question_answer

The truth table given below is for which gate?                                          [AIPMT 1998]

Input		Output
A	B	C
0	0	1
0	1	1
1	0	1
1	1	0

A)  XOR   

B)                   OR

C)  AND

D)                   NAND

Correct Answer: D

Solution :

The given truth table gives

\[0*0=1\]

\[0*1=1\]

\[1*0=1\]

\[1*1=0\]

The above data represents the expression \[Y=\overline{A\,\,.\,\,B}\]

This expression is the Boolean expression of NAND gate.

Note:    NAND gate used as OR function

Thus     \[\overline{A\cdot B}=\overline{A}+\overline{B}\]

This is according to De Morgan’s theorem which states that complements of produces equals the sum or vice-versa.