Non-Essential vs. Essential Prime Implicants

AB

01

0

1

1

1

00

CD

00

1

0

0

0

01

11

10

1

0

1

0

0

0

0

0

11

10

EACH of the coverings is a PRIME IMPLICANT.

BC’ , A’C’D , A’B’D

F(A,B,C,D) = BC’ + A’B’D (minimum # of PIs) 

Prime Implicant A’C’D is a NON-ESSENTIAL prime implicant because its ‘1’s are covered by other PIs . A PI is ESSENTIAL if it covers a MINTERM that cannot be covered by any other PI.

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