question_answer

Which logic gate is represented by the following combination of logic gates?  

A) OR                               

B) NAND

C) AND                

D) NOR

Correct Answer: C

Solution :

First two similar gates are NOT gates and the third one is NOR gate. The simple diagram can be shown as The output of gate \[1 =\,\,\overline{A}\] The output of gate \[2\,\,=\,\,\overline{B}\] The output of gate 3 \[Y=\overline{\overline{A}+\overline{B}}\] Use DeMorgan?s theorem \[\overline{\overline{A}+\overline{B}}\,\,=\,\,\overline{\overline{A}}\,.\,\overline{\overline{B}}\] Hence, \[Y=\overline{\overline{A}}\,.\,\overline{\overline{B}}\] \[Y=A\,.\,B\] This is the Boolean expression of AND gate.