Please show step by step, complete solution and explain if possible. Thank you so much.

3. Six-Sided Die Display Circuit In this problem, you will design a logic circuit to display the six faces of a die using 7 LEDs. For example, the value 5 is shown on the display below. Your circuit takes three bits XYZ as input and outputs the patterns shown in the table below, by lighting up the correspondind LEDs. For example, for the value 5, the input is XYZ-101 and the output is ABCDEFG-1011101 Value input XYZ Output Patern Design the logic circuit following the steps below. Note that it is possible to simplify the Boolean expressions if we assume that we do not care about the behavior for invalid input cases. 1 Write the complete truth table for input variables X, Y and Z to output variables A, B, C. D, E. F and G. Remember that for 3 input variables, the truth table must have 8 rows. 2 Draw K-Maps for all 7 output variables. a Use the above K-Maps to write minimal SOP expressions for the output variables. Show your work. 4 Using only two 2-input logic gates in total, draw the the SOP complete logic circuit diagram based on equations for your system, with inputs X, Y and Z entering on the left side, and outputs A, B, C, D, E, F and G on the right side. Assume complemented inputs are not available s. Redraw your logic circuit diagram using 2-input NAND gates only. Just like before, assume complemented inputs are not available. 6 How many 7400 TTL chips do you need to implement this circuit on a protoboard? See Lab 3 Draw the output patterns that will be displayed if the invalid inputs XYZ-000 and XYZ-111 are entered into your logic circuit