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:
Example Please 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)
Example4 Transform (PQ)R to CNF.
Example DNF (Disjunctive Normal Form)
Example Transform proposition logic to DNF.
Four useful rules:
Example Transform PQ to DNF.
Example Map Table to DNF
Rule (2) is called Idempotent Law. Rule (3) is called Distributive Law. Rule (4) is called Demorgan Law.
Example1 LogicDesign for Full Adder.
Fig.9.4.2 Basic module for two-bit addition.
Fig.9.4.4 Logic design of X+Y
Example Gray code.
Also called Reflected Code
Two-bit Gray code:
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)