Units for measuring information

Содержание и основные понятия

Back to the table of contents
Alterna · Chapter 9 · page 9.2
Units for measuring information
How do you measure information? From bat to petabyte: dual system, Hartley formula, interactive tasks.
Find out how much information is placed on your phone and why it's 1KB = 1,024 bytes, not 1,000.
GEF
PIF
OGE No. 3.4
EEG No. 4
01
Bit — Minimum Unit
Binary Digit is the smallest unit of information: 0 or 1
Definition
Beat
- minimum unit of measurement of information. Only two states may be taken:
0
or
1
The name comes from
binary digit
- a binary number.
Byte
- 8 bits = 256 possible combinations. That's how much it takes to encode one text symbol (a Latin, numbers, specials in ASCII).
Physical Meaning
In the electronics, bits are the presence or absence of an electrical pulse. HIGH (1) is the voltage, LOW (0) is the no voltage. This is how the processor sees all the data: text, photo, video.
⚡
Pulse diagram: 8 bits
8 bits = 1 byte
One byte is 8 bits in a row.
8
=
256
Each combination corresponds to its character in the coding table (ASCII, KOI8-R, etc.).
Why 1 KB = 1,024 bytes?
The computer works in a binary system.
10
= 1024 E 1000. Therefore, 1024 is used instead of "kilo" (1000).
Unit
Meaning
Degree 2
1 bit
0 or 1
—
1 byte
8 bits
2
3
1 KB
1 024 B
2
10
1 MB
1 048 576 B
2
20
1 GB
1 073 741 824 B
2
30
1 TB
2
40
B
2
40
1 BOP
2
50
B
2
50
1 EB
2
60
B
2
60
02
Hartley's formula
Number of information in the N message of equally likely events
Formula
I = log₂(n)
I is the amount of information in bits, n is the number of equals.
What's a logarithm?
log2(n) is the answer to the question:
To what extent should 2 be raised to obtain n?
Examples: log2(2) = 1, log2(4) = 2, log2(8) = 3, log2(16) = 4, log2 (1024) = 10
📐
Interactive logarithm
Logarithm -
uneven
The larger n values give us a smaller result. Try the different bases.
Basis
n =
8
log₂(8) = 3
n=2
Monet (head/resh)
I = 1 bit
n=4
4 cards (ace, king, lady, waltz)
I = 2 bits
n=8
Cube (two throws)
I = 3 bits
03
Additivity of Information Act
Information from several independent sources is collected
Formula
I
General
= I₁ + I₂ + … + Iₖ
If we get information from several
independent bodies
The total amount of information is equal to the sum of the information from each source.
Example
In deck 32 cards (I1 = log232 = 5 bits). Drop the coin (I2 = log22 = 1 bit). General information: I = 5 + 1 =
6 bits
.
When does it work?
Only when events
independent
If the sources are connected (e.g. the letter "I" always after "T" in the word "T", the formula gives an overvalue, then Shannon's approach is needed (Chapter 10.3).
04
IEC standards: BC vs KiB
Why the 64GB flash drive shows 59.6 GB in Windows
Two Worlds of Units
There are two measurement standards for information:
SI / GOST (tenth)
Used by CD manufacturers and in telecommunications.
Unit
Meaning
1 KB (kilobyte)
103 = 1000 B
1 MB (megabyte)
106 = 1 000 000 B
1 GB (gigabyte)
109 = 1 000 000 000 B
IEC 60027-2 (Double)
It is used in operating systems (Windows, Linux) and for OSPs.
Unit
Meaning
1 KiB (kibybybyte)
210 = 1,024 B
1 MIB (webbyte)
220 = 1,048 576 B
1 GiB (bibyte)
230 = 1,073 741 824 B
⚖
Marketing Officer vs Programmer
The manufacturer declared the volume in the GB (ten times). Windows shows in the GiB (two times). Select the size of the flash drive and make sure that no cheating is just different units.
Push the flash drive (GBG GOST)
05
Comparison of values
A graphic comparison of the volume of real data
⚖
Compare Two Volumes
Select two objects and compare their volume.
06
Mini test
Five random questions from Bank 40.
0 / 500 XP
0 / 5
Press "Start Quest" for starters.