Design a circuit whose output is true if its four-bit input is really a prime number – not including “1” – that is, the output is true if the input is 2, 3, 5, 7, 11, or 13. Go through the same steps as in Exercise 6.2. 

Data in Exercise 6.2.

Design a four-bit Fibonacci circuit. This circuit outputs a 1 iff its input is a Fibonacci number (i.e., 0, 1, 2, 3, 5, 8, or 13). Go through the following steps. 

(a) Write a truth table for the function. 

(b) Draw a Karnaugh map of the function. 

(c) Identify the prime implicants of the function. 

(d) Identify which of the prime implicants (if any) are essential. 

(e) Find a cover of the function. 

(f) Draw a CMOS gate circuit for the function.