Numeral systems: position, translation, arithmetic

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Alterna chapter 14
Numeral systems: position, translation, arithmetic
The foundation for OGE No. 10 and EEG No. 14 is with abacus, a partition and a column.
The Numeral systems surround us: the binary, inside the processor, the sixteenth, in the memory and color addresses of the web designer, the eighth, in UNIX access rights. In this chapter, we'll figure out how they're built and how to translate between them.
GEF · Grade 8
PIF · Baseline
OGE No.10
EGE No. 14
14
Chapter Pages
Five pages with theory, interactors and a bank of assignments.
14.1
Positioning Numeral systems
The base, the alphabet, the shape, the weight of the discharge.
Positioning properties
Abacus and the gymnasium.
14.2
Transfer between HS
The split is step-by-step, a universal converter of q1·q2, a fast translation of 2 ~8·16 by a group of bits.
14.3
Duplicate arithmetic
Adding, subtracting to the transport lighting column, multiplying and dividing, connection to the processor.
14.4
EEG/EGL workshop
Bank of 20 jobs: 10 EEG + 10 EGE with reviews. Filters, marathon, progress indicator.
14.5
Polygon examination
Quest 800 XP + test 8 minutes + open task with standard. Dashboard results.
⛳
Heading route
Recommended procedure for passing
14.1 Position MOPs
- Find out what the base is, the alphabet, the shape, the abacus.
14.2 Translations
- Axis three basic algorithms: a dip, a dew, a universal converter.
14.3 Arifmery
This is the basis for chapter 25 (number in memory).
14.4 Workshop
- train on real OGE/EEG review assignments.
14.5 Poligon Examination
- Final check with timer and task.
🔗
Links with other chapters
Numeral systems are a bridge between mathematics and computer engineering, and this chapter builds on several previous ones and prepares for the following.
Chapter 10 Alphavit
In chapter 10, we introduced the concept
alphabet
A. It turns out that the power of the alphabet is nothing but
base of the Numeral systems
. Formula N = Ai (number of words i) becomes formula
weight of discharge
qi. Without understanding the strength of the alphabet, it is impossible to master the positional record.
Chapter 13 ASCII/Unicode
In chapter 13, we studied the encoding: each letter is a number (ASCII 65='A', Unicode 1055='P').
Why?
The same bytes are read differently in different codes: these are different rules of interpretation of the same binary numbers. A 13.2 cross-code converter directly uses a translation between counting systems.
Chapter 12 · Information volume
In chapter 12, we counted the volume in bits: 1 byte = 8 bits; now we understand that 8 is the base of the 8th numeral system, and
1 byte = 23 = 8 values
This binds the two and eight-bit numeral system directly: each eight-digit number is exactly three bits.
How this relates to programming
In chapter 6 (shifts), we learned that the computer stores the numbers in a binary form.
mechanism
variable
int
- it's 32 bits, and the type.
byte
- That's eight orders.
0xFF
- it's just a convenient way to write it down.
11111111₂ = 255₁₀
In chapter 25 (Numbers in memory), we will see that the physical numbers are coded to IEEE 754: sign + exhibitor + mantiss - all in the dual HS.