The output $(\mathrm{Y})$ of the given logic implementation is similar to the output of an/a _____ gate.

• A

  AND
• B

  NAND
• C

  OR
• Correct answer
  D

  NOR

Solution

$\mathrm{Y}=(\overline{\mathrm{A}+\mathrm{B}}) \cdot(\overline{\mathrm{A} \cdot \mathrm{B}})$ $\begin{aligned} & \Rightarrow \overline{\mathrm{A}} \cdot \overline{\mathrm{B}} \cdot(\overline{\mathrm{A}}+\overline{\mathrm{B}}) \\ & \Rightarrow \overline{\mathrm{A}} \cdot \overline{\mathrm{B}} \cdot \overline{\mathrm{A}}+\overline{\mathrm{A}} \cdot \overline{\mathrm{B}} \cdot \overline{\mathrm{B}} \\ & \Rightarrow \overline{\mathrm{A}} \cdot \overline{\mathrm{B}}+\overline{\mathrm{A}} \cdot \overline{\mathrm{B}} \\ & \Rightarrow \overline{\mathrm{A}} \cdot \overline{\mathrm{B}}=(\overline{\mathrm{A}+\mathrm{B}})\end{aligned}$ Behaves as NOR gate

Hence, the correct answer is option: 'D'.