# Simplifying circuits using boolean algebra

I am having a lot of trouble simplifying my circuit using boolean algebra. I am very new to this and any explanation would be greatly appreciated.

I have y'+z+w'x+wx' I feel like I could use DeMorgan's law and somehow omit the last 2 terms but when I run my circuit I cannot seem to get the same result. Also for clarification, can you apply deMorgan's law to only one term, such as to wx' to get y'+z+w'x+(w'+x)? Or am I going about this the wrong way?

Once again thank you so much.

• Also wondering if you can apply the absorption laws to product terms in any way, such as w'x'y+wx'y -> x'(w'y+wy) -> x'(y) or would that be logically equivalent to 0? – Danger Cat May 26 '14 at 3:33
• You can "simplify" this to $y' + z + (w \oplus x)$, but since these three terms are disjoint, you can simplify it further. The term $w \oplus x$ cannot be written as a single product either. So it seems your expression is already "optimal". – Yuval Filmus May 26 '14 at 4:38