logic system specifications-worded problems

8/13/2019 Logic System Specifications-WORDED Problems

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Logic System Specification

Learning Objectives:

At the end of this topic you will be able to;

Translate a specification into a truth table.

Design and test a system, with up to 4 inputs from a specification.


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LOGIC CIRCUITS and SWITCHIG TH!OR"

Logic System Specification#

In the previous section we introduced the function of a number of logicgates that are available for us to use in electronic system design. In this

section we will be developing the process needed to convert the design brief

of a problem into a truth table. Before we can start we must have a problem

that needs to be solved so lets begin with something fairly simple to e!plain

the process.

$rob%em &:

A warning light is to be placed on a s"ip at night to warn any approaching

drivers that there is a ha#ard in the road. The light should only operate in

the dar" and the light should be flashing.

So%'tion :

In any problem of this nature the first stageis to identify the type ofinputs needed to convert e!ternal factors e.g. light or temperature into an

electrical signal that can be processed to perform the function re$uired in

the design brief.In our problem two input systems are re$uired, a light

sensor and a pulse generator. In a real situation you would design the light

sensor to give the output characteristics you would need for the system you

have designed. In all problems you will be given the characteristics of the

light sensor to enable the system to be constructed so for now we will assume

the following %

The light sensor produces a logic & in the dar", and 'ogic ( in daylight.

The pulse generator will be producing a continuous series of on ) off or

'ogic & ) 'ogic ( pulses as soon as the power is switched on.

A simple bloc" diagram of the system can now be constructed.

*ngr. +ulius . -ansino


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/ou will notice that the two inputs have now been given a letter so that

we can identify them in a truth table. In this case there are only two inputs,

and therefore there will be four possible combinations of A and Bthat we

have to consider. The ne!t stage is to construct a truth table to show all the

possible input conditions and for each set of inputs determine when an output

is re$uired.

Input A Input B 0utput Q -omments

( ( ( 'ight ensor 1A2 3 ( 3 Daylight, ulse5enerator 1B2 3 ( 3 0ff, 0utput 1Q2 0ff

( & ('ight ensor 1A2 3 & 3 Dar", ulse

5enerator 1B2 3 ( 3 0ff, 0utput 1Q2 0ff

& ( ('ight ensor 1A2 3 ( 3 Daylight, ulse

5enerator 1B2 3 & 3 0n, 0utput 1Q2 0ff

& & &'ight ensor 1A2 3 ( 3 Dar", ulse

5enerator 1B2 3 & 3 0n, 0utput 1Q2 0n

A close e!amination of the 0utput column reveals that the truth tableis that of a simple A6D gate. i.e. Q = A.B so the only logic gate we need is a

single A6D gate and our system diagram can now be redrawn as shown below.

'ight

ensor(A)

7arning

'amp 1Q)

Logic

System

ulse

5enerator(B)

Light

Sensor (A)

Warning

Lamp (Q)

Pulse

Generator (B)

A

BQ


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$rob%em (:

A mar"et gardener wants to install an automatic watering system for hisgreen houses to ensure that his pri#ewinning plants do not suffer from a lac"

of water. The system however, must have some safeguards whereby plants

should only be watered in daylight, when the soil is dry and the door to the

greenhouse is closed.

The following sensors are available%

A moisture sensor 1A2 which outputs a 'ogic ( when dry, and 'ogic &

when wet.

A light sensor 1B2 which outputs a 'ogic & in daylight, and 'ogic ( at

night.

A door switch 1C2 which outputs a 'ogic ( when closed and 'ogic & when

open.

An overview of the system is therefore as shown below%

The ne!t stage is to construct a truth table for this system, as shown

on the ne!t page.

Moisture

Sensor (A)

Water

On (Q)Logic

System

Light Sensor

(B)

Door Sensor

(C)


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Input A Input B Input C 0utput Q -omments

( ( ( (8oisture ensor 1A2 3 ( 3 Dry,'ight ensor 1B2 3 ( 3 6ight,

Door ensor 1C2 3 ( 3 -losed,

0utput 1Q2 3 0ff

( ( & (

8oisture ensor 1A2 3 & 3 7et,

'ight ensor 1B2 3 ( 3 6ight,


0utput 1Q2 3 0ff

( & ( &

8oisture ensor 1A2 3 ( 3 Dry,

'ight ensor 1B2 3 & 3 Daylight,


0utput 1Q2 3 0n

( & & (




0utput 1Q2 3 0ff

& ( ( (


'ight ensor 1B2 3 ( 3 6ight,

Door ensor 1C2 3 & 3 0pen,

0utput 1Q2 3 0ff

& ( & (


'ight ensor 1B2 3 ( 3 6ight,Door ensor 1C2 3 & 3 0pen,

0utput 1Q2 3 0ff

& & ( (




0utput 1Q2 3 0ff

& & & (




0utput 1Q2 3 0ff

-areful study of the truth table shows that the output must come on

when Ais 'ogic (, A6D Bis 'ogic & A6D Cis 'ogic ( or in Boolean Algebra

terms this can be written as % CBAQ ..= .

