Question

In the following digital circuit, the output 'Y' will be '1' (one) for inputs 'A' and 'B' having values

• A. \(A = 0,B = 0\)
• B. \(A = 0,B = 1\)
• C. \(A = 1,B = 0\)
• D. \(A = 1,B = 1\)

Hint:

Trace each gate: a NOR followed by a NOT, an AND gate, and a final NOR.

Answer 1

The Correct Option is D

Step 1: Understanding the Circuit:
From the figure: inputs A and B go to a NOR gate, and its output goes to a NOT gate to give \(Y_1\). Inputs C and D go to an AND gate to give \(Y_2\). \(Y_1\) and \(Y_2\) go to a NOR gate to give \(Y_3\).

Step 2: Write the outputs:
NOR followed by NOT is an OR gate, so \(Y_1 = A + B\). Also \(Y_2 = C\cdot D\) and \(Y_3 = \overline{Y_1 + Y_2}\).
Check with the given case, A = B = C = D = 1: \(Y_1 = 1\), \(Y_2 = 1\), \(Y_3 = 0\). This matches (1, 1, 0).

Step 3: New inputs:
Now A = 0, B = 1, C = 0, D = 1:
\(Y_1 = 0 + 1 = 1\). \(Y_2 = 0\cdot1 = 0\). \(Y_3 = \overline{1 + 0} = 0\).
So the outputs are (1, 0, 0).

Final Answer:
The outputs are \(Y_1, Y_2, Y_3 = 1, 0, 0\), option (B). \[ \boxed{1,\ 0,\ 0} \]