Design a circuit whose output is true if its four-bit decimal input is really a prime number – not including “1” – that is, the output is true if the input is 2, 3, 5 or 7. The output is an X (don’t care) for input combinations 10–15. 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.