Exercises:

Design a $4$ input, $1$ output combinational circuit. The inputs represent a $4-$bit number, $N=x_3{x}_2{x}_1{x}_0,$ which ranges from $0$ to $15.$ The output, $F,$ is $1$ when $N$ represents a prime number. Otherwise, F is $0.$

a$.$ Set up a truth table for the circuit.

b$.$ Write a Boolean Equation for F$.$

c$.$ Draw a logic diagram for F using AND$-$OR$-$NOT gates.

d$.$ Reduce F using a Karnaugh Map.

e$.$ Draw a logic diagram for the reduced circuit using only NAND gates.

f$.$ Determine the "costs" $($hardware and time$)$ for F from part c and part e$.$

g$.$ Develop a Quartus version of the circuit for part e$.$ Show the waveforms in a vector waveform file and save the file.