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Discussion_1 - CSE 140 DISCUSSION # 1 (9/29/2010) Swathi...

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CSE 140 DISCUSSION # 1 (9/29/2010) Swathi Karunamurthy
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Canonical Form Representation
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Canonical Form Representation Sum-of-products (SOP) form Y = A’B’C’+A’BC’+AB’C’+AB’C+ABC = Σ m(0,2,4,5,7) Product-of-sums (POS) form Y = (A+B+C’)(A+B’+C’)(A’+B’+C) = Π M(1,3,6) SOP and POS Relationship Σ m(0,2,4,5,7) = Π M(1,3,6) = ( Σm(1,3,6))’ = (ΠM(0,2,4,5,7))’
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Boolean Algebra - Simplification 1. Y = A’B’C’+A’BC’+AB’C’+AB’C+ABC = (A’B’C’+A’BC’)+(A’B’C’+AB’C’)+(AB’C+ABC) ( associativity and idempotency) = A’C’(B’+B) + B’C’(A’+A)+AC(B’+B) ( distributivity) = A’C’ 1 + B’C’ 1 + AC 1 ( Complement) = A’C’ + B’C’ + AC (Identity ) 2. Y = (A+B+C’)(A+B’+C’)(A’+B’+C) = ((A+C’)+BB’) (A’+B’+C) ( distributivity) = ((A+C’)+0) (A’+B’+C) (Complement) = (A+C’) (A’+B’+C) (Identity)
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Boolean Algebra - Simplification 3. Y = BC+A’B’C’+BC’ = BC+BC’ +A’B’C’ ( commutativity + associativity)
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Discussion_1 - CSE 140 DISCUSSION # 1 (9/29/2010) Swathi...

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