Boolean Algebra

[cahlucas]

Hello everyone,

For a programming project I am dealing with Boolean algebra which I cannot figure out. It's about minimizing gate logic using Petricks method. For those of you who are not familiar with this, I have added a link at the bottom. The part that I can't figure out is just after the part where it says: = (K + LM) (N + LQ) (P + MQ). I cannot follow how the Bolean algebra ends up on this, given the formulas in the text. I hope that maybe someone among you is very adept at this and can explain it to me. Thanks in advance. Kind regards, Karel.

https://en.wikipedia.org/wiki/Petrick%27s_method

 

[HarryA]

from Wikipedia:

 = (K+L)(K+M)(L+N)(M+P)(N+Q)(P+Q)
 = (K+LM)(N+LQ)(P+MQ)
 = (KN+KLQ+LMN+LMQ)(P+MQ)
 = KNP + KLPQ + LMNP + LMPQ + KMNQ + KLMQ + LMNQ + LMQ

-----------------------------------------------------------------------------------------

K * N+LQ   +  LM*(N+LQ)

K * N+LQ = KN+KLQ    and LM*(N+LQ) =  LMN+LMQ

for the : (KN+KLQ+LMN+LMQ)

for the fourth line multiply the third line  by P and then by MQ from (P+MQ)

[SebastianFlood]

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