T A logic circuit with m binary inputs and n binary outputs is shown in figure 2.9. It is described by a function F: X ? Y where X = Binm and Y = Binn. (In a circuit, the signal values 1 and 0 in Bin...

T A logic circuit with m binary inputs and n binary outputs is shown in figure 2.9. It is described by a function F: X ? Y where X = Binm and Y = Binn. (In a circuit, the signal values 1 and 0 in Bin correspond to voltage High and Low, respectively.) How many such distinct logic functions F are there? T The following system S takes a discrete-time signal x ? X and transforms it into a discretetime signal y ? Y whose value at index n is the average of the previous 4 values of x. Such a system is called a moving average. Suppose that X = Y = [Nats ? Reals], where Nats is the set of natural numbers. More precisely, the system is described by the function S such that for any x ? X, y = S(x) is given by y(n) = [x(1) + ··· + x(n)]/4 for 1 = n