. An electronic device that conducts current in one direction
only and illuminates when it is conducting.

6.

Engineering
Notation

I
Component made of material that opposes flow of current and therefore has some
value of resistance
.

7.

Fuse

H
Num
bers entered as a number from one to ten multiplied by a power of ten.

8.

LED

C
A very common IC package with two parallel rows of pins intended to be inserted
into a socket of through holes drilled in a printed circuit board.

9.

Plastic Leaded
Chip Carrier
(
PLCC)

E
Term derived from "transfer resistor." Semiconductor device that can be used as
an amplifier or as an electronic switch.

10.

Printed Circuit
Board

N
Process

of joining two metallic surfaces to make an electrical contact by melting
solder (usually tin and lead) across them.

11.

Resistor

A
An electrical device used to store electrical charge.
.

12.

Resistor Color
Code

Q
An array of seven independently controlled ligh
t
-
emitting diodes (LED) or liquid
crystal display (LCD) elements, shaped like a figure
-
8, which can be used to display
decimal digits and other characters by turning on the appropriate elements.
.

13.

Scientific Notation

B

A protective device in the current path that melts or breaks when current exceeds
a predetermined maximum value.

14.

SI Notation

G
A square IC package with leads on all four sides designed for surface mounting on
a circuit board


15.

Seven
-
Segment
Display

K
Metal
lic alloy of tin and lead that is used to join two metal surfaces.

16.

Small Outline IC
(SOIC)

M
Abbreviation of System International, a system of practical units based on the
meter, kilogram, second, ampere, Kelvin, mole, and candela.

17.

Solder

L
The

process of applying a thin coat of solder to materials prior to their being
soldered; for example, application of a light coat of solder to the filaments of a
conductor to hold the filaments in place prior to soldering the conductor.

18.

Solder Bridge

R
Insu
lating board containing conductive tracks for circuit connections


19.

Soldering

P
A floating point system in which numbers are expressed as products consisting of
a number greater than one multiplied by an appropriate power of ten that is some
multiple of thre
e

20.

Soldering Iron

D
An IC package similar to a DIP, but smaller, which is designed for automatic
placement and soldering on the surface of a circuit board.

21.

Tinning

J
A solder connection that exhibits poor wetting and is characterized by a grayish,
porous
appearance due to excessive impurities in the solder, inadequate cleaning
prior to soldering, and/or the insufficient application of heat during the soldering
process..

22.

Transistor

F
Tool

with an internal heating element used to heat surfaces being soldered to the
point where the solder becomes molten.





1.

Basics of Electricity, Ohm’s Law

2.

Scientific Notation Prefixes

3.

Resistors and Resistor Color Codes

4.

Parallel Circuits

5.

Series Parallel

6.

Number Systems

7.

Logic Gates


1.
Basics of Electricity, Ohm’s Law

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Resistance is t桥 彟彟彟彟彟彟彟彟彟彟彟彟彟彟彟彟彟彟弮

units彟彟彟彟_


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u
nits彟彟彟彟_


Current is t桥 彟彟彟彟彟彟彟彟彟彟彟彟彟彟彟彟彟彟彟彟彟彟彟彟弮

units彟彟彟彟_


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app汹 t桥 汥ads in 彟彟彟彟彟彟彟彟彟彟彟彟彟彟_to t桥 circuit


T桥 too氠l
or measuring current is ca汬ed an 彟彟彟彟彟彟彟彟彟彟彟彟彟_ To use t桩s,
app汹 t桥 汥ads in 彟彟彟彟彟彟彟彟彟彟彟彟彟彟_to t桥 circuit



The tool for measuring resistance is called an ______________________ . To use this,
disconnect the source from the

circuit so there is no other current being introduced.
Then, apply the leads in parallel to the device or devices you wish to measure.


Solving Series Circuit Problems:

A series circuit is one in which_________________________________________

A parallel
circuit is one in which_________________________________________


To analyze a series circuit,

1.

Find Equivalent resistance by summing the resistance of all devices (Er = the size
of one resistor if all of the resistance in a circuit where combined into one
resistor)

2.

Find the current by applying Ohm’s Law

3.

Find voltage drops across each resistive element

Example 1:


















Example 2:

If a 1k resistor has 50 mAmps of current flowing through it, what is the voltage across
the resistor?










2.
Scientific Notation Prefixes

10
-
9
_____________________

10
-
6
_____________________

10
-
3
_____________________

10
3
_____________________

10
6
_____________________

10
9
_____________________


Convert the following

1.

200K Ohm resistor to Ohms



2.

35 milliamps of
current to amps



3.

2.1 MegaOhm resistor



4.

4.7µFarad capacitor



5.

.000025 volts to appropriate notation (smallest whole number)



6.

