question_answer

                Following diagram performs the logic function of:                                                                            

A)                 OR gate                               

B)                 AND gate                            

C)                 XOR gate            

D)                 NAND gate

Correct Answer: B

Solution :

                For our convenience, the output of first NAND gate is chosen as X as shown                                 Output of first NAND gate,                 \[X=\overline{A\,.\,B}\]                 So,          \[X=\bar{A}+\bar{B}\]                 Now, output of 2nd NAND gate,                 \[Y=\bar{X}\,=\overline{\bar{A}+\bar{B}}\]                 Again,   \[\overline{\bar{A}+\bar{B}}=\bar{\bar{A}}+\bar{\bar{B}}=A.\,B\,(\because \,\,\bar{\bar{A}}=\bar{A})\]                 Hence,  Y = A.B                 This is the logic function of AND gate.