digital electronics tutorial: word problems solutions

ELEC1041 – Word Problems - 1

Digital Electronics

Tutorial: Word Problems

Solutions


Alarm Clock

Consider the design of a simple digital alarm clock. The clock can display the current time in HH:MM notation along with a single LED that is illuminated when the time is PM (it is NOT lit up in the AM). There are several control inputs for setting the current time and the alarm time. The TIME SET HH button allows you to rapidly advance through the hours 1 through 12 AM and 1 through 12 PM. The time advances one hour for each time the button is pressed. The TIME SET MM button does the same thing for the minutes 00 through 59. In addition, the clock has a toggle input that indicates CLOCK in one position and ALARM in the other. This refers to which time is being set by the TIME SET buttons: either the current time (CLOCK) or the alarm time (ALARM). If the ALARM button is set, the clock displays the last set alarm time. Finally, there is another input controlled by a push button: ALARM ON when pushed in and ALARM OFF when popped out. Your job is define the state diagram for the clock controller. It should support normal clock display (when CLOCK is set), alarm display (when ALARM is set), set current time (CLOCK + TIME SET buttons), set alarm time (ALARM + TIME SET buttons), and of course, the alarm should sound when current time equals alarm time.(a) Identify your inputs, outputs, and name and describe your states.(b) Draw a symbolic state diagram for your design, labeling all state

transitions.


Alarm Clock Solution (1/8)

In addition, the clock has a toggle input that indicates CLOCK in one position and ALARM in the other. This refers to which time is being set by the TIME SET buttons: either the current time (CLOCK) or the alarm time (ALARM). If the ALARM button is set, the clock displays the last set alarm time.

Current Time: 10:23 PM

Alarm Time: 06:30 AM

AM/PM Indicator. Light indicates PM

Current Time Mode

Alarm Time ModeDiplayMode

DiplayMode



SetTimeHHSetTimeHH

SetTimeHH SetTimeHH

SetTimeHH SetTimeHH

The TIME SET HH button allows you to rapidly advance through the hours 1 through 12 AM and 1 through 12 PM. The time advances one hour for each time the button is pressed.

Design Assumption

?



SetTimeMMSetTimeMM

SetTimeMM SetTimeMM

SetTimeMM

The TIME SET MM button does the same thing for the minutes 00 through 59..

Design Assumption

?

SetTimeMM



Alarm Sounds

Finally, there is another input controlled by a push button: ALARM ON when pushed in and ALARM OFF when popped out.

Assumption: When the alarm is NOT set, pressing the alarm set button turns ON

the alarm (AlarmSet = 1).(1) When the alarm is set and sounds, pressing the alarm set

button again turns off the alarm (AlarmSet = 0).

=



(a) Identify your inputs, outputs, and name and describe your states.

Inputs:TimeSetHH 1 incrementing HH of clock or alarm by 1 TimeSetMM 1 incrementing MM of clock or alarm by 1DisplayMode 0 Clock , 1 AlarmAlarmSet 1 alarm is set Outputs:HH++ HH is advanced by 1MM++ MM is advanced by 1Alarm sounds



(b) Draw a symbolic state diagram for your design, labeling all state transitions.

States: Clock normal clock display mode where HH and MM

of current time can be adjusted. Alarm – alarm display where HH and MM can be set for

alarming time. Alarm Sounding – Alarm sounds at this state




Clock

Alarm Sounding

TimeSetHH/HH++

TimeSetHH/HH++

TimeSetMM/MM++

AlarmSet = 1 &HH:MM (clock) =HH:MM (alarm)/Alarm sounds

TimeSetMM/MM++

AlarmSet = 1 &HH:MM (clock) =HH:MM (alarm)/Alarm sounds

DispalyMode=0 &AlarmSet = 0


DispalyMode=0

DispalyMode=1Alarm

[Alarm sounds]




Clock

Alarm Sounding

TimeSetHH/HH++

TimeSetHH/HH++

TimeSetMM/MM++

DispalyMode=0 &AlarmSet = 1 &HH:MM (clock) =HH:MM (alarm)/Alarm sounds

TimeSetMM/MM++

DispalyMode=1 &AlarmSet = 1 &HH:MM (clock) =HH:MM (alarm)/Alarm sounds



DispalyMode=0

DispalyMode=1

[Alarm sounds]

Alarm


Cloth Dryer

Captain of the Enterprise has one of those incredibly complicated European Miele clothes dryers. The machine has dryer settings for three mutually exclusive option settings, one of which MUST be selected: Cotton fabrics (Extra Dry, Normal+, Normal, Hand Iron, Hand Iron Damp, Machine Iron Wet), Permanent Press fabrics (Normal+, Normal, Hand Iron), or Timed Drying (15 minutes, 20 minutes, 30 minutes). Presumably the dryer has some kind of embedded humidity sensor that can determine just how wet the wash is, and when this sensor value is reached, the dryer can advance to the next phase. This is Cool Down, which turns off the drying action until the clothes reach a predetermined “cool” temperature. The final stage is Anticrease, which intermixes a tumbling action with periods for which nothing happens (e.g., 10 second spin followed by 30 seconds of nothing). This goes on for five minutes. The machine then advances to Stop, and is ready for the next load.

(a) Identify your inputs, outputs, and name and describe your states.(b) Draw a symbolic state diagram for your design, labeling all state

transitions. Write down any additional assumptions you are making.


