Answer part (a) amd (b)

5) (A Digital Design Example - 15 points) You are asked to design a controller for a printer as follows. This controller has 4 inputs, to, ti, t2, corresponding to 3 paper trays, and input j signaling a paper jam. The circuit has 3 outputs: E for error, fo, and f1. Description of inputs: Inputs toti, t2 show the status of paper trays. If there is no paper in any of the trays, the corresponding input (to, t or tz) goes low (logical 0), indicating that there is no paper in the particular tray. Otherwise, ti = 1. If paper gets jammed in the printer, input j is asserted high (j = 1), indicating a paper jam. Description of outputs: Signal E should be set to high if a paper jam occurs OR all trays run out of paper. Signals fo and fi imply the tray from which papers should be fetched: {fo = 0, f1 = 0} imply that tray 0 is selected; {fo = 1, f1 = 0} imply that tray 1 is chosen; and {fo = 0, f1 =1} indicates that papers will be fetched from tray 2; and finally {fo = 1, f = 1} indicate that no tray is selected. To generate fo and fi, the controller should check the following conditions: If there is a paper jam or all trays are empty, then no tray should be selected (fo = 1, and fi = 1). Trays are selected based on their priority. The lower the number, the higher the priority, i.e. to >t > t2. In other words, first, the controller checks tray 0. If it has papers, tray ( is selected. If tray 0 is empty, the controller checks tray 1; and if both tray 0 and tray 1 run out of paper, then tray 2 is checked. Your assignment: a) Derive the truth table of this 4-input 3-output Boolean function according to the above specifications. b) Subsequently, derive a simplified Boolean expression and draw the corresponding logic circuit