120000 Ohm resistor



3.
Resistors and Resistor Color Codes

Resistors are devices manufactured to control the flow of current and

the amount of
push (voltage) in a particular part of a circuit.

There are many different types of resistors, including carbon film, wire wound and
ceramic. The through hole resistors typically have a color code on them to indicate
their size.

A mnemoni
c to help you remember the numeric values associated with the
resistors is as follows;







The first two values are the numeric values for the resistor size followed by the third
band which is the _____________________________ or the number of zeros to ad
d to the
end of the size. The forth band is the ______________

Gold

Silver

None



1.

A 450 Ohm resistor with a 5 % tolerance has what color bands?

2.

Red Orange Brown Silver has what range of acceptable values?




4.
Parallel Circuits

In circuits where there
are multiple paths for current flow, analyzing how much current is
in each branch is similar to analyzing a series circuit. For a parallel circuit, equivalent
(or total) resistance is ALWAYS LESS THAN ANY OF THE INDIVIDUAL RESISTORS!


1.

Find Er by applying
the following formula 1/Er = 1/r1 + 1/r2 + 1/r3

or Er =


Example 1: Find Er










Find Vdrop R2

Example 2:Find Er








5.

Series Parallel

KVL/KCL Demonstration

Kirchoff’s Voltage Law: Sum of the sources = sum of drops

Kirchoff’s Current Law: Sum of currents entering a node = sum of currents exiting a
node


Using the circuit below, set up the KCL equations for N1, N2, N3 and N4

(For N4, Use IR3,R4 as your unknown)




Using the circuit below, set up the KVL Equations for
the 3 closed loops. Solve for the
unknown voltages



















6
.
Number Systems


We have looked at various number systems, including decimal (base _____) binary (base
____) and hexadecimal (base ______)


Remember, binary acts like a bridge system,
when in doubt, convert to binary first.

Also, each hex digit represents ________ binary digits. Start at the far right when doing
your grouping


Binary

Decimal

Hex

1001011




61




E3









7
.
Logic Gates

Draw the logic symbol, truth table (2 input) and boolean expression for the following
gates;

and

or

not (1 input)

nand

nor

xor

xnor



















Which are the universal gates?





Replacing aoi gates with the universal gates.


Draw the equivalent of an

AND, OR and NOT gate using NANDS













Draw the equivalent of an AND, OR and NOT using NORS


Convert this circuit to NAND only












Convert this circuit to NAND only










Convert this circuit to NOR only



Which of the following represents the boolean equation shown? (Could be more than
one)

F =



1.


2.





8.

Seven segment displays

9.

Programmable Logic Devices

10.

Flip Flops and Counters

11.

Square Waves

12.

Boolean Simplification

13.

Karnaugh Simplification

14.

Adders


8
.
Seven Segment Displays

Seven Segment displays allow an engineer to display numeric or alpha
-
numeric
information using displays that have a common connection and several individual
connections.


This is a common anode 7 s
egment display. The anode is the positive side of the
diode, so a __________ causes the segments to glow.

1.


a.

b.
c.
d.





This is a common cathode 7 segment display. The cathode is the negative side of the
diode, so a __________ causes the segments t
o glow.




a.
b.
c.
d.



8.
Programmable Logic Devices

Programmable logic device

is a
_______________________________________________________________________________________
_______________________________________________________

_______________________________________________________________________________________
_______________________________________________________


Advantages of PLD’s







9.
Flip Flops and Counters


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n store 彟彟彟_bit o映
in景rmation.


Here is a D 晬ip 晬op


W桡t conditions wou汤 cause it to stay 汯w no matter w桡t t桥 CP does?彟彟彟彟彟_



Here is a JK flip flop




What conditions would cause it to stay low no matter what the CP does?___________


Waveform Problems: Let’s look at how to predict the behavior of a ff over time



1.

Suppose the following waveforms were inputs into a D Flip Flop as follows;

Assume that Q starts low



CLK

SET

RESET

DATA


A

B

C


2.

Repeat last question with
these new inputs, assume that Q starts low


3.

What is necessary to keep this flip flop’s output low?

a) S=1, R=1

b) S=0, R=1

c) S=1, R=0

d) S=0, R=0


CLK

SET

RESET


DATA


A

B

C


4.

What is the modulus of the ripple counter below?

a) 5

b) 6

c) 7

d) 14

e) 15



5.

In order for a change to occur on the output of a negative edge triggered flip
flop, what condition needs to be present on the CLOCK input?

a) low


b) high to low

c) high


d) low to high

e) not the
answer


6.

What is the highest count you can reach using a counter with
5

flip flops?

a) 256


b) 127


c) 8


d) 255


e) 31



What are the differences between asynchronous (ripple) and synchronous counters?


Asynch






Synch









10.

Square Waves

By varying voltage over

time, we can create a square wave. Square Waves are the
digital heartbeats of any circuit, providing the timing for events to happen.


