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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Normal Formsand Logic Design
9.2PNF and CNF Normal Forms
9.3DNF Normal Form and Boolean Function
PNF:Prenix Normal Form
CNF:Conjunction Normal Form
DNF:Disjunctive Normal Form
(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:
ExamplePlease transform x y ((z (P(x, z) Q(y, z))r R(x, y, r)) to PNF.
It can be transformed to
Example CNF(Conjunction Normal Form)
Example4Transform (PQ)R to CNF.
Example DNF (Disjunctive Normal Form)
ExampleTransform proposition logic to DNF.
Four useful rules:
Example Transform PQ to DNF.
ExampleMap Table to DNF
Rule (2) is called Idempotent Law. Rule (3) is called Distributive Law. Rule (4) is called Demorgan Law.
Three Main Logic Gates
Example1LogicDesign for Full Adder.
Fig.9.4.2 Basic module for two-bit addition.
Two-bit adder module
Fig.9.4.4 Logic design of X+Y
Also called Reflected Code
Two-bit Gray code:
Three-bit Gray code:
0U and 1L:
0 0 0
0 0 1
0 1 1
0 1 0
1 1 0
1 1 1
1 0 1
1 0 0
ExampleInteger to Gray code.
b=(01)2, we have g=(g1g0)=(01)