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

1st case: 

2nd case:  

3rd case: 

4rth case:

switch a to b is 1 and a to c is 0 ... so bulb will glow when s1(0)   s2(0)    On  and s1(1)   s2(1)   On

so EXnor is used.

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how can a bulb glow when switch is off?

even if it is closed ckt , what is the guarantee that current is flowing through it , enough to glow that bulb?

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@Pranavpurkar in the qustion it tells in ON position ( it doesnot tell switch is ON…...it is just name of one of two way of connection) ON means a connected to b and OFF means a is connected to c.thats it.