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 xnor 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