You will be responsible for finding the frequency of a square wave, given a graph as
below.


Example 1:

a. What is the

period of the square wave shown below?

b. What is the frequency of the square wave shown below?

c. What is the duty cycle of the square wave shown below?

d. What is the amplitude of the square wave shown below?











































































12 mSec













5
vol ts












































































































Example 2:

a. What is the period of the square wave shown below?

b. What is the frequency of the square wave shown below?

c. What is the duty cycle of the square wave shown below?

d. What is the amplitude of the square wave shown below?











































































4 mSec













5
vol ts














































































































11.

Boolean Simplification

a.

A+0=A

b.

A+1=1

c.

A+A=A

d.


e.

A

0=0

f.

A

1=A

g.

A

A=A

h.


i.


j.

A+AB=A

k.


l.


m.

(A+B)(A+C)=A+BC





̅


̅




̅
̅
̅
̅
̅
̅
̅
̅

or

̅


̅




̅
̅
̅
̅
̅
̅
̅




You can DeMorganize by;


1.

Complement the whole
expression

2.

Change the lowest order
precedence sign(s)!

3.

Complement the terms






Example1:


Since we are breaking the
bar, Lets
Demorganize the



̅
̅
̅
̅
̅
̅
̅
̅

part.

1.

Complement the whole
expression we are
targeting:







̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅


2.

change the sign(s)






̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅


3.

Complement the terms



̅


̅

̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅



Cancel stuff out to simplify



̅

̅




What is the simplest boolean expression for the equation shown?


Example 2:




̅

̅
̅
̅
̅


̅
̅
̅
̅

?m
%
?n
$
$
$
$
E
?n?o
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$

?m
%
?n
$
$
$
$

?n?o
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$

Lowest order prec



̅

̅
̅
̅
̅
̅
̅
̅
̅


̅
̅
̅
̅
̅
̅
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̅
̅
̅
̅

?m
%
?n

?n?o
$
$
$
$
$
$
$
$
$
$
$

?m
%
?n?n?o
$
$
$
$
$
$
$
$

?m
%
?n?o
$
$
$
$
$
$




Example 3:




̅
̅
̅
̅
̅






̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅
̅

Let’s apply DeMorgan’s Law to the left to Break

the Bar and the right to
break the bar separately!!!!!!





̅
̅
̅
̅
̅
̅
̅
̅
̅






̅
̅
̅
̅
̅
̅
̅
̅
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̅




̅
̅
̅
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̅






̅
̅
̅
̅
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̅
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̅
̅
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̅



̅
̅
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̅


̅


̅


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̅


̅
̅
̅
̅
̅
̅
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̅

Simplify

Simplify


̅

̅



̅







̅



̅

̅


?m
%
?o
?:
Ú
E
?n
%
?;

?m
%
?o



What is the simplest boolean expression for



















12.
Karnaugh Simplification

Remember Kmaps are useful for 4 or 5 variables at most when solving for
the simplest possible circuit. X’s are created from “don’t care” situations in
the problem.

Circle subcubes

of maximal size (must be a power of 2) and cover all 1’s








0

0

1

1


0

0

0

1


0

0

1

1


1

0

1

1




+


Try setting up a KMap for the following problem

NOTE: 3
rd

and 4
th

rows changed due to oversimple answer of C!!!


A

B

C

X

0

0

0

0

0

0

1

1

0

1

0

0

0

1

1

0

1

0

0

0

1

0

1

X

1

1

0

0

1

1

1

1






̅









̅




0

1

0

0



0

X

1

0






̅




Give the NAND only version of this circuit
(remove double inverters)




















13.

Adders

Design a half adder using gates


A

B

Cout

Sum

0

0

0

0

0

1

0

1

1

0

0

1

1

1

1

0




14.

Mathematical Law

Remember the commutative, associative, transitive and distributive
properties of math.

a.

Associative:
(A+B)+c = A+(B+C)

b.

Commutative:

B+A

c.

Transitive:
If A=B and B=c Then A=C

d.

Distributive:

AB + AC

15.

Sum of Products and Product of Sums

A

B

C

X

0

0

0

1

0

0

1

1

0

1

0

0

0

1

1

0

1

0

0

1

1

0

1

1

1

1

0

0

1

1

1

0


Example 1: What is the unsimplified Sum of Products expression for the

above cir
cuit?





























xample

2


hat

is

the

unsimplified

roduct

of

ums

expression

for

the

above

circuit











(





)
(





)











xample 3: hich of the following Kmaps has the 1’s and 0’s properly
placed for this function?










1

1

1

1


0

0

1

1


0

0

0

0


0

1

0

0








1

0

1

1


0

0

1

1


0

0

0

0


0

1

0

0








0

1

1

1


0

0

1

1


0

0

0

0


1

1

0

0






Example 4: Which of the following Kmaps

has the 1’s and 0’s properly
placed for this function?










