Question: A multiplexor is a control circuit with 2n input lines (numbered 0 through 2n - 1), n selector lines, and exactly one output line. The signal on the output line is to match the signal on one of the input lines; the selector lines determine which of the input line signals will be propagated to the output line. Signals on the n selector lines determine an n-bit binary number, which can range in value from 0 to 2n - 1; hence the numeric value on the selector lines identifies exactly one input line. The arithmetic-logic unit of a computer processor contains circuits for various operations (addition, subtraction, comparison, and so forth), and when an arithmetic or comparison operation is to be done, the ALU may activate all these circuit. A multiplexor then picks out the one desired result.
a. Write a truth function for a multiplexor where n = 1; that is, there are 2 input lines, 1 selector line and, of course, one output line.
b. Draw the logic network (as simple as possible).