DSF, KNF, PNDF, SNPF

Содержание и основные понятия

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Alterna chapter 28
DSF, KNF, PNDF, SNPF
Normal shapes, minterms, mackerels, Carno cards, minimization.
Any logical function shall be recorded in two standard forms:
DPF
(Continuing) and
KNF
The perfect shapes of the NSF and the SNTF are built directly on the truth table and the Carno map allows them to be minimized.
GEF
PIF
EEG No. 2.15
He's got a little bit of depth.
Relationship to the previous chapter.
B
Chapter 27 "Measurement of information"
We have studied the alphabetical approach, the entropy of Shannon, and the Hartley formula, and here we turn to logic: by the truth table, we build
normal forms
- NDF, KNF, SNDF, SNCF - and minimize the function with Carno maps.
Chapter 29, "Algebra logic"
and all programming.
01
NDLF
NDLF
(perfect dissunctive normal shape) is the disjunction of the mintherms (line where F=1).
Minterm
- the condition of all variables (=1 ~ without denial, = 0 ~ with denial).
Example: Based on the truth table of the JNDF
A
B
C
F
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
The lines where F=1:
001, 011, 101, 111
Minterms:
¬A∧¬B∧C
,
¬A∧B∧C
,
A∧¬B∧C
,
A∧B∧C
JNDF = (BA) (BA)(B)(C) (A)B (C)
Each one in F gives one minterm: the variable without V if equals 1, with B if equal to 0.
02
SNCF
SNCF
- Macsterm conditions (line where F=0).
Macsterm.
- dissucation of all variables (=0 ~ without denial, =1 ~ with denial).
Example: From the truth table ♪ SNCF
A
B
C
F
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
The lines where F=0:
000, 010, 100, 110
Macsterms:
A∨B∨C
,
A∨¬B∨C
,
¬A∨B∨C
,
¬A∨¬B∨C
SNCF = (A)B (C) ♪ (A~B~C) Original: ENGLISH
Each 0 in F gives the same model: the variable with B if equals 1, without V if equal to 0.
03
Carno Map: Minimization
🗺
Carno map (4 variables, 4×4)
The clicks on the cells (F=1) will find groups 2, 4, 8 cells and select them in color.
Введи 1 в ячейки, нажми «Минимизировать».
How it works:
The map uses a gray code -- the adjacent cells are different in 1 bits. Groups 2, 4, 8 cells give the thermoms with 3, 2, 1 literal. The greedy algorithm first looks for groups of 8, then 4 and then 2 each.
🎯
Mini-test: 5 questions
XP: 0
🧩
Quick test on the subject
Five questions, 20 XP for every correct answer.