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Hi PLOTTWIST Labyu!
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Ate Rics! Miss you so much..
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Hexadecimal to octal conversion
Hexadecimal to octal conversion proceeds by first converting the hexadecimal digits to 4-bit binary values, then regrouping the binary bits into 3-bit octal digits.
For example, to convert 3FA516:
To binary:
3 F A 5
0011 1111 1010 0101
then to octal:
0 011 111 110 100 101
0 3 7 6 4 5
Therefore, 3FA516 = 376458.
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Octal to decimal conversion
To convert a number k to decimal, use the formula that defines its base-8 representation:
k = ∑ i = 0 n ( a i × 8 i ) k=\sum _{{i=0}}^{n}\left(a_{i}\times 8^{i}\right)
In this formula, ai is an individual octal digit being converted, where i is the position of the digit (counting from 0 for the right-most digit).
Example: Convert 7648 to decimal:
7648 = 7 × 82 + 6 × 81 + 4 × 80 = 448 + 48 + 4 = 50010
For double-digit octal numbers this method amounts to multiplying the lead digit by 8 and adding the second digit to get the total.
Example: 658 = 6 × 8 + 5 = 5310
Octal to binary conversion
To convert octal to binary, replace each octal digit by its binary representation.
Example: Convert 518 to binary:
58 = 1012
18 = 0012
Therefore, 518 = 101 0012.
Binary to octal conversion
The process is the reverse of the previous algorithm. The binary digits are grouped by threes, starting from the least significant bit and proceeding to the left and to the right. Add leading zeroes (or trailing zeroes to the right of decimal point) to fill out the last group of three if necessary. Then replace each trio with the equivalent octal digit.
For instance, convert binary 1010111100 to octal:
001 010 111 100
1 2 7 4
Therefore, 10101111002 = 12748.
Convert binary 11100.01001 to octal:
011 100 . 010 010
3 4 . 2 2
Therefore, 11100.010012 = 34.228.
Octal to hexadecimal conversion
The conversion is made in two steps using binary as an intermediate base. Octal is converted to binary and then binary to hexadecimal, grouping digits by fours, which correspond each to a hexadecimal digit.
For instance, convert octal 1057 to hexadecimal:
To binary:
1 0 5 7
001 000 101 111
then to hexadecimal:
0010 0010 1111
2 2 F
Therefore, 10578 = 22F16.
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Decimal to octal conversion
Method of successive Euclidean division by 8
To convert integer decimals to octal, divide the original number by the largest possible power of 8 and divide the remainders by successively smaller powers of 8 until the power is 1. The octal representation is formed by the quotients, written in the order generated by the algorithm. For example, to convert 12510 to octal:
125 = 82 × 1 + 61
61 = 81 × 7 + 5
5 = 80 × 5 + 0
Therefore, 12510 = 1758.
Another example:
900 = 83 × 1 + 388
388 = 82 × 6 + 4
4 = 81 × 0 + 4
4 = 80 × 4 + 0
Therefore, 90010 = 16048.
Method of successive multiplication by 8
To convert a decimal fraction to octal, multiply by 8; the integer part of the result is the first digit of the octal fraction. Repeat the process with the fractional part of the result, until it is null or within acceptable error bounds.
Example: Convert 0.1640625 to octal:
0.1640625 × 8 = 1.3125 = 1 + 0.3125
0.3125 × 8 = 2.5 = 2 + 0.5
0.5 × 8 = 4.0 = 4 + 0
Therefore, 0.164062510 = 0.1248.
These two methods can be combined to handle decimal numbers with both integer and fractional parts, using the first on the integer part and the second on the fractional part.
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The octal multiplication table × 1 2 3 4 5 6 7 10
1 1 2 3 4 5 6 7 10
2 2 4 6 10 12 14 16 20
3 3 6 11 14 17 22 25 30
4 4 10 14 20 24 30 34 40
5 5 12 17 24 31 36 43 50
6 6 14 22 30 36 44 52 60
7 7 16 25 34 43 52 61 70
10 10 20 30 40 50 60 70 100
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Octal
From Wikipedia, the free encyclopedia
Numeral systems
Numeral Systems of the World.svg
Hindu–Arabic numeral system
Western Arabic
Eastern Arabic
Bengali
Gurmukhi
Indian
Sinhala
Tamil
Balinese
Burmese
Dzongkha
Javanese
Khmer
Lao
Mongolian
Thai
East Asian
Chinese
Suzhou
Hokkien
Japanese
Korean
Vietnamese
Counting rods
Alphabetic
Abjad
Armenian
Āryabhaṭa
Cyrillic
Ge'ez
Georgian
Greek
Hebrew
Roman
Former
Aegean
Attic
Babylonian
Brahmi
Egyptian
Etruscan
Inuit
Kharosthi
Mayan
Muisca
Quipu
Prehistoric
Positional systems by base
2
3
4
5
6
8
10
12
16
20
60
Non-standard positional numeral systems
Bijective numeration (1)
Signed-digit representation (Balanced ternary)
factorial
negative
Complex-base system (2i)
Non-integer representation (φ)
mixed
List of numeral systems
v
The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping consecutive binary digits into groups of three (starting from the right). For example, the binary representation for decimal 74 is 1001010. Two zeroes can be added at the left: (00)1 001 010, corresponding the octal digits 1 1 2, yielding the octal representation 112.
In the decimal system each decimal place is a power of ten. For example:
74 10 = 7 × 10 1 + 4 × 10 0 {\mathbf {74}}_{{10}}={\mathbf {7}}\times 10^{1}+{\mathbf {4}}\times 10^{0}
In the octal system each place is a power of eight. For example:
112 8 = 1 × 8 2 + 1 × 8 1 + 2 × 8 0 {\mathbf {112}}_{8}={\mathbf {1}}\times 8^{2}+{\mathbf {1}}\times 8^{1}+{\mathbf {2}}\times 8^{0}
By performing the calculation above in the familiar decimal system we see why 112 in octal is equal to 64+8+2 = 74 in decimal.