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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 ?

1. $S1.\overline{S2}$
2. $S1 + S2$
3. $\overline {S1\oplus S2}$
4. $S1 \oplus S2$

edited | 1.8k views

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.

by Boss (43.8k points)
edited
+40

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.