My lecturer sometimes asks questions about functions that have a single minimal expression, I have trouble understanding what I can conclude from the fact that the expression is single. I know that a minimal expression consists of PI, but what does the fact that it is single imply about the K-map? I would be happy to receive a suggestion regarding a correct way of thinking to solve such problems. Thanks in advance!
Here are two examples of questions:
1) Given Boolean function f(x,w,y,z). It is known that f has a single SOP expression containing exactly 4 products and the total number of literals is 8. What is the best upper bound on the number of input vectors (a,b,c,d) for which f(a,b,c,d) = 0?
2) Prove or disprove: Given a K-map of a Boolean function. If after drawing all the EPIs there is at least one minterm that does not belong to any of the EPIs, then the function has more than a single minimal expression as SOP. (Of course, two expressions that can be reached from one to the other by The distributive property and associative property are not considered different)