Question

Express the following switching circuit in the symbolic form of logic. Construct the switching table and interpret it. \includegraphics[width=0.5\linewidth]{01.jpeg}

Hint:

For switching circuits, express the logic using AND, OR, and NOT operations and construct a truth table for analysis.

Answer 1

Step 1: Understand the circuit.
The given circuit consists of two switches \( S_1 \) and \( S_2 \), with their complements \( S_1' \) and \( S_2' \) also involved. The circuit configuration suggests a combination of AND, OR, and NOT logic gates.

Step 2: Assign logic variables.
Let the logic variables be \( S_1 \) for switch 1, \( S_2 \) for switch 2, and \( L \) for the output.

Step 3: Determine the symbolic expression.
Based on the circuit, the expression can be written as: \[ L = (S_1 \cdot S_2') + (S_1' \cdot S_2) \] Where: - \( S_1 \cdot S_2' \) represents the AND operation between \( S_1 \) and \( S_2' \). - \( S_1' \cdot S_2 \) represents the AND operation between \( S_1' \) and \( S_2 \). - The OR operation is denoted by the plus sign \( + \).

Step 4: Construct the switching table.
The switching table for the above logic expression is as follows: \[ \begin{array}{|c|c|c|} \hline S_1 & S_2 & L
\hline 0 & 0 & 0
0 & 1 & 1
1 & 0 & 1
1 & 1 & 0
\hline \end{array} \]

Step 5: Interpret the results.
- When both switches are off (\( S_1 = 0, S_2 = 0 \)), the output is off (\( L = 0 \)). - When \( S_1 = 0 \) and \( S_2 = 1 \), the output is on (\( L = 1 \)). - When \( S_1 = 1 \) and \( S_2 = 0 \), the output is on (\( L = 1 \)). - When both switches are on (\( S_1 = 1, S_2 = 1 \)), the output is off (\( L = 0 \)).

Final Answer: \[ L = (S_1 \cdot S_2') + (S_1' \cdot S_2) \]