In a digital logic circuit, two inputs A and B are fed into two different gates simultaneously: a NAND gate and an OR gate. The outputs of these two gates are then connected to the inputs of an AND gate, which produces the final output Y . The input signals A and B are given as sequences of bits over four consecutive time intervals: A = 0, 1, 0, 1 B = 0, 0, 1, 1 The corresponding output sequence Y over these four tim

Step-by-step solution

Output of the NAND gate: Y₁ = A B Output of the OR gate: Y₂ = A + B Final output from the AND gate: Y = Y₁ Y₂ = ( A B ) (A + B) Using De Morgan's law, we can write A B = A + B . Substituting this into the expression for Y : Y = ( A + B ) (A + B) Expanding the expression: Y = A A + A B + B A + B B Since A A = 0 and B B = 0 , the expression simplifies to: Y = A B + A B (which represents an XOR gate). Now, evaluating Y for the given input sequences: For A=0, B=0 : Y = 1 0 + 0 1 = 0 For A=1, B=0 : Y = 0 0 + 1 1 = 1 For