Question

To get the truth table shown from the following logic circuit, the gate G should be

• A. NAND gate.
• B. NOR gate.
• C. AND gate.
• D. OR gate.

Hint:

The output is \(Y=A+G(A,B)\) and the table shows \(Y=A\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
From the figure, input A goes straight to an OR gate, and also into gate G together with B. The OR gate then combines A with the output of G. So \(Y=A+G\).

Step 2: Key Formula or Approach
The truth table shows \(Y=0\) for \(A=0\) (for both values of B) and \(Y=1\) for \(A=1\). So \(Y=A\).

Step 3: Detailed Explanation
When \(A=0\): \(Y=0+G(0,B)\). This must be 0 for \(B=0\) and \(B=1\), so \(G(0,0)=0\) and \(G(0,1)=0\).
When \(A=1\): \(Y=1+G=1\) whatever \(G\) is.
An AND gate gives \(G(0,0)=0\) and \(G(0,1)=0\), which matches. Then \(Y=A+AB=A(1+B)=A\).

Final Answer:
Gate G is an AND gate, option (C). \[ \boxed{\text{AND (C)}} \]