The simplified block diagram of a $$10$$-bit $$A/D$$ converter of dual slope integrator type is shown in Fig. The $$10$$-bit counter at the output is clocked by a $$1$$ $$MHz$$ clock. Assuming negligible timing overhead for the control logic, the maximum frequency of the analog signal that can be converted using this $$A/D$$ converter is approximately. Input sample to be converter

The following program is written for an $$8085$$ microprocessor to add two bytes located at memory addresses $$1FFE$$ and $$1FFF$$
$$\eqalign{ & LXI\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,H,\,\,\,1FFE \cr & MOV\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,B,\,\,\,M \cr & INR\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,L \cr & MOV\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,A,\,\,\,M \cr & ADD\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,B \cr & INR\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,L \cr & MOV\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,M,\,\,\,A \cr & XRA\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,A \cr} $$

On completion of the execution of the program, the result of additional is found.

The Boolean expression $$X\overline Y Z + XYZ + \overline X Y\overline Z + \overline X \overline Y Z + XY\overline Z $$ can be simplified to

Figure shows a $$4$$ to $$1$$ $$MUX$$ to be used to implement the sum $$S$$ of a $$1$$-bit full adder with input bits $$P$$ and $$Q$$ and the carry input $${C_{in}}.$$ Which of the following combinations of inputs to $${{\rm I}_0},\,\,{{\rm I}_1},\,\,{{\rm I}_2}$$ and $$\,\,{{\rm I}_3}$$ of the $$MUX$$ will realize the sum $$S$$?