Application of logic to the switching circuit part-1


We know that a statement in logic is either true or false. 


 The same situation occurs in electric switches. 
A working switch is either on (closed) or off (open).
If a switch is ‘on’ it allowed electric current to pass the circuit and lamp glows and if the switch is ‘open’ it does not allow current to pass the circuit and lamp does not glow.
We shall denote ‘on’ switches by letters S, , , ,… and open switches are denoted by letters
S’, , ,…But the symbol is used to denote both the switches are the same  only differ by the letters S and S’.
Let the statement p denote the ‘switch S is closed’ and lamp with light by l. Then its symbolic form is p  l.
Let ~p: the switch S’ is closed and lamp with no light by l’
Then its symbolic form is ~p  l’.
Switches connected in the circuit in two different ways
1. In series 2. In parallel.
1. Switches connected in series
switching circuit
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Let p: the switch is closed and
q: the switch is closed
If and  are both closed  then lamp glows. If either or or both are open then the lamp does not glow. Its input output table is
S1
S2
Lamp
1
1
glows
1
0
does not glow
0
1
does not glow
0
0
does not glow
 This table is same as truth table of p q i.e. conjunction of p and q. Therefore switches connected in series can be represented by  p q  l and its input output table is
p
q
p q
1
1
1
1
0
0
0
1
0
0
0
0
2. Switches connected in parallel
switching circuit

 Let p: the switch is closed and
q: the switch is closed
If and  are both open  then lamp does not glow. If either or or both are closed  then the lamp  glows. Its input output table is
S1
S2
Lamp
1
1
glows
1
0
 glows
0
1
 glows
0
0
does not glow
 This table is same as truth table of p V q i.e. disjunction ‘p or q’. Therefore switches connected in parallel can be represented by  p V q  l.and its input output table is
p
q
p V q
1
1
1
1
0
1
0
1
1
0
0
0
In this way we have seen how a switching circuit is represented by a logical statement.
 In my next post we are going to solve more examples on the switching circuits.

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