Application of logic to the switching circuit part-2
In this post we are going to see two types of examples on the application of logic to the switching circuits.
A) how to express
the given circuit in symbolic form of logic and
B) how to construct the switching circuits if the
logical statements are given.
So let’s begin.Ex. A) Express the following circuits in symbolic form
of logic.
In the circuit there are one S1 switch, two S2’ switches, one S3 switch and one S3’ switch.Let p: the switch S1 is closed. ~q: the switch S2’ is closed.
r: the switch S3 is closed. \
~r:
the switch S3’ is closed.
The switch S2’ and S3 are connected in parallel and they are connected in series with the switch S1. Its symbolic form is
p &(~q
v r).
The switches S2’ and S3’ are connected in series.Its symbolic form
is ~q 
~r.
These branches are connected in parallel.
Hence given circuit in symbolic form
is [p (~q
v r)]v( ~q ~r)
2)
In the circuit there are one S1 switch, two S2
switches, one S3 switch and one S1’ switch.
Let p: the switch S1 is closed.
~p:
the switch S1’ is closed.
q:
the switch S2 is closed.
r: the switch S3 is closed.
The switches S1 and S2 are connected in parallel
similarly the switches S3 and S’1 are connected in parallel their symbolic forms
are (p v q) and
(r v ~ p) respectively.
These two branches are connected in series with the switch S2. Hence given
circuit in symbolic form is
(p v q)& q& (r v ~ p)
Ex. B) Construct the switching circuit for the
following statements.
1) (p
q)v
[~p (~q
v p v r)]
q)v
[~p (~q
v p v r)]
In this statement p, q, r, ~p and ~q are distinct statements.
Let p: the switch S1 is closed.
~p:
the switch S1’ is closed.
q:
the switch S2 is closed.
~q: the switch S2’ is closed.
r: the switch S3 is closed.
(p& q) represents two switches connected
in series and its circuit diagram is
and (~q v p v r) represents
three switches connected in parallel and its circuit diagram is
this branch is connected in series with the switch S1’
(~p) and its circuit diagram is
These two branches are connected in parallel. Hence
the final circuit diagram is
2) (p& q)v [~p& (q& ~ r)]
In this statement p, q, r, ~p and ~r are distinct statements.
Let p: the switch S1 is closed.
~p:
the switch S1’ is closed.
q:
the switch S2 is closed.
r: the switch S3 is closed.
~r: the switch S3’ is closed.
(p& q&r) represents
three switches connected in series and its circuit diagram is
this branch is connected in parallel with the switch
S1’ (~p) and its circuit diagram is
These two branches are
connected in parallel. Hence the final circuit diagram is
In this way we have seen two types of examples in
switching circuit.
In my next post we are going to see more examples of
different types.
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