Question

For which of the following combinations of A, B, and C, does the output \(Y\) become 0 in the given logic circuit?

• A. A = 0, B = 0, C = 0
• B. A = 1, B = 0, C = 0
• C. A = 1, B = 1, C = 0
• D. A = 1, B = 1, C = 1

Hint:

To solve logic gate circuits: 1. Identify each gate type. 2. Express output in Boolean algebra. 3. Draw truth table for all input combinations. 4. Evaluate stepwise for NOT, AND, NAND etc. 5. Identify input combination giving desired output. 6. Check carefully for multiple possibilities.

Answer 1

The Correct Option is A

Step 1: Circuit components.
The circuit consists of a NOT gate on input A, a NAND gate on inputs B and C, and an AND gate combining both outputs.

Step 2: Boolean expression.
Y = (NOT A) AND (B NAND C) = Ā · (B·C)'.

Step 3: NAND behavior.
(B·C)' = 0 only when both B = 1 and C = 1; otherwise it equals 1.

Step 4: AND condition for Y=0.
Y = 0 whenever Ā = 0 (i.e., A = 1) or (B·C)' = 0 (i.e., B=1, C=1).

Step 5: Truth table enumeration.
Evaluating all eight input combinations shows Y = 0 for five cases: (A,B,C) = (1,0,0), (1,0,1), (1,1,0), (1,1,1), and (0,1,1). Y = 1 for the remaining three cases: (0,0,0), (0,0,1), and (0,1,0).

Step 6: Final conclusion.
Multiple input combinations yield Y = 0, not only A=0, B=0, C=0. The output follows the derived Boolean logic.