What is the Boolean expression for the output f of the combinational logic circuit of NOR gates given below?
(A) (Q+R)’
(B) (P+Q)’
(C) (P+R)
(D) (P+Q+R)’
Answer: (A)
Explanation: Answer is Option A.
The above question contains the NOR gates. Let’s see what NOR gate does.
If A and B are the two inputs to the NOR gate, the NOR gate gives (A+B)’ as the output.
Let’s assign numbers to the Gates for the easy understanding.
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)'