"Sharpening Skills.....
Serving Nation"
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459 (Online), Volume 4, Special Issue 1, February 2014)
International Conference on Advanced Developments in Engineering and Technology (ICADET-14), INDIA.
Some Applications of Boolean Algebra in Switching Circuits
TARUNA BHASKAR
Department of mathematics, I.P.E.C, SAHIBABAD
[email protected]
Abstract— Our main motive of work in this thesis is to
provide some information of understanding the use of
Boolean algebra with the help of switching circuits
combining with some relay circuits and with some practical
examples which completely makes us enable to understand
why Boolean algebra is so important. The examples which
are used in this thesis are simple to understand and will able
to clarify the main purpose of this work.
Keywords—Air conditioner, sensors, circuits, output, gas
leakage, choking, plasma gasification, heat torch, air
pressure, waste valve.
I. INTRODUCTION
This document is a template. An electronic copy can
be downloaded In this paper some applications of
Boolean algebra are shown through some real life
examples using relay circuits. An example of toxic waste
incinerator in which the author uses the sensors to detect
a good flame in toxic waste incinerator to open the waste
valve so that toxic waste could not come out if the waste
in chamber not burn properly. So minimizing the time
and to reduce the cost and to prevent the environment
from toxic fuels, we apply the sensors. Using this idea I
used these sensors on another example such that A.C and
PLASMA GASIFICATION by which we can increase
the life of object and by saving energy and cost
accompany can make more profit. In this paper we
consider an example of A.C and apply four sensors to
check the leakage of gas, choking, temperature and
pressure
The English mathematician George Boole (1815-1864)
sought to give symbolic form to Aristotle's system of
logic. Boole wrote a treatise on the subject in 1854, titled
An Investigation of the Laws of Thought, on Which Are
Founded the Mathematical Theories of Logic and
Probabilities, which codified several rules of relationship
between mathematical quantities limited to one of two
possible values: true or false, 1 or 0. His mathematical
system became known as Boolean algebra. It is a world
in which all other possibilities are invalid by fiat.
As one might guess, this is not the kind of math you
want to use when balancing a checkbook or calculating
current through a resistor. However, Claude Shannon of
MIT fame recognized how Boolean algebra could be
applied to on-and-off circuits, where all signals are
characterized as either "high" (1) or "low" (0). His 1938
thesis, titled A Symbolic Analysis of Relay and Switching
Circuits, put Boole's theoretical work to use in a way
Boole never could have imagined, giving us a powerful
mathematical tool for designing and analyzing digital
circuits. It is an abstract mathematical system primarily
used in computer science and in expressing the
relationships between sets (groups of objects or concepts).
The notational system was developed by the English
mathematician George Boole c.1850 to permit an
algebraic manipulation of logical statements. Such
manipulation can demonstrate whether or not a statement
is true and show how a complicated statement can be
rephrased in a simpler, more convenient form without
changing its meaning.
Boolean arithmetic
Let us begin our exploration of Boolean algebra by
adding numbers together:
A.
Boolean algebra by multiplication:
B.
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"Sharpening Skills.....
Serving Nation"
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459 (Online), Volume 4, Special Issue 1, February 2014)
International Conference on Advanced Developments in Engineering and Technology (ICADET-14), INDIA.
And there circuits
A simple stylized diagram of the refrigeration cycle:
1) Condensing coil, 2) expansion valve, 3) evaporator
coil, 4) Compressor.
Boolean multiplication
AIR CONDITIONER
What is an air conditioner?
An air conditioner is an appliance, system or
mechanism designed to extract heat from an area using a
refrigeration cycle. In construction, a complete system of
heating, ventilation, and air conditioning is referred to as
HVAC. Its purpose, in the home or in the car, is to
provide comfort during either hot or cold weather.
A poorly maintained air conditioning system can
occasionally promote the growth and spread of
microorganism, such as legion Ella pneumophila, the
infectious agent responsible for legionnaire‟s disease or
thermophilic actinomycetes.
We can assume some conditions in AC where we can
use Boolean algebra‟s application and will see how our
A.C can be more secure from internal problems which
occurred in it and can have long life. These conditions
are like level of the gas, inner temperature of A.C,
choking problem in window due to some waste and
leakage of gas.
The level of the gas should be proper in the A.C, if the
level of the gas is low, AC will not work efficiently and
also lead to the power wastage. Our aim is to monitor this
level of the gas at a saturated level for keeping A.C
continues on working. Now we want to implement a
sensor which senses the level of gas in the refrigerator
section of A.C. Let level of the gas is maintained at a
saturated level and if level of gas goes down from that
level, sensor will automatically shut off the A.C. Suppose
low level of gas is denoted by”0” and saturated level is
denoted by“1”.Hence power supply to the A.C will be
“on” till the sensor show constant level.
