A Digital Logic Problem

A Logic Problem (3.4)

Your favorite professor, the ever-ebullient Dr. Abner Mallity, is working on a little consulting project. As usual he is going to stiff one of his graduate students, Willy Nilly and Millie Farad, and get one of them to do the project for him. They could use some help. They are also working hard to finish a term project. Here's the story.

You need to do a design for the logic circuit that adds ingredients to an ice cream sundae. Mallity's client - the NutCase Sundae Company - wants to develop a product that makes sundaes automatically. They plan to add ingredients chosen from the following list. The list has 16 different ingredients

1. Avocado Slush
2. Bannanas
3. Chocolate Syrup
4. Dacamania Nuts (Newly discovered in the Fiji Islands, and not related to macadamia nuts)
5. Something starting with the letter "E", but the only thing they've thought of so far is Eggplant.

Here is the truth table for the Avacodo Slush used for different sundaes. The sundaes are numbered from 0 to 15 (in binary numbers) in the truth tables. They plan to come up with some interesting names later, and will get rid of the numbers ASAP.

Sundae #	W	X	Y	Z	A
0	0	0	0	0	0
1	0	0	0	1	0
2	0	0	1	0	0
3	0	0	1	1	1
4	0	1	0	0	1
5	0	1	0	1	1
6	0	1	1	0	1
7	0	1	1	1	0
8	1	0	0	0	1
9	1	0	0	1	0
10	1	0	1	0	1
11	1	0	1	1	0
12	1	1	0	0	1
13	1	1	0	1	0
14	1	1	1	0	1
15	1	1	1	1	1

Here is what you need to do.

Determine the Karnaugh map for the Avocado Slush function (A).

From the Karnaugh map determine the smallest sum-of-products form for the Avocado Slush function.
Show an AND-OR-NOT implementation for the circuit.