Editing Octal (section)

===Decimal to octal conversion===

====Method of successive Euclidean division by 8====
To convert integer decimals to octal, [[Euclidean division|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 125<sub>10</sub> to octal:
:125 = 8<sup>2</sup> × '''1''' + 61
:61 = 8<sup>1</sup> × '''7''' + 5
:5 = 8<sup>0</sup> × '''5''' + 0
Therefore, 125<sub>10</sub> = 175<sub>8</sub>.

Another example:
:900 = 8<sup>3</sup> × '''1''' + 388
:388 = 8<sup>2</sup> × '''6''' + 4
:4 = 8<sup>1</sup> × '''0''' + 4
:4 = 8<sup>0</sup> × '''4''' + 0
Therefore, 900<sub>10</sub> = 1604<sub>8</sub>.

====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, 0.1640625<sub>10</sub> = 0.124<sub>8</sub>.

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.

====Method of successive duplication====
To convert integer decimals to octal, prefix the number with "0.". Perform the following steps for as long as digits remain on the right side of the radix:
Double the value to the left side of the radix, using ''octal'' rules, move the radix point one digit rightward, and then place the doubled value underneath the current value so that the radix points align. If the moved radix point crosses over a digit that is 8 or 9, convert it to 0 or 1 and add the carry to the next leftward digit of the current value. ''Add'' ''octally'' those digits to the left of the radix and simply drop down those digits to the right, without modification.

Example:
<pre>
 0.4 9 1 8 decimal value
  +0
 ---------
   4.9 1 8
  +1 0
  --------
   6 1.1 8
  +1 4 2
  --------
   7 5 3.8
  +1 7 2 6
  --------
 1 1 4 6 6. octal value
</pre>