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