A logic circuit has three input bits: $x_0$, $x_1$, and $x_2$, where $x_0$ is the least significant bit and $x_2$ is the most significant bit. The output from the circuit is $1$ when its input is any of the $3-bit$ numbers $1$, $4$, $5$, or $6$; otherwise, it is $0$. Which of the following expressions represents the output from this circuit?
Here $\sim x$ means Inverse of $x$ .
- $\sim x_2 +\sim x_1 + \sim x_0$
- $\sim x_2x_0 + \sim x_2 +\sim x_1$
- $x_2+ \sim x_1x_0$
- $\sim x_1x_0+x_2 \sim x_0$