Msg 10 0 DUNFO Don't Cares Now 0.8 ms 20 ns ng 4ng 5ns 6ns 7 ns Bno Design a "Banner Number Detector that can detect the binary coded decimals (BCD) in your banner number. The circuit has 4 inputs connected to four switches: A, B, C, and D, with A being the MSB of the inputs, and D being the LSB of the inputs. The circuit has one output F connected to a LED. F should be '1' when the inputs represent one of the decimals in your banner number. For example, if your Banner number is B00120088, the output F should be '1 when the inputs are "0000"fie. Od), "0001"(10), "0010"(2d), and "1000"(8d). Fshould be 'o' when the inputs represent other decimals, and for the combinations of the inputs that are not used for BCD, the outputs are Don't Cares, Please write down your Banner number here (i.e. 8-digit number after B): B_ 00842405 AJ (a) If the above waveform is used to represent your detector, list the time periods that the output F should be high ('1') for your Banner numbers. Answer: e.g. 0-0.5ns, ... (b) Use K-map to represent the function F. Making use of the Don't Cares, simply output Fto the simplest SOP or POS format: F= A/ (c) Is the Fyou obtained hazard-free or not? If not, please make it hazard-free: (d) Synthesize the hazard-free function Fusing basic logic gates, then convert it to a NAND-only network List the number of NAND gates you used here. (d) Synthesize the hazard-free function Fusing basic logic gates then convert it to a NAND-only network List the number of NAND gates you used here.