A device accepts natural binary numbers in the range 0000 to 1111 that represent 0 to 15. The output of the circuit is True if the input to the circuit represents a prime and odd number. Cant occur (dont care) if the input to the circuit represents a prime and even number. False otherwise. A prime number is an integer that is greater than 1 and is divisible only by itself and 1. Zero and one are not prime numbers.

a) Draw a truth table to represent the problem and use it to construct a Karnaugh map.

b) Use the Karnaugh map to obtain a simplified expression for the function.

c) Construct a circuit to implement the function using AND, OR and NOT gates.

d) Construct a circuit to implement the function using NAND gates only.

e) Construct a circuit to implement the function using NOR gates only.