Q:

boolean algebra: DeMorgan's law confusion

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?

A:

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
$$
(\overline a + \overline b + \overline d * \overline c) = \overline a + \overline b + (\overline d * \overline c).
$$

