Question

The given combination represents the following gate

• A. OR
• B. XOR
• C. NAND
• D. NOR

Answer 1

Answer: (A)

The given combination can be represented as
All the gates in the combination are NAND gates. Output of gate-1, $Y_1=\overline{A\cdot A}$ Output of gate-2, $Y_2=\overline{B\cdot B}$ Output of gate-3, $Y=\overline{Y_1\cdot Y_2}$
$\therefore$ $Y=\overline{\overline{A\cdot B}\cdot \overline{B\cdot B}}$ .. (i)
By Demorgans theorem, we have
$\overline{A\cdot A}=\overline{A}$ and $\overline{B\cdot B}=\overline{B}$
Therefore, Eq. (i) becomes,
$Y=\overline{\overline{A}\cdot \overline{B}}$
Again from Demograns theorem
$\overline{\overline{A}\cdot \overline{B}}=\overline{\overline{A}}+\overline{\overline{B}}$
$\therefore$ $Y=\overline{\overline{A}}+\overline{\overline{B}}=A+B$ $(as\overline{\overline{A}}=A)$
Hence, the combination behaves as $OR$ gate.