Algebra logic: advanced course

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Alterna · Chapter 18 · page 18.0
Algebra logic: advanced course
From laws to schemes, from tables to NSFS, from simplification to EGE.
Chapter 18
If you've studied in chapter 15,
Framework
(what is a saying, how do , ,, B), here we move on to
instruments
:: How to simplify complex formulas, how to construct formulas and how to read truth tables and turn them into NWFS.
GEF · 10 grade
PLF · Infred
EEG No. 2.15
Why is this chapter important
EEG No. 2 needs
Simplify formulas
- Applying the laws of de Morgan, absorption, binding.
build diagrams
Both tasks are done systematically if you know all nine laws and you can build the NWFS.
Relationship to Chapter 17 (Graphs)
The logic is
Focus box
The top of chapter 17 was shown by DAG: vertices + pointed ribs. Here we use the same structure, but ribs are wires, and vertebrates are valves.
Mathematics
to work with the same connections.
01
What you already know (Chapter 15)
∧ ∨ ¬
Basic operations and, or, not, tables of truth.
→ ↔ ⊕
Implicit, equivalent, excluding or.
De Morgan.
B(A-B) = B-A and B-B = BA.
If any of this is not familiar, start with
Chapter 15
And then come back here.
02
What's new in this chapter
18.1 Simplifier of formulas
9 laws +
Step-by-step animation
The task generator: a huge formula of 30 seconds response.
18.2 NPF and Carno maps
According to the truth table, the formula is: Visualization: why the minterms, not something else.
18.3 - Logical diagrams
Simulator: Schematic formula. SVG ventile, signal trace.
18.4 - EGE No. 2
The bank has 50 tasks, an interactive table to find an answer.
18.5 - EEG No. 15
Interactive trainer: diagram ~ formula ~ simplification.
03
Key idea: diagram = graph = formula
The logic is
acyclic box (DAG)
The entrances are the origin of the graph, and the exit is the flow of the count. Each valve is the top with the incoming wires.
A
B
AND
NOT
OR
F
Entrys
Valves
Withdrawal
Schematic: F = (A~B) (B) is a right-to-left row
Why It Matters
From Chapter 17, you know that DAG can go around in a topological order, count the number of tracks, and here the same ideas are -- but instead of counting the tracks, we're going to
calculate the value of the formula
For every set of entrances.
04
Head navigation
18.1
Simplifying formulas
Nine laws, step-by-step animation, task generator.
Mini test: 5 out of 50.
18.2
PNDF and Carno maps
Table: formula: Visualization of mines.
Mini test: 5 out of 50.
18.3
Logical diagrams
The sympathy scheme is the formula. SVG-ventilly.
Mini test: 5 out of 50.
18.4
EEG No. 2 - 50 Tasks
Interactive response table: OGE/EEG filters.
18.5
EGE No. 15 - Schemes
Trainer: the diagram of the formula of simplification.
The bank's 50 targets.