The given circuit works as :

Step-by-step solution

Let the inputs be A and B. The circuit is composed of NOR gates. A NOR gate with its inputs tied together acts as a NOT gate. The output of the first NOR gate (input A) is Y₁ = A+A = A . The output of the second NOR gate (input B) is Y₂ = B+B = B . These outputs are fed into a third NOR gate. Its output is Y₃ = Y₁ + Y₂ = A + B . Using De Morgan's theorem, Y₃ = ( A ) ( B ) = A B . This output Y₃ is the input to the fourth NOR gate, which is configured as a NOT gate. The final output is Y_ out = Y₃ = A B . The expres