# Unable to simplify this Boolean algebra equation $\overline{(AB ⊕ CD) + (D ⊕ A)(\overline{\overline A\ \overline B\ \overline C}})$

Our professor gave us this equation to simplify and after 3 hours and countless attempts I'm still stuck. I'm very new to Boolean logic so thats probably not a good indication at its difficulty :p.

Inputs: A, B, C, D Output: Y

Anyways here is the equation:

$$\overline{(AB ⊕ CD) + (D ⊕ A)(\overline{\overline A\ \overline B\ \overline C}})$$

Key:

A ⊕ B = A xor B

AB = A and B

A + B = A or B

$\overline A$ = not A

Any help would be really appreciated.

(Need to submit my assignment tomorrow, need help asap pls. I'm really stuck and came here only after trying it myself as much as I could.)

EDIT: There was a typo in the question, updated it with the correct question in both post and title.

• What have you tries? What rules do you know for simplifying these things? May 13, 2018 at 20:45
• @ThomasAndrews I've used the basic Boolean algebra laws. electronics-tutorials.ws/boolean/bool_6.html And ive tried using demorgans law to split the main complement line by changing the + to a *. I seem to keep cycling back to the same equation and it doesn't become any simpler, just more complicated. May 13, 2018 at 21:17

$$x_{1}\oplus x_{2}=x_{1}\bar{x}_{2}+\bar{x}_{1}x_{2}$$
$$\overline{\bar{x}_{1}\bar{x}_{2}}=x_{1}+x_{2}$$