# ZDD to FDD Conversion

I am solving exam question 2(d) on page 8 (es.cs.uni-kl.de/teaching/vrs/exams/2021.02.17.vrs/2021.02.17.vrs.solutions.pdf)

Here it says function can be minimized to !b | a & b & c , but when I am trying to minimize the function it comes as !b | a & c.

Could you please explain how this is minimized in this solution ?

edited

+1 vote

The given function is equivalent to !b | a & b & c and as you wrote, also equivalent to !b | a & c which is a minimal DNF. Note that the text above does not state that  !b | a & c is a minimal DNF, it just says that the formula can be shrinked down (minimized/reduced) to that.

The minimal DNF is however not useful, since we want a DNF whose cubes are non-overlapping, i.e., do not share common minterms, since if we have a DNF with non-overlapping cubes, we can replace the disjunction with an exclusive disjunction as explained in the text. You cannot do the same for !b | a & c since these cubes share the minterm a&!b&c.
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Thanks for this explanation.