Prime Implicants of a Non-Coherent Fault Tree

[surreystudent]

I am stuck on some non-coherent fault tree analysis. I have a non-coherent fault tree for which the TOP event breaks down to TOP = AD' + DA' + A'E. These are (I think) some of the prime implicants of the fault tree. There is also another prime implicant ED'. I've been trying to work through it with De Morgan's laws but with no luck getting that final prime implicant (ED'). I've attached an image of the fault tree. Any ideas?

 

[STEMucator]

So you have a boolean function:

$$TOP(A, D, E) = A \bar D + D \bar A + \bar A E$$

These are (I think) some of the prime implicants of the fault tree.

You would be correct. ##A \bar D, D \bar A,## and ##\bar A E## are prime implicants of the ##TOP## function because they are minimal implicants. We cannot expand the terms by removing literals because they would then become non-implicants. It is also worth noting these prime implicants cannot be covered by a more general implicant.

In fact, ##A \bar D, D \bar A,## and ##\bar A E## are the only prime implicants of the function because the function is a sum of minterms already.

What exactly are you trying to do here anyway? Are you trying to apply De-Morgan's laws to find different prime implicants?