Question

Use consensus theorem 2 times to simplify to only 3 product terms each of 3 variables.

            MN’P + M’NP’ + MO’P + NO’P’ + MNO’

Answer 1

Simplify the following boolean expression using the consensus theorem for 2 times:

MN’P + M’NP’ + MO’P + NO’P’ + MNO’

Answer: MN’P + M’NP’ +  MNO’

Description:

• The consensus theorem:

• Consider AB + A'C + BC expression. According to consensus theorem, BC is the consensus or the resolvent term for AB and A’C terms.

• If there is one variable in complement form with other variable repeated in other product term then that product term can be eliminated.

• Simplifying MN’P + M’NP’ + MO’P + NO’P’ + MNO’ using the consensus theorem:

⇒ MN’P + M’NP’ + MO’P + NO’P’ + MNO’

STEP 1 : Take Term 1 and Term 5  ---- eliminate ----> Term 3

( MN’P and MNO’ has (N + N') with rest MPO' ---- eliminate---->Term 3: MO’P  )

⇒ MN’P + M’NP’ + NO’P’ + MNO’

STEP 2 : Take Term 2 and Term 5 ---- eliminate ----> Term 4

( M’NP' and MNO’ has (M + M') with rest NP'O' ---- eliminate---->Term 4: NO’P’ )

⇒ MN’P + M’NP’ + MNO’ (Simplified form: 3 product terms form each with 3 variables)