(20 points) A system has three input buttons labeled 1, 2, and 3. The buttons can be pressed individually, or multiple buttons can be pressed at once. In this problem, you will design a digital circuit that outputs the number of the highest button pressed as a 2-bit binary number. For example, if buttons 1 and 3 are pressed, then the circuit should output 11, meaning that button 3 (binary 11) is the highest button pressed. a. Draw a truth table for the behavior or the circuit b. Derive equations for the circuit outputs in sum-of-products form c. Minimize the logic for the outputs using Karnaugh maps d. Draw a logic-level (not CMOS transistor) schematic for the circuit