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# Chapter 9 - PowerPoint PPT Presentation

Chapter 9. Normal Forms and Logic Design. 9.2 PNF and CNF Normal Forms 9.3 DNF Normal Form and Boolean Function 9.4 Logic Design PNF:Prenix Normal Form CNF:Conjunction Normal Form DNF:Disjunctive Normal Form. 9.2 PNF and CNF Normal Forms. Example PNF

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### Chapter 9

Normal Formsand Logic Design

9.2PNF and CNF Normal Forms

9.3DNF Normal Form and Boolean Function

9.4Logic Design

PNF:Prenix Normal Form

CNF:Conjunction Normal Form

DNF:Disjunctive Normal Form

9.2 PNF and CNF Normal Forms

Example PNF

(1) x in P(x) and x in Q(x) are in different domains, i.e.

two x’s are different local variable

transform it to the following PNF:

Example Please transform x y ((z (P(x, z) Q(y, z))r R(x, y, r)) to PNF.

Ans.

It can be transformed to

Example CNF(Conjunction Normal Form)

Ans.

ci:clause

pij:literal

e. g.

Example4 Transform (PQ)R to CNF.

Ans.

9.3DNF Normal Form and Boolean Function

Example DNF (Disjunctive Normal Form)

Ans.

e. g.

Example Transform proposition logic to DNF.

Ans.

Four useful rules:

Example Transform PQ to DNF.

Example Map Table to DNF

Ans.

Rule (2) is called Idempotent Law. Rule (3) is called Distributive Law. Rule (4) is called Demorgan Law.

9.4 Logic Design

Ans.

represents carry.

Fig.9.4.2 Basic module for two-bit addition.

Extension:

Fig.9.4.4 Logic design of X+Y

Example Gray code.

Ans.

Also called Reflected Code

Two-bit Gray code:

0 0

0 1

1 1

1 0

Mirror

0 0

0 1

1 1

1 0

U

1 0

1 1

0 1

0 0

L

0 0 0

0 0 1

0 1 1

0 1 0

1 1 0

1 1 1

1 0 1

1 0 0

0U

1L

ExampleInteger to Gray code.

e.g.

b=(01)2, we have g=(g1g0)=(01)