A digital system is expected to receive a number between $0$ and $15$ and decide if the number is a prime one. a$)$ Use the map method and design the system. b$)$ Redraw the circuit using only NAND and NOR gates. c$)$ Assuming AND, OR and NOT gates have $6$ns$,4$ns and $2$ns delays what is the delay of your answer to part a$?$ Assume that you have access to the input signal only in the regular form and not the inverted form. d$)$ Assuming that NAND and NOR gates have $5$ns second delay then what are the delays for your answers to part b$.$ e$)$ The system requirements have changed so it only receives numbers between $0$ and $10.$ Use don't care conditions and repeat parts a$,$ b$,$ c and d$.$