A two-way switch has three terminals a, b and c. In ON position (logic value…
2005
A two-way switch has three terminals a, b and c. In ON position (logic value 1), a is connected to b, and in OFF position, a is connected to c. Two of these two-way switches S1 and S2 are connected to a bulb as shown below.
Which of the following expressions, if true, will always result in the lighting of the bulb ?
- A.
S1.S2'
- B.
S1+S2
- C.
(S1⊕S2)'
- D.
S1⊕S2
Attempted by 851 students.
Show answer & explanation
Correct answer: C
Answer: (S1⊕S2)' (exclusive OR)
To keep the bulb ON, both switches must complete the circuit through the same path.
That means:
If S1 is in position a–b, then S2 must also be in the same position.
If S1 is in position c–d, then S2 must also match that position.
So the bulb glows only when both inputs are the same.
This behavior matches the EX-NOR gate, because:
For same inputs (0-0 or 1-1), EX-NOR output = 1 → bulb ON
For different inputs, EX-NOR output = 0 → bulb OFF
Thus the correct Boolean expression is:
(S1⊕S2)EX-NOR gives 1 when inputs are equal — exactly what the circuit requires.