For 4 to 1 mux truth table SEL INPUT O/P
Q | P | R | R’ | R’ | R | F |
0 | 0 | X | X | X | 1 | 1 |
0 | 1 | X | X | 1 | X | 1 |
1 | 0 | X | 1 | X | X | 1 |
1 | 1 | 1 | X | X | X | 1 |
In the 1st column there are 4 NOR Gates, number them as 1 to 4 ( top to down).
In the 2nd column there are 2 NOR Gates, number them as 5 and 6 ( top to down).
In the 3rd column there is only 1 NOR Gate, number it as 7.
1st numbered Gate gives output as : ( P + Q )'
2nd numbered Gate gives output as : ( Q + R )'
3rd numbered Gate gives output as : ( P + R )'
4th numbered Gate gives output as : ( R + Q )'
5th numbered Gate gives output as :
(( P + Q )' + ( Q + R )')'
= ((P + Q)'' . ( Q + R )'') ( De Morgan's law)
= (P + Q ) . ( Q + R ) ( Idempotent Law, A'' = A)
= (PQ + PR + Q + QR )
= (Q(1 + P + R) + PR)
=> Q + PR ( as, 1 + " any boolean expression" = 1 )
Similarly 6th numbered Gate gives output as : R + PQ (as this time R is common here)
Now 7th numbered Gate gives output as :
((Q + PR) + (R + PQ))'
= (Q( 1+P) + R(1+P))'
= (Q+R)'