Realization
of the Diagram of Indication by reversers |
Realization
of the Diagram of Indication by means of electronic symbols |
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Created it, 06/09/09
Update it, 06/09/13
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4. - EXAMPLE OF APPLICATION PRACTICES TABLES OF KARNAUGH
4. 1. - Let us suppose that when the alarm clock sounds the morning, one wants to know how to get dressed before to have even opened the shutters.
We have for that an appropriate provision placed outside and in particular including a thermometer and a barometer and which gives us the following indications : hot time, soft time, cold time, rainy weather.
It is decided that in all the cases, one will put pants, shoes and a shirt.
It now remains to determine if it is necessary to put in more one jacket, a coat, impermeable or to take an umbrella.
We will call the variables of entry :
hot time : c
soft time : d
cold time : f
rainy weather : p
The variables of exit will be materialized by lamps and will be called :
jacket
: V
coat
: M
impermeable : I
umbrella : P
It will be admitted that when the weather is warm a jacket is put, when the weather is cold one puts a jacket and a coat and that when the weather is hot, one does not put anything. When it rains, one puts impermeable on the jacket if not one takes an umbrella when one has already a coat or when the weather is hot.
From these postulates, let us draw up the truth table of the system (figure 70).
We reserved a column which corresponds to impossibilities. Indeed, the weather cannot be hot and cold for example.
Let us draw up the tables of Karnaugh whom we will draw from the truth table and this, for each variable of exit.
4. 2. - TABLE OF KARNAUGH RELATING TO THE JACKET (figure 71)
This confirms the table of Karnaugh.
4. 3. - TABLE OF KARNAUGH RELATING TO THE COAT (figure 72)
What confirms the table of Karnaugh.
4. 4. - TABLE OF KARNAUGH RELATING TO the IMPERMEABLE one (figure 73)
4. 5. - TABLE OF KARNAUGH RELATING TO THE UMBRELLA (figure 74)
4. 6. - REALIZATION
OF THE DIAGRAM
One will use make-break contacts, which will be ordered by the suitable device evoked previously, as represented figure 75.
In the example of figure 75,
according to the position of the switch one a : d = 1 (high), d = 0 (low)
is 
,
so that d = soft and
= nonsoft.
a) - Diagram for the jacket has (figure 76)
In the diagram of figure 76, one
represented the case 
,
i.e. the lamp (to take your jacket) is lit, since time is soft.
It is easy to include/understand
that the lamp (to take your jacket) will be also lit for the switches position
,
i.e. soft time.
b) - Diagram relating to the coat (figure 77)
By using same conventions, one can,
knowing the equality 
,
to draw up the diagram.
c) - Diagram relating to impermeable (figure 78)
d) - Diagram relating to the umbrella (figure 79)
e) - general Outline (figure 80)
It represents the case where the lamps V and I are lit.
In the truth table (figure 70), we envisaged a column called “impossibilities” or breakdowns of the system.
There is, indeed, absolute impossibility so that the indications heat and cold, soft and cold, hot and soft, etc… are present simultaneously.
These cases are impossible or then the system is broken down.
One can, starting from these cases, to light a lamp which will indicate that the system does not function correctly.
f) - Table of Karnaugh detection defect (figure 81)
From the table of Karnaugh, let us establish the equation of D.
This leads us to the diagram of the indicator defect represented figure 82.
4. 7. - REALIZATION OF
THE DIAGRAM OF INDICATION
BY MEANS OF ELECTRONIC SYMBOLS
a) - Diagram of the indication of the jacket has (figure 83)
b) - Diagram of the indication of the coat (figure 84)
c) - Diagram of the indication of impermeable (figure 85)
d) - Diagram of the indication of the umbrella (figure 86)
e) - general Outline (figure 87)
The general outline will be consisted the assembly of the other diagrams so that the number of logical operators is minimum.
For this purpose, the partial
diagrams are examined and knowing for example that
is used in the diagrams partial of V and P
one can not thus use that only one reverser to produce the signal
starting from variable d. One thus succeeds
in with a little good direction gathering the whole in only one diagram.
f) - Diagram of indication defect (figure 88)
In the next theory, we will examine on the one hand new methods to transform the Booléennes expressions and on the other hand logical circuits derived from the three circuits fundamental AND, OR, NOT, seen in this theory.
The circuits examined until now are the base of all the assemblies known as “combinative” i.e. whose state (1 or 0) of the exits depends only on the state of the entries at the time when we examine the assembly.
We finish this 2nd lesson thus.
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