The complete system diagram therefore now becomes the following%

*ngr. +ulius . -ansino 9


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An alternative design that does the same thing can be formed if only

two input A6D gates are available, by combining two such units together as

shown below%

pend a few minutes convincing you that these two designs are indeed the

same.

6ow its time for you to have a go.

Moisture

Sensor (A)

Water

On (Q)

Light Sensor

(B)

Door Sensor

(C)

Moisture

Sensor (A)

Water

On (Q)

Light Sensor

(B)

Door Sensor

(C)


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)esign $rob%em *#

An e!pensive painting in an art gallery is protected by a modest securitysystem. The picture is protected by a pressure switch which is normally

closed when the picture is in place, but opens if the picture is removed from

the wall. Design a system to sound the alarm if the picture is removed from

the wall only when the gallery is closed at night.

The specification for the available sensors are as follows%

icture ressure sensor 1A2 which outputs a 'ogic ( when picture is in

place, and 'ogic & when the picture is removed.

A light sensor 1B2 which outputs a 'ogic ( during the day, and 'ogic & at

night.

A door switch 1C2 which outputs a 'ogic ( when loc"ed and 'ogic & when

unloc"ed.

-omplete the following system diagram%

6ow complete the truth table opposite.

*ngr. +ulius . -ansino :


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( ( (

ressure ensor 1A2 3 ( 3 icture resent,

'ight ensor 1B2 3 ( 3 Daytime,

Door ensor 1C2 3 ( 3 'oc"ed,

0utput 1Q2 3

( ( &

ressure ensor 1A2 3 & 3 icture 8issing,



0utput 1Q2 3

( & (


'ight ensor 1B2 3 & 3 6ight


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6ow draw a suitable arrangement of logic gates to meet the needs of

your system.

If

we reconsider the specification for the alarm that you have ?ust designed,

you should have realised that it is a pretty poor design for an alarm, since if

someone wal"ed in during the day and removed the picture from the wall no

alarm would sound.

This is clearly an unacceptable position and a better system would sound

the alarm every time the picture was removed from the wall. The owner of

the gallery was not happy with this suggestion as once a wee" the picture was

removed for cleaning, and the alarm should not sound during this period. The

owner stated that when cleaning was ta"ing place, the gallery was closed, and

only too" place during daytime hours.

The modified truth table opposite shows the modifications needed to

meet the demands of this enhanced alarm system.

-hec" through the table carefully to see if you agree @

*ngr. +ulius . -ansino &(


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( ( ( (ressure ensor 1A2 3 ( 3 icture resent,'ight ensor 1B2 3 ( 3 Daytime,


0utput 1Q2 3 0ff

( ( & (

ressure ensor 1A2 3 & 3 icture 8issing,



0utput 1Q2 3 0ff 1-leaning in progress2

( & ( (


'ight ensor 1B2 3 & 3 6ight


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This is $uite a comple! system for what is essentially $uite a straight

forward system. Imagine what this would loo" li"e if only two input gates

were available@ It would appear that system design is going to become very

complicated surely there must be an easier way C

7ell you will be pleased to "now that there are some additional

techni$ues we can use to ma"e our designs a little bit more straight forward

Indeed this system that we have ?ust designed can be reduced to the system

shown opposite.

*ngr. +ulius . -ansino &

PressureSensor (A)

Alarm

On (Q)

Light Sensor

(B)

Door Sensor

(C)


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-omplete the truth table below and compare it with the one on page &&.

Input A Input B Input C 0utput Q

( ( (

( ( &

( & (

( & &

& ( (

& ( &

& & (

& & &

All we need do now is find out how this dramatic simplification can ta"e

place, as this design is significantly easier to build than the original.

Pressure

Sensor (A)

Alarm

On (Q)

Light

Sensor (B)

Door

Sensor (C)


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7e will stop loo"ing at system design for the moment even though we

have not considered 4 input systems as suggested in the learning ob?ectives,because these would inevitably lead to very comple! designs if we used the

techni$ues introduced so far in this section.

Before considering such large systems we must have the tools re$uired

to simplify our design after wor"ing out the conditions needed for an output

to operate from the system specification.

0ur ne!t topic of wor" &.. Boolean Algebra will provide us with a

set of rules we can use to simplify the logic system.

ystem design will temporarily be put on hold while we learn the

simplification techni$ues of Boolean Algebra 5ood 'uc"@

*ngr. +ulius . -ansino &4


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logic system specifications-worded problems

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