$(25$ pts$.)$ Assume we will read two binary values x and y$($x and y can be either $\text{'}0\text{'}$ or $\text{'}1\text{'}),$ where x is the value generated by a sensor and y is the value generated by an algorithm. Our objective is to compare these two values x and y$.$ We will record the values x and y every $10$ minutes and we will use the last $3$ recorded values $($present$,10$ minutes ago and $20$ minutes ago$)$ as follows: Produce an output z$,$ which will be equal to either the x or y value recorded $20$ minutes ago. If the current and previous recorded values of x and y are equal, then z will be equal to x$,$ otherwise to y$.$ Ex$1$: If the stored x and y values are as in the following table, both the current and $10$ min. ago values are the same for x and y$,$ so z is equal to the value of x stored $20$ min. ago, that is z is $1.$ Ex$2$: If the stored x and y values are as in the second table, the current values are equal but $10$ min. ago values are not, so z is equal to the value of y stored $20$ min. ago, that is z is $0.$ Do not forget that we have a stream of x and y values, so make sure that you have a design that updates values every $10$ minutes.