1

1

1

1


0

0

0

0


1

1

0

0


0

1

1

0








1

1

1

1


0

0

0

0


1

1

0

0


0

1

0

0








1

1

0

0


1

0

0

0


1

1

0

0


1

1

0

0


17.

Fewest I C chips
to implement

Remember there are
4

AND gates on a typical IC

There are
4

OR gates on a typical IC

There are
6
INVERTER on a typical IC




What is the fewest number of integrated circuits to implement the above circuit?

3

Assuming 2 input OR and AND chips


18.

Flip Flops and Counters


Ex 1: How many flip flops are required for a divide
-
by
-
12 circuit?

counts 0


11, need 2
4
=16 states so 4 flip flops min

Ex 2: How many
flip flops are required for a divide
-
by
-
7 circuit?

counts 0


6, need 2
3
=8 states so 3 flip flops min

Ex 3: How many flip flops are required for a mod 24 circuit?

counts 0


23, need 2
5
=32 states so 5 flip flops min


Ex 4: Which of the following is a negat
ive edge triggered JK Flip Flop?





34

19.

Ex 5: What will Q be on the next clock pulse?









35



Boolean Simplification and DeMorgan’s Law

Simplify the following expression:






























14.
Logic Families


There are two broad categories of logic families; TTL or Transistor Transistor Logic and
CMOS or Complementary Metal Oxide SemiConductor.


The TTL Family is mostly what we used this year. They feature fast operation. CMOS
chips feature low power consumpt
ion, better noise tolerance and a larger fan out (see
above

for fanout)


In general, use TTL for speed and CMOS for power savings. Also, CMOS chips can be
damaged by static electric discharges.


36



37

15.
Predicting JK FF Waveforms

1.

For the following J/K Flip
Flop, Decide which waveform would represent the Q
value.


Assume that Q starts low, find the waveform that corresponds to X




CLK

J

K

A

B


C


38

2.

Find the waveform that corresponds to X using these as inputs for the same j
-
k
flip flop pictured
above. Assume that Q starts high


16.

Solving KMaps and Converting to NAND/NOR only

Charlie likes to study on Mondays, Tuesdays and Wednesdays, Practice football on
Thursdays and Sundays and go to the movies on Fridays and Saturdays.
Assuming a 3 digit binary number can represent the days of the week with
Monday = 0 0 0, etc. Develop a
truth table for the problem, use X’s for an
additional values for days beyond Sunday.






CLK

J

K

A

B


C


39

Solving KMaps and Converting to NAND/NOR only

Charlie likes to study on Mondays, Tuesdays and Wednesdays, Practice football on
Thursdays and Sundays and go to the

movies on Fridays and Saturdays.
Assuming a 3 digit binary number can represent the days of the week with
Monday = 0 0 0, etc. Develop a truth table for the problem, use X’s for an
additional values for days beyond Sunday.


Day

A

B

C

Study

Foot

ball

Movi es

Mon

0

0

0

1

0

0

Tues

0

0

1

1

0

0

Wed

0

1

0

1

0

0

Thur

0

1

1

0

1

0

Fri

1

0

0

0

0

1

Sat

1

0

1

0

0

1

Sun

1

1

1

0

1

0


X

X

X

X

X

X



Study






1

1

0

1


0

0

X

0


Study =
~A~B +
~A~C


40



Limiting your design to two
-
input AND & OR gates (74LS08 &
74LS32) and Inverters (74LS04), draw the A
-
O
-
I implementation
for the study activity




Limiting your design to two
-
input NAND gates (74LS00), draw the
NAND ONLY implementation for study activity. (Note: Inverters
MAY NOT

be used for this implementation)





41



Use the K
-
Mapping technique; determine the simplest Sum
-
of
-
Pr oducts Bool ean expressi
on f or the f ootball acti vity.


Footbal l






0

0

1

o


0

0

X

1


Football =
BC +
AB

Li mi ting your design to two
-
input AND
& OR gates ( 74LS08 & 74LS32) and
I nverters ( 74LS04), draw the A
-
O
-
I i mpl ementation f or the f ootball activity.








Li mi ting your design to two
-
input NOR gates ( 74LS2), draw the
NOR ONLY i mpl ementation f or the f ootball activity ( Note:
I nverters
MAY NOT

be used f or thi s i mpl ementation)








42






Use the K
-
Mapping technique; determine the simplest Sum
-
of
-
Pr oducts Bool ean expression f or the movi e acti vity.


Movies






0

0

0

o


1

1

X

0




Movies =
A~B


Li mi ti ng your desi gn to two
-
input AND & OR gates ( 74LS08 &
74LS32) and I nverters ( 74LS04), dr aw the A
-
O
-
I i mpl ementati on
f or the movi e acti vi ty.