Question

An AND gate, an OR and a NAND gate are connected as shown in the figure. If the inputs are \(A=0\), \(B=1\) and \(C=0\), then the outputs \(y_{1}\), \(y_{2}\), \(y_{3}\) are respectively

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

Hint:

For logic-gate questions, always evaluate gates from left to right. Compute intermediate outputs first and then use them as inputs for the final gate.

Answer 1

The Correct Option is C

Concept: To solve logic gate problems, evaluate the output of each gate one by one.
• AND gate output = 1 only when all inputs are 1.
• NAND gate output = Complement of AND gate output.
• OR gate output = 1 when at least one input is 1. The output of one gate may become the input of another gate. Therefore, we proceed systematically.

Step 1: Find the output \(y_1\) of the AND gate.
The upper gate is an AND gate receiving inputs: \[ A=0,\qquad B=1 \] Therefore, \[ y_1=A\cdot B \] \[ y_1=0\times1=0 \] Hence, \[ \boxed{y_1=0} \]

Step 2: Find the output \(y_2\) of the NAND gate.
The lower gate is a NAND gate with inputs: \[ B=1,\qquad C=0 \] First compute the AND output: \[ 1\times0=0 \] Since NAND is the complement of AND, \[ y_2=\overline{0}=1 \] Therefore, \[ \boxed{y_2=1} \]

Step 3: Find the final output \(y_3\) of the OR gate.
The OR gate receives inputs \(y_1\) and \(y_2\): \[ y_1=0,\qquad y_2=1 \] Thus, \[ y_3=y_1+y_2 \] \[ y_3=0+1=1 \] Hence, \[ \boxed{y_3=1} \]

Step 4: Write the ordered triple of outputs.
Combining all three outputs: \[ (y_1,y_2,y_3)=(0,1,1) \] Thus the required output combination is \[ \boxed{(0,1,1)} \] Hence, the correct option is \[ \boxed{\text{(C)}} \]