Question

The output of following combination is same as that of}

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

Hint:

Identical logic signals combined via an OR gate result in the same logic signal: $X + X = X$.

Answer 1

The Correct Option is D

Step 1: Analyze the logic gates in the circuit. There are two NOR gates in the first stage, both receiving inputs $A$ and $B$.
Step 2: Determine the outputs of the first stage. Since both gates are NOR gates with the same inputs, their outputs $C$ and $D$ are identical. \[ C = \overline{A + B} \] \[ D = \overline{A + B} \]
Step 3: Observe the final stage. The signals $C$ and $D$ are fed into an OR gate. \[ Y = C + D \]
Step 4: Substitute the expressions for $C$ and $D$ into the output equation. \[ Y = (\overline{A + B}) + (\overline{A + B}) \]
Step 5: Using Boolean algebra identities ($X + X = X$), simplify the expression. \[ Y = \overline{A + B} \]
Step 6: Recognize that the final expression $Y = \overline{A + B}$ corresponds to the logic operation of a single NOR gate.