Boolean Algebra simplify minterms

Question

I need to simplify this minterns equation with theorems and I'm really stucked (like stucked for real something like 3 hours),

F = A' B' C' D' + A' B' C D' + A' B C D' + A B' C' D' + A B' C D + A B C' D + A B C D' + A B C D

Thanks for helping me, good evening.

Answer 1

HINT

Here are some principles that will help you simplify:

Adjacency

$PQ+PQ'=P$

(for example, in your case you can combine the first two terms into $A'B'D'$ and the last two terms into $ABC$)

Absorption

$P + PQ=P$ (The $P$ term 'absorbs the $PQ$ term)

Reduction

$P+P'Q=P+Q$ (given $P$, the $P'Q$ term 'reduces' to $Q$)

Distribution

$P(Q+R) = PQ+PR$

Consensus

$PQR+PQ'=PR+PQ$$

Note that Consensus is a combination of Reduction and Distribution:

$PQR+PQ'=P(QR+Q') = P(R+Q')=PR+PQ'$

but it's useful to be able to do this in 1 step.

(for example, after you have combined the first two terms to $A'B'D'$, you can do Consensus with the third term to reduce the third term to $A'CD'$, and also use $A'B'D'$ to do Consensus with the fourth term to reduce that fourth term to $B'C'D'$. Likewise, after you have combined the last two terms to $ABC$, you can apply Consensus to reduce the fifth term to $ACD$ and the sixth term to $ABD$)