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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?

ChrizZz
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    I think you are missing parenthesis in the second expression, it should be $(\tilde a + \tilde b + \tilde d)*c$ – Quimey Jul 19 '13 at 12:46
  • you are right, that's what the tool does. But why the parenthesis? Is there a special rule saying so? in usual algebra 1+2+34 = 1+2+(34). – ChrizZz Jul 19 '13 at 12:55
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    Right, if $1+2+34=1+2+(34)$, then you've misapplied DeMorgan's law, which really is best to only apply to expressions that are well-parenthesized to make sure this sort of thing doesn't happen. – Thomas Andrews Jul 19 '13 at 12:58
  • If you enter into that software ~(abc+d) you get (~a+~b+~c) * (~d). So it seems to think adjacency $ab$ has precendence over $+$, but $*$ and $+$ are evaluated left-to-right. – Thomas Andrews Jul 19 '13 at 13:32

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

Tunococ
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  • so is the software solution incorrect? – ChrizZz Jul 19 '13 at 12:59
  • The software might be assuming no order of operations, just left-right application, in which case it is correct.@ChrizZz – Thomas Andrews Jul 19 '13 at 13:02
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    Your formulas are probably incorrect. If you put proper parentheses, the software should say that the two formulas match. (Not that I can read German though...) – Tunococ Jul 19 '13 at 13:03
  • All right i think i get it! in the first part ("whole-term-negation") i should have set the parentheses before i converted with LeMogan. – ChrizZz Jul 19 '13 at 13:07