Question

What is the boolean expression for the output f of the combinational logic circuit of nor gates

Answer 1

Answer:

since you have not given any diagram i m assuming one diagram as given below to explain you

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)'