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

#### shamieh

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

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
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?