Build a circuit that takes a $3-$bit number x$2$x$1$x$0$ as an input, and provides one output indicating whether the number of bits equal to $1$ in the input is even $(0)$ or odd $(1).$ For example, if the input is $110,$ there are $2$ bits set to $1$; since $2$ is an even number, the output should be $0.$ If the input is $111,$ there are $3$ bits set to $1$; since $3$ is an odd number, the output should be $1.$