Question

The output Y, when all the three inputs are first high and then low, will respectively be

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

Hint:

The first two inputs go to an AND gate, and its output and the third input go to a NAND gate.

Answer 1

The Correct Option is D

Step 1: Reading the Circuit
The first two inputs feed an AND gate.
Its output and the third input feed a NAND gate that gives Y.

Step 2: Boolean Expression
\(Y = \overline{(A\cdot B)\cdot C}\)

Step 3: All Inputs High
\(A = B = C = 1\), so \(A\cdot B = 1\) and \(1\cdot 1 = 1\).
The NAND of \(1\) is \(\overline{1} = 0\), so \(Y = 0\).

Step 4: All Inputs Low
\(A = B = C = 0\), so \(A\cdot B = 0\) and \(0\cdot 0 = 0\).
The NAND of \(0\) is \(\overline{0} = 1\), so \(Y = 1\).

Final Answer:
The output is 0 when all inputs are high and 1 when all inputs are low. \[ \boxed{\text{(D) }0,1} \]