The three counters are used for building the minute and the

Solution

Yes these counters are in cascade,because it follows the properties of Cascade combination as below.

Timer programs also have type Sig In view of cascading timers, it does notsuce to express behavior as the output signal with the program as the onlyinput parameter. Doing so would only model a single timer plugged into an outlet(without power failures), i.e., an uninteresting autonomous system. Rather, wemodel behaviors as input-output system functions.

The usual notion of piecewise continuity over a closed interval is assumed gen-eralized to possibly innite intervals: a function is piecewise continuous (p.c.)over an interval i in every nite closed subinterval it has at most a nite num-ber of discontinuities, and left and right limits exist at each discontinuity (plusright limit at the start and left limit at the end of each of the subintervals). If the interval of interest is not stated explicitly, it is taken to be the domain of the function. For the predicates at hand, p.c. amounts to piecewise constant.Calculational reasoning about limits and derivatives using functional predicate in calculus.