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Find the simplified equation (SOP Form) corresponding to the following circuit (Demorgans Theorem)

shamieh

Active member
Sep 13, 2013
539
Find the simplified equation (SOP FORM) corresponding to the following circuit (i.e. apply Demorgan's theorem to bring the negations inside the parenthesis).

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So is it saying W NAND X which means (w!x!) + YNORZ so (w!x!) + (y!z!) = wxyz?
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,797
Find the simplified equation (SOP FORM) corresponding to the following circuit (i.e. apply Demorgan's theorem to bring the negations inside the parenthesis).

View attachment 1466


So is it saying W NAND X which means (w!x!) + YNORZ so (w!x!) + (y!z!) = wxyz?
Your notation is a bit confusing to me. So let me write it as I'm used to.

You have f = (w NAND x) NOR (y NOR z).

Written in boolean form this is:
$$f = \overline{\overline{wx} + \overline{y+z}}$$
Applying De Morgan's Theorem ($\overline{p+q} = \overline p \cdot \overline q$) yields:
$$f = \overline{\overline{wx}} \cdot \overline{\overline{y+z}} = wx(y+z)$$

Perhaps you can simplify it further to SoP form?