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 fi. Description of inputs: Inputs to, t, t2 show the status of paper trays. If there is no paper in any of the trays, the corresponding input (to, ti or t2) 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, f = 0} imply that tray ( 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, fi = 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 0 is selected. If tray ( is empty, the controller checks tray 1; and if both tray O 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