Cloth Dryer Solution (1/2)

(a) Identify your inputs, outputs, and name and describe your states.Inputs: Externally: any of the drying options, such as: cotton fabrics, permanent press fabrics, timed drying and their

settings such as: Extra Dry, Normal+, Normal, Hand Iron, Hand Iron Damp, Machine

Iron Wet Internally: information from temperature and humidity sensors,

timer.

Output: Lights indicating which stage it is in, i.e. drying, cool down, stop

States: Different drying options, cool down and stop states.


Cloth Dryer Solution (2/2)

(b) Draw a symbolic state diagram for your design, labeling all state transitions. Write down any additional assumptions you are making.

Idle

Permanentpress

Timeddrying

cotton

Extra N+ N Hand I H I Damp MachineI W

CoolDown

NOT WET

WET

WETWET

WETWETWET

AntiCrease

coolNot cool

Timer not expired

Timer expired

…

…


Traffic Light Controller (1/3)

Consider the following variation on the classical traffic light controller. The intersection in question is shown in Figure below.

A Street runs north-south, B Street runs east-west, and C Street enters the intersection from the southeast.

A Street is quite busy, It is frequently difficult for cars heading south on A to make the right turn

onto either B or C Streets. In addition, cars rarely enter the intersection from C Street.

Right turn path

A

B

C



Design a traffic light state diagram for this three way intersection to the following specifications:

1. There are 5 sets of traffic lights facing cars coming FROM A North, A South, B East, B West, and C Southeast respectively.

2. The red, yellow, and green lights facing cars FROM A North, are augmented with a RIGHT TURN ARROW, which can be lit up as either green or not lit up at all.

3. The normal sequencing of light facing the cars coming from A North is: Arrow Green, Arrow Yellow, Traffic Light Green, Traffic Light Yellow, Traffic Light Red, and repeat. In other words, the Right Turn Arrow light is illuminated in every complete cycle of lights.

Lights as seen in other directionsLights as seen in from A North heading South



However, it should be possible for the traffic going from north to south on A Street to cross the intersection even when the RIGHT TURN ARROW illuminated. Therefore, the Traffic Light Green should also be illuminated while the RIGHT TURN ARROW is lit up.

Cars travelling from the south to north on A Street (and all directions on B and C Streets) must see a red light while the RIGHT TURN ARROW is illuminated for the traffic heading south.

A car sensor C is embedded in C Street to detect whether a car is waiting to enter the intersection from the southeast.

A timer generates a long interval signal TL and s short interval signal TS when set by an ST signal.

Red and green lights are lit up for at least a TL unit of time. Yellow lights, the green arrow, and the yellow arrow are lit up for exactly a TS unit of time

The C Street lights cycle from red to green only if the embedded car sensor indicates that a car is waiting. The lights cycle to yellow then red as soon as there are no cars waiting. Under no circumstances is the C Street green light to be lit for longer than TL unit of time.


Reset

C (async)

Clk

Car Sensor C (sync)

State Register

2

Next State Output Logic

TS TL

controller fsm

2

Encoded Light

Signals

Light Decoders

F

3

3

H

ST

short time/ long time counter

ResetClk

22

3

5

North facing

South facing

C

3

East facingWest facing3

Traffic Light Controller Solution (1/4)



S0G ATS/ST

TS’S1

Y A

TS’TS/ST

S2N-S G TL’

TL/STTS’

TS/ST

S3N-S Y

S4E-W G TL/ST

TL’ S5

E-W YTS’

TS . C/ST

TS . C’S6

SE GTL’ . C

TL + C’/ST

S7SE Y

TS’TS/ST

Reset/ST

Recall:NOT A = A = A’ = /A =\A



4 5 6 7

Y R R R R Y R R R R

R G Y R R

R R R G Y

G,GA G,YA G R R G

R R R

R R R

0 1 2 3

A Street North Facing Lights

A Street SouthFacing Lights

B Street East & West Facing Lights

C Street South-east Facing Lights

State Numbers



Jump Counters

CLR, CNT, LD implemented via Mux Logic

CLR = CLRm + Reset

CLR = /CLRm + /Reset

/CLR

163138

151

/CLRm/Reset /CLR

CNT

P T

CLK

D C B A

RCO

QD QC QB QA

LOAD

CLRReset /Reset

G2 G1

D C B A

EOUTCNT

/CLRm

76543210

/S7/S6/S5/S4/S3/S2/S1/S0

E7E6E5E4E3E2E1E0

G

S0 S1 S2

151

EOUT

E7E6E5E4E3E2E1E0

G

S0 S1 S2

Controller Implementation

Active Lo outputs:hi input inverted atthe output

Note that CNT isactive hi on counterso invert MUX inputs!

/TS/(TL + /C)

/(TS.C)/TL/TS/TL/TS/TS

+

00

TS.C00000

/GA = /s0/N-SG = /s0. /s1. /s2/N-SY = /S3/N-SR =/S4./S5./S6./S7/S-NG = /S2/S-NY = /S3/S-NR = /S0./S1./S4./S5./S6./S7/W-EG = /E-WG = /S4/W-EY = /E-WY = /S5/W-ER = /E-WG = /S0./S1./S2./S3./S6./S7/CG =/S6/CY = /S7/CR = /S0./S1./S2./S3./S4./S5

OUTPUTS

digital electronics tutorial: word problems solutions

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