question_answer

The given combination represents the following gate

A)  OR                        

B)         XOR

C)  NAND                 

D)         NOR

Correct Answer: A

Solution :

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.