The K-map for a Boolean function is shown in figure. The number of essential prime implicants for this function is

Two 2' s complement numbers having sign bits x and y added and the sign bit of the result is z. Then, the occurrence of overflow is indicated by the Boolean function.

Figure shows a mod-K counter, Here K is equal to

The threshold voltage for each transistor in Fig.2.5, is 2V. For this circuit to work as an inverter, Vi must take the values