Maharashtra State BoardHSC Arts 12th Board Exam
Advertisement Remove all ads

Represent the following switching circuit in symbolic form and construct its switching table. Write your conclusion from the switching table. - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Sum

Represent the following switching circuit in symbolic form and construct its switching table. Write your conclusion from the switching table.

Advertisement Remove all ads

Solution

Let p: the switch S1 is closed
q: the switch S2 is closed
r: the switch S3 is closed
 ∼ q: the switch S2′ is closed or the switch S2 is open
∼ r: the switch S3′ is closed or the switch S3 is open
Then the symbolic form of the given circuit is:
[p ∨ (∼ q) ∨ (∼ r)] ∧ [p ∨ (q ∧ r)]

Switching Table

p q r ∼q ∼r p∨(∼q)∨(∼r) q∧r p∨(q∧r) Final column
          (I)   (II) (I) ∧ (II)
1 1 1 0 0 1 1 1 1
1 1 0 0 1 1 0 1 1
1 0 1 1 0 1 0 1 1
1 0 0 1 1 1 0 1 1
0 1 1 0 0 0 1 1 0
0 1 0 0 1 1 0 0 0
0 0 1 1 0 1 0 0 0
0 0 0 1 1 1 0 0 0

From the table, the ‘final column’ and the column of p are identical. Hence, the given circuit is equivalent to the simple circuit with only one switch S1.
∴ the simplified form of the given circuit is:

Concept: Application of Logic to Switching Circuits
  Is there an error in this question or solution?

APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 17 | Page 35
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×