Sum
Write the symbolic form of the following switching circuit construct its switching table and interpret it.
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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 switching table, the ‘final column’ and the column of p are identical. Hence, the lamp will glow which S1 is ‘ON’.
Concept: Application of Logic to Switching Circuits
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