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System octal
The system octal has base 8 and is represented by the set {0, 1, 2, 3, 4, 5, 6, 7}
Conversions
To convert decimal system to octal
The binary representation of a decimal number (the passage of a number in base 10 to its corresponding in base 8), is calculated by successively dividing the quotient of the division of the number by the divisor 8, until obtaining a quotient less than 8. The representation in base 8 it will be the last quotient followed by the last remainder followed by the previous remainder followed by the previous remainder and so on until the first remainder obtained
Example: Convert 3737 to octal representation
| Number | Ratio | Rest |
| \frac{3737}{8} | 467 | 1 |
| \frac{467}{8} | 58 | 3 |
| \frac{58}{8} | 7 | 2 |
So we have to:
3737_{(10} = 7231_{(8}To convert decimal system to octal with decimal
La representación binaria de un número decimal con decimales (el paso de un número en base 10 a su correspondiente en base 8), se calcula multiplicando sucesivamente el número (después los resultados) sin su parte entera por 8, hasta obtener un número sin decimales, hasta una cantidad que se repita periódicamente (en el caso de números periódicos), o hasta un número de dígitos predefinido por la precisión de la máquina. La representación en base 8 será, la parte entera sin modificaciones, después se le añade la coma y por último la parte entera del resultado de las multiplicaciones sucesivas
Example: Convert 56.75 to octal representation with decimals
| Number | Ratio | Rest |
| \frac{56}{8} | 7 | 0 |
So we have that the integer part is:
56_{(10} = 70_{(8}
| Number | Result | Integer part |
| 0,75 \cdot 8 | 6 | 6 |
So we have that the decimal part is:
0,75_{(10} = 6_{(8}
So we have to:
Convert system-octal to decimal
The decimal representation of an octal number would correspond to applying the formula:
b_1 \cdot 8^{(n - 1)} + \cdots + b_n \cdot 8^0
Where n would be the length of the string, and b_i the value corresponding to the i-th position of the string, starting from left to right
Example: Convert 7231 to decimal representation
7231_{(8}=7 \cdot 8^3 + 2 \cdot 8^2 + 3 \cdot 8^1 + 1 \cdot 8^0 = 7 \cdot 512 + 2 \cdot 64 + 3 \cdot 8 + 1 \cdot 1 = 3584 + 128 + 24 + 1 = 3737_{(10}
So we have to:
Convert system octal to decimal with decimal places
If the number also has decimals, it will be expressed with the following formula:
b_1 \cdot 8^{(n - 1)} + \cdots + b_n \cdot 8^0+ b_{(n + 1)} \cdot 8^{-1} + \cdots+ b_{(n + m)} \cdot 8^{-m}
Where n would be the length of the string without decimals, m the length of the string with decimals, b_i the value corresponding to the i-th position of the string, starting from left to right
Example: Convert 70.6 to decimal representation
70,6_{(8}=7 \cdot 8^1 + 0 \cdot 8^0 + 6 \cdot 8^{-1} = 7 \cdot 8 + 0 \cdot 1 + 6 \cdot 0,125 = 56 + 0,75 = 56,75_{(10}
So we have to: