Special case of four variable logic function (k-maps)

[Orikon]

I need help with this problem, so far I've only been using trial and error but I'm getting nowhere, and can't think of any other way to figure this out.

Anyway, the problem is to find a four-variable logic function whose minimal sum-of-products realization is not hazard free, but for which there exists a hazard-free sum-of-products realization with fewer product terms than the complete sum.

Any help would be appreciate :)

 

[berkeman]

I asked in your other thread, but I'll ask again here too in case the threads get separated. What do you mean by the term "hazard" in the context of logic design?

 

[piercas]

Hello,

Thank you for reaching out for help with your problem. I understand that you are working on a four-variable logic function and have been using trial and error but have not been successful. I would suggest approaching this problem in a more systematic way.

First, let's define what a hazard is in the context of logic functions. A hazard occurs when there is a momentary glitch or fluctuation in the output of a logic function due to a change in one or more inputs. This can happen when there is a delay in the propagation of signals through the logic gates.

Now, to find a four-variable logic function that meets the criteria given, we need to consider the properties of a minimal sum-of-products realization and a hazard-free sum-of-products realization. A minimal sum-of-products realization is one that has the fewest possible product terms, while a hazard-free sum-of-products realization is one that does not have any hazards.

One approach to finding this special case would be to start with a minimal sum-of-products realization and then introduce a hazard by adding an extra product term. This extra product term could be strategically placed to create a hazard. Then, you can try to find a different sum-of-products realization with fewer product terms that does not have this hazard.

Another approach would be to start with a hazard-free sum-of-products realization and then try to reduce the number of product terms while still maintaining a hazard-free solution.

I suggest using a Karnaugh map to visualize and manipulate the logic function. This will help you to see the patterns and identify any potential hazards.

I hope this helps guide you in finding the solution to your problem. Remember to approach it systematically and consider the properties of both minimal and hazard-free sum-of-products realizations. Good luck!