Detecting prime numbers:

Derive the simplified Boolean expression for the output function for a circuit with four inputs. The output should be 1 if the 4-bit value on the inputs is a prime number, and zero otherwise. Please name the inputs a, b, c, d and the output f. The input a corresponds to the most significant digit of the number on the inputs.

Show: (i) the truth table, and (ii) the simplified expression only.

No programming language is require. You can just make the truth table and simplified expression.

(Note: when typing Boolean expressions use a single quote character to indicate the complement, for example, for the minterm m0 you would type: a'b'c'd')