Question

For the given logic gate circuit, which of the following is the correct truth table ?

• A.
• B.
• C.
• D.

Hint:

XOR gate output is 1 only when inputs are different.

Answer 1

The Correct Option is B

Gate 1 (Top) is NAND: Output $X = \overline{nm}$.
Gate 2 (Bottom) is OR: Output $Y = n+m$.
Gate 3 (End) is AND: Output $z = X \cdot Y$.
$z = (\overline{nm})(n+m) = (\bar{n} + \bar{m})(n+m)$.
$z = \bar{n}n + \bar{n}m + \bar{m}n + \bar{m}m = 0 + \bar{n}m + n\bar{m} + 0$.
$z = \bar{n}m + n\bar{m}$. This is the XOR function.
Truth Table for XOR: 0, 1, 1, 0.