We can implement an another sensor for the inner
temperature of A.C, the temperature of inner equipments
reaches so high that a fault can be occurred in the A.C for
safety purpose we can put a sensor in A.C which will
shut down A.C before reaching the temperature at that
level automatically.
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"Sharpening Skills.....
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International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459 (Online), Volume 4, Special Issue 1, February 2014)
International Conference on Advanced Developments in Engineering and Technology (ICADET-14), INDIA.
For this we set a critical temperature for that sensor
beyond which it will not allow A.C to work. Let us
consider temperature less then that critical temperature
is”1” and >or = to that critical temperature is “0”.
Third sensor is for choking, as it is not so important
but we can‟t neglect it. If the flow of air is not as smooth
as it should be from all over the window of the A.C or
there is some waste in the window, by putting a sensor,
we can keep an eye on it and if it happens A.C will
automatically shut down.
We can put a fourth sensor which is for leakage of gas,
if there is a leakage in gas chamber then A.C will not
cool properly and it is also unhealthy, so we will put a
sensor so if gas is leaking, A.C will shut down .So we
consider leakage as“0” and not showing leakage as“1”.
Now from above discussion we reach at a situation
that if all sensors are showing value “1” then only in that
condition A.C will be “on” and for designing the circuit
for this situation we have to first draw the truth table.
Low level of gas sensor value is “0”
Otherwise “1”
Temperature above critical value sensor value “0”
Otherwise “1”
If there is some choking sensor value is “0”
Otherwise “1”
If there is a leakage of gas sensor value “0”
Otherwise “1”
Nothing is so ideal or remains ideal like that always.
There will occur some little bit problem and. A rare
problem in A.C between these four conditions will
instantly closed our A.C. but there are some conditions at
which we can allow or compromise our A.C to be “on”.
Such that level of the cooling gas is low or choking is
also compromisable to some extent. Then we want to
continue our A.C “on” with this problem. But we can‟t
compromise with leakage and temperature because these
conditions will lead to a big problem. Now our A.C will
be “on” when input has value “1” in leakage and
temperature both, either sensor for level of gas or
choking has value “0”. Thus if our output is “1” then A.C
will be “on” and if “0” A.C will be “off”.
From above discussion our new truth table is.
Truth table for this design is as followed:
Out put = XYZW
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"Sharpening Skills.....
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International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459 (Online), Volume 4, Special Issue 1, February 2014)
International Conference on Advanced Developments in Engineering and Technology (ICADET-14), INDIA.
And the corresponding circuit will be:
Implemented in a Programmable Logic Controller
(PLC), the entire logic system might resemble something
like this:
Plasma Gasifiacation
Plasma gasification is a processing of cleaning the
waste ecologically. Pure highly calorific synthetic gas
consists of CO, H2, CH, etc. The conversion rate of
plasma gasification exceeds 99%. Non-flammable
inorganic components in the waste stream are not broken
down. This includes various metals. A phase change
from solid to liquid adds to the volume of slag.
A plasma torch uses an inert gas such as steam.
The electrodes
vary
from copper
or tungsten or zirconium, along with various other alloys.
A strong electric current under high voltage passes
between the two electrodes as an electric arc. Pressurized
inert gas is ionized passing through the plasma created by
the arc. The torch's temperature ranges from 4,000 to
25,000 °F (2,200 to 13,900 °C).The temperature of the
plasma reaction determines the structure of the plasma
and forming gas. This can be optimized to minimize
ballast contents, composed of the byproducts of oxidation:
CO2, N, H2O, etc.
Principle of this is that an intense heat of the fire and
oxygen air is intended to ionize of waste product. The
lack of oxygen prevents the formation of many toxins.
The high temperatures in a reactor also prevent the main
components of the gas from forming toxic compounds
such as furans, dioxins, NOX, or sulfur dioxide. Water
filtration removes ash and gaseous pollutants. So a
necessity is caused to make a system which assure us or
prove us that the waste would be allowed to inject only if
the presence of a right temperature and air pressure is
detected in the chamber.
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"Sharpening Skills.....
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International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459 (Online), Volume 4, Special Issue 1, February 2014)
International Conference on Advanced Developments in Engineering and Technology (ICADET-14), INDIA.
Excessive exhaust gas temperatures can be the result
of poor heat transfer in the furnace. If the combustion
gases are unable to transfer the maximum possible heat to
the furnace and its contents, they will leave the furnace at
higher temperatures than necessary. Optimizing heat
transfer within the furnace requires different methods for
different situations.
