PNDF, SNTF and Carno maps

Содержание и основные понятия

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Alterna · Chapter 28 · page 28.3
PNDF, SNTF and Carno maps
Perfect normal shapes, minimalisation, Carno cards.
NDLF
- A special NRF where every mintherm contains all the variables.
SNCF
- a special KNF with the same properties for the macsters.
Carno map
- A visual tool to minimize any of them.
GEF
PIF
EEG No. 2.15
He's got a little bit of depth.
Relationship to the previous one.
B
28.1 "DNF"
and
28.2 "CNF"
Here we built arbitrary normal shapes, perfect: the PNLF (all minterms) and the SNCF (all macsterms), plus the method of minimizing Carno cards.
01
JNDF and JNTF: Definition
NDLF
(perfect NDF)
Building on strings
F=1
Each minter contains
All
variables
Minterms
Not repeated
"Performed" = "full" = `canonical'
SNCF
(perfect KNF)
Building on strings
F=0
Every mackerel contains
All
variables
Macsterms
Not repeated
"Performed" = "full" = `canonical'
JNDF and JNSF communications:
The number of minterms + the number of maxerms = 2n (total number of rows). Knowing one shape, it is easy to restore the other: the FCN is built on a "rest" line.
02
Automated builder of the STNF/SCNF
⚙️
Enter the F values to receive the NSF and the NCFS
Enter a row of 0 and 1 (the F values in order of increasing the sets). For 3 variables, 8 characters, 4 - 16 characters.
СДНФ появится здесь
СКНФ появится здесь
03
Carno map (4 variables)
Why do you need Carno's map?
The NSF can be very long, dozens of minterms.
Minimize
The result is a compact formula without unnecessary input.
How to use the map — 3 Steps:
Blade by Cell
- it changes between 0 and 1. Units are the lines where F is equal to 1 (minterm).
Press "Minimize"
The algorithm will find the maximum rectangular groups of units. Each group will be illuminated in its own color.
Read the result
The bigger the group, the shorter the heat.
Cell = 0
Not selected. The function is 0 on this set of variables.
Cell = 1
The function is one of the mintherms of the NSF.
Group frame
Unit consolidation. Each group . . one conct as a result.
Group Size
Removes variables
In the term
Example of term
1
0
4
A∧B∧C∧D
2
1
3
A∧B∧C
4
2
2
A∧B
8
3
1
A
16
4
0
1 (always true)
Group rules (required to know for the EGE):
Group — Only
rectangle
(with "slips" being taken into account)
Size - Only
D-2 level
: 1, 2, 4, 8, 16
Groups may
overlap
(one cell in several groups is normal)
The ends of the columns/rows are considered
neighbouring countries
(Close card)
We must strive for
minimum number of maximum
groups
🗺
Carno interactive map 4×4
👆
Screw the cells.
Then press "Minimize".
Units:
0
of 16
|
Minterm NPF:
0
Line:
AB
Columns:
CD
(00→01→11→10)
Examples:
Введи 1 в ячейки, нажми «Минимизировать».
Why are the lines 00\01\11\10 rather than 00\1\10\11?
It's
grey code (Grey code)
III. Main characteristic: neighbouring lines/tables differ
1 bit exactly.
This means that visually adjacent cells give "spilling" mortars — a variable that changes — are excluded from the heat.
🎯
Mini-test: 5 questions on the NRF/SCNF
XP: 0
🧩
Test on the theme of the NWFS/SCNF
Five questions, 20 XP for every correct answer.