Alphabet and number of words

Содержание и основные понятия

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Alterna chapter 10
Alphabet and number of words
Power of alphabet A, Hartley formula N=2
i
number of words A
n
, alphabetical and substantive approaches to measuring information are all GEF/OPFs with interactive OGE/EGE assignments.
In this chapter, you will study how to measure information through the capacity of the alphabet, learn how to count the number of possible words, learn about two approaches to measuring information, and solve dozens of problems from the OGE Bank and the EGE.
GEF
PIF
OGE No. 1-4
EEG No. 4
📐
Key formulas
Three formulas to know by heart
Hartley's formula
N = 2
i
N is the power of the alphabet, i is the weight of the symbol (bit)
Symbol Weight
i = log
2
(N)
How many bits carry one alphabet symbol
Number of words
N = A
n
A is the capacity of the alphabet, n is the length of the word
10
Chapter Pages
Five pages with theory, interactors and a bank of assignments.
10.1
Alphabet and its power
The power of alphabet A, the Hartley N formula = 2 ×i, the information weight of the symbol i=log2(A). Calculator, task bank.
GEF
OGE No. 3.4
EEG No. 4
10.2
Number of words length n
Formula A to n, rule of work. Visualization of all possible words. Tasks in combination.
GEF
OGE No. 1-4
10.3
Alphabetic and informative approaches
A comparison of two approaches, through the power of the alphabet and through probability, the Shannon formula, the entropy calculator.
GEF
EEG No. 4
10.4
Workshop
The OGE and EEG trainers, the combined trainer, the formula scavenger, the progress counter.
OGE No. 1-4
EEG No. 4
10.5
Polygon examination
Final test with timer (10 questions). Tasks of increased complexity.
OGE No. 1-7
EEG No. 4
📊
What do you study?
🔤
Capability of the alphabet
What's an alphabet, what's its power, Hartley's formula N is equal to 2xi.
📏
Information weight
How many bits carry one symbol. Formula i = log2(N).
📝
Number of words
Formula A ton, rule of work, visualization.
⚖
Two approaches
Alphabet vs informative, Shannon formula.
🎯
Examination preparation
OGE/EGE bank, timer test, error resolution.
💻
Interactives
Calculators, visuals, entropy, mini tests.
🚀
Quick Start: Examples
Example 1: Find the weight of the symbol
Objective:
Alphabet contains 64 characters. What is the information weight of one symbol?
Решение:
i = log₂(N) = log₂(64) = log₂(2⁶) =
6 бит
Example 2: Find the number of words
Objective:
The Alphabet consists of four characters. How many different words of length 3 can be made up?
Решение:
N = Aⁿ = 4³ =
64 слова
Example 3: Interpretation of text
Objective:
The text of 256 characters is written by an alphabet of 32 characters. What is the length of the text in the bits?
Решение:
i = log₂(32) = 5 бит
I = K × i = 256 × 5 =
1280 бит