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# =Electronics Hardware Questions=

Q:
There are 3 switches that can turn on and off a light in the room.
How to connect them?

A:

Anon1
Just wondering what would be the boolean equation for this diagram?

H.T
This should do, I think

```X1	X2	X3	Y
-----------------------------
0	0	0	0
1	0	0	1
0	1	0	1
1	1	0	0
0	0	1	1
1	0	1	0
0	1	1	0
1	1	1	1
```

komalpatidar
Y = x1x2'x3' + x1'x2x3' + x1'x2'x3 + x1x2x3

from 1st and 4th term, take out x1 as a common.
and from 2nd and 3rd term, take out x1' as a common.

Y = x1( x2'x3' + x2x3 ) + x1'( x2x3' + x2'x3 )
= x1( x2 x-nor x3 ) + x1' ( x2 xor x3 )
= x1( x2 xor x3 )' + x1'( x2 xor x3 )
lets take (x2 xor x3) = A and x1 = B

Y = AB'+ A'B = A xor B
substituet the A and B values in above equation.

Y = x1 xor x2 xor x3