Prelab Assignment a 4-bit binary code representing the decimal numbers O through 9. The binary numbers 1010 through 1111 are not used in BCD. Design a digital circuit to detect only valid BCD Codes at its inputs. a. Construct a truth tabl le containing all possible inputs and desired output. Assume that the desired b. Draw the Karnaugh map, and write the simplified Boolean expression for the valid codes as Sum of e p Draw the Karnaugh map, and write the simplified Boolean expression for the valid codes as Product output for a valid code is a 1, and for an invalid code is 0. A is the most significant bit (MSB), and D is the least significant bit (LSB). Products. c. Draw the circuit diagram of the SOP function using NOR gates only. Of Sums. Draw the circuit diagram of the POS function using NAND gates only. Is POS SOP? Prove it. 2. Consider a sliding switch that can be in one of five positions with 3 outputs x, y, z indicating the position of switch in binary. So x, y, z can take one of the values of 001, 010, 011, 100, or 101. The other values are impossible. We wish to design a combinational circuit that takes inputs x, y, z and outputs F positions 2, 3 or 4. 1 if the switch is in Slide Switch 1 2 34S 4sDetector 2, 3, 4 a. b. c. Determine the truth table for the function F. Using the Karnaugh Map, get the simplest sum-of-products form for this function Draw the simplified function final form using NAND gates