Transfer between counting systems

Содержание и основные понятия

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Alterna chapter 14 page 14.2
Transfer between counting systems
Three basic algorithms: 10th, 10th and between Arbitrary numeral system. With a step-by-step visualization.
Main skill
For OGE No. 10 and EEG No. 14: the ability to translate the number from one MOP to another. The three basic algorithms cover all cases.
GEF
PIF
OGE No.10
EGE No. 14
01
Algorithm 1: from 10th to q-bit
Delilka: divided by q, collected from the bottom up
Diffusion method with balance
We divide the reference number by q, remember the rest (it becomes the lower digit of the result).
We take a private one and we divide it by q again, we remember the rest.
Repeat until private is equal to 0.
Read Balances
bottom up
- that's the number in the HS q.
Example: 4510 ? ? 2
45 ÷ 2 = 22, остаток
1
(младший бит)
22 ÷ 2 = 11, остаток 0
11 ÷ 2 = 5, остаток 1
5 ÷ 2 = 2, остаток 1
2 ÷ 2 = 1, остаток 0
1 ÷ 2 = 0, остаток
1
(старший бит)
Ответ: читаем снизу вверх → 101101₂
🪜
Spill: Animation with a column
Enter the number and base, you see the division in the column like in school.
Number (10th)
Target cause
Готов к работе
02
Algorithm 2: from q-i-o to 10 o'clock
Deployed shape: each class multiplied by q to its degree
Algoritm
Number the bit from right to left, starting with 0.
Each digit is multiplied by q to the extent of its discharge.
We build all the works, we get the 10th number.
Example: 3FA16 ♪ ♪? 10
3FA₁₆ = 3·16² + F·16¹ + A·16⁰
= 3·256 + 15·16 + 10·1
= 768 + 240 + 10 =
1018₁₀
🔁
Detachment: q 10
Number
Basis
Введи число и нажми «Развернуть»
03
Algorithm 3: between Arbitrary HS
q1 10 x q2 = two steps through the decimal
Universal method
To transfer from the numeral system
q₁
in the HS
q₂
two crossings:
Let's move the number from q1 to the 10th (deployed form).
Translate the 10th number to q2 (the division method with the remainder).
🌐
Universal converter q1 ~ q2
Number
From numeral system
In the HS
Введи число и нажми «Перевести»
Communications 2 8 16
Since 8 = 23 and 16 = 24, the translation between the binary, eight and 16th MOP is made
Bits Group
:
• Bibular: 8-bit groups of 3 bits to the right.
• Bibliography: 4 bit groups on the right.
It's
Faster.
than the universal method.
Example: 1A2F16 8th (rapid route)
Каждая hex-цифра → 4 бита:
1 = 0001, A = 1010, 2 = 0010, F = 1111
Итого: 0001 1010 0010 1111₂
Группируем по 3 бита справа: 000 110 100 010 111
= 0 6 4 2 7₈ =
6427₈
(ведущий 0 отбрасываем)
04
Split part: fractional numbers in the HS
The fraction is multiplied by the base.
From q-ic to 10th (drum)
Each figure after the point is multiplied by q
−k
where k is the entry number after the point (1, 2, 3, ...):
0.d
1
d
2
d
3
…
q
= d
1
·q
−1
+ d
2
·q
−2
+ d
3
·q
−3
+ …
Example: 0.1012 ♪? 10
0.101₂ = 1·2
−1
+ 0·2
−2
+ 1·2
−3
= 1·0.5 + 0·0.25 + 1·0.125
= 0.5 + 0.125 =
0.625₁₀
From 10th to q-thin (drum)
Multiply the fraction by q.
The whole part of the result is the next digit in the q-same.
Take a new fraction and repeat it until it becomes 0 (or achieve the correct accuracy).
Example: 0.7510 ? ? 2
0.75 × 2 =
1
.5 → цифра 1, дробь 0.5
0.5 × 2 =
1
.0 → цифра 1, дробь 0.0
Ответ:
0.11₂
🔬
Scratch number converter
Enter the fractional number (point) and base
Number (point)
From numeral system
Введи дробное число и нажми «Перевести»
05
Grouping bits: 2 x 8 x 16
Quick translation without translation through decimal place
Grouping method
Since 8 = 23 and 16 = 24, the translation between the two, eight and sixteen-story HS is made
Bits Group
:
Twinial 8th:
We break the bits into groups of three (right to left), add zeros to the left, replace each group by 0 to 7.
Bibular:
Four-bit teams, replace each by 0-9, A-F.
Back:
each digit is replaced by three (or 4) bits.
Example: 110101102 8th and 16th
Группы по 3:
011
010
110
→ 3 2 6₈ =
326₈
Группы по 4:
1101
0110
→ D 6₁₆ =
D6₁₆
🧩
Group Trainer
Enter the binary number to see groups of three and four.
Binary number
06
D2 level table
Background table for rapid translation 2 ♪ 8 ♪ 16
The two steps and their relationship
Each degree of two corresponds to one bit. Knowing the degree of the two by heart, you can instantly translate the numbers between the second, the eighth and the 16th HS.
n
2ⁿ
2ⁿ₂
8th
16th
Council
For translation
from 16th to binary
: Each hex digit = 4 bits.
F1₁₆
=
1111 0001₂
For translation
of the 8th
: Each number = 3 bits.
75₈
=
111 101₂
.
07
Bit Field: Switch and Count
Switch the bits -- you see the value instantly in the 10th, 8th and 16th HS.
🎛️
16-bit slider
Press the bats or use the presets.
Decimal:
Eight:
Sixteenth:
Units:
Bizarre:
08
Mini test
📝
5 random translation questions
1 / 5
0 ✓