A prime number is defined as a natural number which is greater than 1 that has no positive divisors other than one and the number itself.

1. A prime number is defined as a natural number which is greater than 1 that has no positive divisors other than one and the number itself. You are to design a digital circuit that takes a 4-bit binary number corresponding to a natural number as an input and produces a one bit output which is 1 if the number is prime and 0 if not.
2. (a) Build the truth table of this circuit 

2.Synthesize the logic diagrams for the following Boolean expressions:

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(a) f(w,x,y,z)=w·(x·y)' +y' ·z

(b) g(w,x,y,z)=(w+x+y)·z' +(w' +z)·y'