Question

The given circuit consists of five logic gates. If the inputs are \(A=0\), \(B=1\), \(C=1\) and \(D=0\), then the outputs \((y_1,y_2)\) are respectively

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

Hint:

Remember: \[ \text{NAND}=(AB)', \] \[ \text{NOR}=(A+B)', \] \[ \text{OR}=A+B. \] Evaluate the outputs gate-by-gate from left to right.

Answer 1

The Correct Option is A

Concept: Evaluate logic gate outputs step by step with given inputs \(A=0,B=1,C=1,D=0\).

Step 1: Top NAND: inputs A,B \(\Rightarrow X = (0\cdot1)' = 1\). Middle NOR: inputs B,C \(\Rightarrow Y = (1+1)' = 0\). Bottom OR: inputs C,D \(\Rightarrow Z = 1+0 = 1\). Upper OR: \(y_1 = X+Y = 1+0 = 1\). Lower NAND: \(y_2 = (Y\cdot Z)' = (0\cdot1)' = 1\).

Step 2: Write the final answer. \(\boxed{(y_1,y_2)=(1,1)}\)