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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
The binary representation of a decimal number with decimals (the passage of a number in base 10 to its corresponding in base 8), is calculated by successively multiplying the number (after the results) without its integer part by 8, until obtaining a number without decimals , up to an amount that is repeated periodically (in the case of periodic numbers), or up to a number of digits predefined by the precision of the machine. The representation in base 8 will be the integer part without modifications, then the comma is added and finally the integer part of the result of successive multiplications
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: