Picture a typical 7-segment LED display (e.g. one digit of a typical digital alarm clock). Your task is to design combinational circuit that controls whether the bottom (LED z_7) is lit. LED z_7 is lit for numbers 0, 2, 3, 5, 6, and 8, and blank for all other inputs (including invalid inputs). 0123456789 27 A. Write the truth table for this circuit. (LED z_7 only) Think carefully about what the inputs and outputs to your truth table signify. Consider: Why are there 4 inputs in the table given below? (Hint: how many states can the LED system be in?) B. Express the truth table in Sum-of-Products form. Do not simplify the equations. D B B Y 0 D 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 Boolean expression