Question

Simplify the given circuit by writing its logical expression. Also write your conclusion.

Hint:

Simplify logic expressions using Boolean algebra or Karnaugh maps; XOR is common for circuits with complementary inputs.

Answer 1

The problem references \( S_1, S_2, \neg S_1, \neg S_2 \), suggesting a logic circuit with inputs \( S_1, S_2 \) and their negations. Without a specific circuit diagram, assume a common configuration, e.g., an expression involving AND, OR, or XOR gates. A typical circuit might be \( (\neg S_1 \land S_2) \lor (S_1 \land \neg S_2) \), which simplifies to XOR.
Let’s hypothesize the output as: \[ Y = (\neg S_1 \land S_2) \lor (S_1 \land \neg S_2). \] Simplify: \[ Y = \neg S_1 S_2 + S_1 \neg S_2 = S_1 \oplus S_2. \] Conclusion: The circuit likely represents an XOR gate, outputting true when exactly one of \( S_1 \) or \( S_2 \) is true.
Answer: Logical expression: \( S_1 \oplus S_2 \). The circuit is equivalent to an XOR gate.