tutorial2 - ERG2020A&B Tutorial2 23/01/2007 YU Xi...

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ERG2020A&B Tutorial2 23/01/2007 YU Xi
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Outline • Canonical form • Boolean logic Duality • Introduction to combinational circuit analysis
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Canonical Form • Two forms: Sum of Product (SoP) Product of Sum (PoS) • Conversion between SoP and PoS It can be derived based on DeMorgan Theory
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Example 1 (Eg. 4 in Tuto1) F’=A’B’C’+A’B’C+A’BC’ Æ F=(F’)’=(A’B’C’+A’B’C+A’BC’)’ (DeMorgan Law) =(A’B’C’)’(A’B’C)’(A’BC’)’ =(A+B+C)(A+B+C’)(A+B’+C’)
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Boolean logic • How to represent boolean logic True table — exhaustive way Logic expression — used widely in analysis and design • Please remember the axioms of Boolean Algebra
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• Duality property: For one logic equation, if we swap 0&1, AND&OR. The equation will still hold. Pay attention to the operator precedence X+XY=X ÅÆ XX+Y=X(?) X+XY=X ÅÆ X(X+Y)=X
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• One possible alternative to prove the logic equations — Venn diagram X Y XY
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• Example 2 (problems in DDPP) to simplify the logic expressions a) b) For (a), combing the same term together
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This note was uploaded on 05/18/2010 for the course INFORMATIO IEG 2810AB taught by Professor Professork.w.cheung during the Spring '09 term at CUHK.

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tutorial2 - ERG2020A&B Tutorial2 23/01/2007 YU Xi...

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