Can this expression $(\neg B \land \neg D) \lor (\neg A \land B \land C) \lor (A \land C \land D)$ be further simplified?

Question

I have assignment for computer architecture where I have to simplify a big boolean function:

f(a, b, c, d) = a'b'c'd + a'bcd' + abcd + a'bcd + a'b'cd' + ab'cd' + ab'c'd' + ab'cd + a'b'c'd'

Now I arrive at this point

$(\neg B \land \neg D) \lor (\neg A \land B \land C) \lor (A \land C \land D)$

but it still seems too complicated, but I am not able to simplify it further, can someone help me?

Answer 1

You can use Karnaugh maps to simplify this function. The result is:
$${A'B'C'+ AB'D' + A'BC + A'CD' + ACD}$$

Answer 2

As far as I can see no further simplification is needed.

Besides, note that your formula

$$(\neg B \land \neg D) \lor (\neg A \land B \land C) \lor (A \land C \land D)$$

is in disjunctive normal form already (this does not imply that no simplification is needed though).

Good work!