boolean algebra: DeMorgan's law confusion

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the following function should be put into table values: $$y = \overline{(a*b*d+c)}$$ So the first thing i am doing is using DeMorgan to get rid of the "whole-term-negation": $$y = (\tilde a + \tilde b +\tilde d * \tilde c)$$

from here all i do is making a 4 variables truth table (4 columns, 16 rows) and set a "1" if the row equals the term.

However, i used an online tool (http://www.elektroniker-bu.de/kvdiagramm.htm) to check my solution and depending on the term i am using {~(a*b*d+c); (~a+~b+~d*~c)}, i get different results. Am i using De Morgan wrong?

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There could be a problem with precedence. For example, assuming $*$ is done before $+$. Then the correct application of De Morgan's law is $$ y = \overline{(a*b*d) + c} = \overline{(a*b*d)} * \overline c = (\overline a + \overline b + \overline d) * \overline c. $$ This does not match $$ (\overline a + \overline b + \overline d * \overline c) = \overline a + \overline b + (\overline d * \overline c). $$