The logic levels of two inputs A and B , and the corresponding output Y of a logic circuit for four consecutive time intervals are given below: Interval 1: A = 0 , B = 0 , Y = 0 Interval 2: A = 0 , B = 1 , Y = 0 Interval 3: A = 1 , B = 0 , Y = 0 Interval 4: A = 1 , B = 1 , Y = 1 Which of the following logic circuits, constructed entirely from NOR gates, produces this output?

Step-by-step solution

From the given logic levels, the truth table is: A=0, B=0 Y=0 A=0, B=1 Y=0 A=1, B=0 Y=0 A=1, B=1 Y=1 This corresponds to the logic of an AND gate, i.e., Y = A B . Let us evaluate the boolean expression for each option: Option 1: The first NOR gate gives A+B . The second NOR gate acts as a NOT gate, giving A+B = A+B (OR gate). Option 2: The first two NOR gates act as NOT gates, giving A and B . The third NOR gate gives Y = A + B . By De Morgan's law, Y = A B = A B (AND gate). Option 3: A single NOR gate gives Y = A+