Overloading a furnace can also lead to excessive stack
temperature. To get the proper rate of heat transfer,
oxygen gases must be in the gasification chamber for the
right amount of time. The natural tendency of an
overloaded furnace is to run colder than optimal, unless
the temperature is set artificially high. This causes the
burners to operate at higher than normal firing rates,
which increase combustion gas volumes. The higher gas
flow rates and shorter time in the furnace cause poor heat
transfer, resulting in higher temperature for the flue gases.
Increased volumes of higher temperature flue gases lead
to sharply increased heat losses. Overly ambitious
production goals might be met, but at the cost of
excessive fuel consumption and forming of toxin waste
can be high.
Higher values of oxygen and flue gas temperature
offer higher fuel savings. Obviously, the fuel savings
would have to be compared to the cost of oxygen to
estimate actual economic benefits. Waste heat recovery.
Reducing exhaust losses should always be the first step in
a well-planned.
It would be very unsafe to continuously injecting the
waste into the gasification chamber. As if the right
temperature and air pressure has not been extinguished, it
may exit the exhaust a great amount of toxins in air
which is dangerous to health and threat to anyone in
close proximity to the exhaust.
Let we consider a task of designing a circuit to detect
the right temperature and air for plasma gasification.
Through truth table, this functionality could be generated
with a three-input AND gate: the output of the circuit
will be "1" if and only if input X and input Y and input Z
are all "1"
Thus, our truth table would look like this:
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International Journal of Emerging Technology and Advanced Engineering
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International Conference on Advanced Developments in Engineering and Technology (ICADET-14), INDIA.
As this designing has its own advantages and assures
maximum safety, it makes the system very susceptible to
sensor failures of another kind. Now It will be
comfortable to design logic system that can allow this
kind of failure and continue the process without shutting
the system down unnecessarily, but not ignoring sensor
redundancy so as to maintain safety in the event and that
any single failure will not affect the system .A strategy
that fulfills our need or condition will be a "two out of
three" sensor logic, according to that the waste valve will
allow to open if at least two out of the three sensors show
the right temperature and pressure. The truth table for
such a system would look like this:
It is a Boolean Sum-Of-Products expression for the
truth table's function; we can easily design a logic gate or
relay logic circuit based on that expression:
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International Conference on Advanced Developments in Engineering and Technology (ICADET-14), INDIA.
If all three sensors are operating properly, they should
detect appropriate temperature and gas definitely with
equal accuracy. Thus, sensors will either register 000 i.e.
no flame or all register 111i.e, good flame. Any other
output like 001, 010, 011, 100, 101, or 110 constitutes
will show a disagreement between sensors, and may
therefore indicate a sensor of a potential failure. Now if
with the previous circuit which has already drawn, we
add a circuitry to detect any one of the six "sensor
disagreement" conditions, we can use the output of that
circuitry to activate an alarm. Whoever is monitoring the
gasification chamber will then instantly judge that either
he should continue to operate with a possible failed
sensor where inputs are 011, 101, or 110, or shut the
chamber down to be absolutely safe. Also, if the
gasification chamber shut down , and one or more of the
sensors still indicates appropriate conditions (001, 010,
011, 100, 101, or 110) while the others indicates no , it
will be known that a definite sensor problem exists.
The first step in designing this "sensor disagreement"
detection circuit is to write a truth table describing its
behavior. Since we already have a truth table describing
the output of the "good flame", we can simply add
another output column to the table to represent the
second ciruit and make a table representing the entire
logic system
An alternative process to generating a Sum-OfProducts expression to account for all the 1 output
conditions in the truth table is to generate a Product-OfSums, or POS, expression, to account for all the 0 output
conditions.
Whereas a Sum-Of-Products expression could be
implemented in the form of a set of AND gates with their
outputs connecting to a single OR gate, a Product-OfSums expression can be implemented as a set of OR
gates feeding into a single AND gate:
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"Sharpening Skills.....
Serving Nation"
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459 (Online), Volume 4, Special Issue 1, February 2014)
International Conference on Advanced Developments in Engineering and Technology (ICADET-14), INDIA.
And the relay circuit:
Programmers learn that logic is a foundation of
programming, but they don't often use it to program.
Mathematicians study about logic, but they don't often
use it in their proofs. Logic is a tool, like a knife. People
have looked at it from every angle; they've described
how it works at great length; now it's time to pick it up
and use it.
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[1]
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[4]
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[9]
[10]
[11]
II. CONCLUSIONS
Through this research paper by using sensors and by
forming their circuits and we show how they can
implement in relay circuits. With use of Boolean algebra
we can simplify complex circuits in a simple way. Logic
has been well studied and is now well understood, but it
is not well used.
[12]
[13]
[14]
[15]
[16]
[17]
[18]
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