GATE IT 2005 | Question: 10

Question

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. $S1.\overline{S2}$ 
• B. $S1 + S2$
• C. $\overline {S1\oplus S2}$
• D. $S1 \oplus S2$

Answer 1

If we look carefully, bulb will be ON when both switches $S1$ and $S2$ are in the same state, either off or on.$$\begin{array}{c|c|c} S1&S2&\text{Bulb}\\\hline0&0&\text{On}\\0&1&\text{Off}\\1&0&\text{Off}\\1&1&\text{On} \end{array}$$ This is $\text{Ex-NOR}$ operation, hence (C) is the correct option.

Comments

See though the crnt will flow but to light the bulb ckt should be complete right? See the possible states of the switches only in two states ckt is complete.

Hence xnor is used, opt C is ✔️

---

@gvinay Best Comment bhaiya.Now able to understand the real meaning of question.

---

nice explaination

 

Answer 2

Answer is option C

Answer 3

First of all to make always the bulb on a should be connected to b for both Switch 1 and Switch 2.

This means S1 and S2 should be present always in non comlementary form.

Option B : is not true as it is OR and OR can be true also if any of the one is true.

Option C: is the correct answer as it is exnor and exnor have two operands always in uncomplemented form. which makes S1 and S2 always true.

Option A : obvious reasons for not true

Option D: Exor never have both operands true simultaneously.