A multiplexer is a combinational circuit that selects binary information from one of many input lines and directs the information to a single output line. The selection of the input line is controlled by a set of input variables.

a.) Determine the maximum number of input signals that a multiplexer can accommodate. Justify your answer by mathematical means and clearly identify all variables used

b.) Construct an 8-input multiplexer (with proper labeling) with the most economical design by using 2-input multiplexers as its basic building block.