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. $(5$ points$)$

b$)$ Redraw the circuit using only NAND and NOR gates. $(2$ points$)$

c$)$ Assuming AND, OR and NOT gates have $6ns,4ns$ and $2ns$ 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. $(3$ points$)$

d$)$ Assuming that NAND and NOR gates have $5ns$ second delay then what are the

delays for your answers to part b$.(2$ points$)$

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$.(12$ points$)$