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Binary and octal systems are different number systems commonly used in computing. They have different bases -- binary is base-two and octal base-eight -- meaning they must be grouped to convert. This, however, sounds far more complicated than this very easy conversion actually is.

Quick Steps to Convert Binary to Octal By Hand

To convert binary numbers to octal, split the binary into groups of 3, starting from the right. Add zeroes to the left of the last set if it's not a trio, then write "421" under each number. If there's a 1 above the 4, 2, or 1, write that digit down. Then, add up each set and combine the numbers to make an octal.

Method 1
Method 1 of 2:

Converting by Hand

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  1. Binary numbers are simply strings of 1's and 0's, such as 101001, 001, or even just 1. If you see this kind of string it is usually binary. However, some books and teachers further denote binary numbers through a subscript "2", such as 10012, which prevents confusion with the number "one thousand and one."
    • This subscript denotes the "base" of the number. Binary is a base-two system, octal is base-eight.
  2. There are two different binary numbers and only eight octal. Since you'll need three binary numbers to designate each octal number. Start from the right to make your groups. For example, the binary number 101001 would break down to 101 001.
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  3. The binary number 10011011 has eight digits, which, though not a multiple of three, can still convert to octal. Just add extra zeros to your front group until it has three places. For example:
    • Original Binary: 10011011
    • Grouping: 10 011 011
    • Adding Zeros for Groups of Three: 010 011 011[1]
  4. Each of the three binary numbers in a set stands for a place in the octal number system. The first number is for a 4, the second a 2, and the third a 1. To keep things straight, write these numbers underneath your sets of three binary numbers. For example:
    • 010 011 011
      421 421 421
    • 001
      421
    • 110 010 001
      421 421 421
    • Note, if you're looking for a shortcut, you can skip this step and just compare your sets of binary numbers to this octal conversion chart.
  5. If there is a one above the "4," then your octal number has a 4 in it. If there is a 0 above the one's place, the octal number does not have a one in it, so leave a blank, zero, or dash. As seen in an example:
    • Problem:
      • Convert 1010100112 to octal.
    • Separate into threes:
      • 101 010 011
    • Add placeholders:
      • 101 010 011
        421 421 421
    • Mark each places:
      • 101 010 011
        421 421 421
        401 020 021[2]
  6. Once you know what places are in the octal number, simply add up each set of three individually. So, for 101, which turns into 4, 0, and 1, you end up with 5 (). Continuing the example above:
    • Problem:
      • Convert 1010100112 to octal.
    • Separate, add placeholders, and mark each place:
      • 101 010 011
        421 421 421
        401 020 021
    • Add up each set of three:
  7. Splitting up the binary number was just to make solving easier -- the original number was one lone string. So, now that you've converted, put everything back together to get your final answer. That's all it takes.
    • Problem:
      • Convert 1010100112 to octal.
    • Separate, add placeholders, mark places, and add totals:
      • 101 010 011
        5 — 2 — 3
    • Put converted numbers back together:
      • 523
  8. There is technically no way to know if 523 refers to an octal number or a normal base-ten number without proper notation. To ensure that your teacher knows you've been doing the work well, place a subscript 8, referring to octal as a base-8 system, on your answer.
    • Problem:
      • Convert 1010100112 to octal.
    • Conversion:
      • 523.
    • Final Answer:
      • 5238[3]
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Method 2
Method 2 of 2:

Converting Shortcuts and Variations

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  1. This won't work on a test, but is a great choice in any other setting. Since there are only 8 possible combinations of numbers, it is actually a pretty easy chart to memorize. All you have to do is separate the numbers in groups of three, then match them with the chart in the pictures.[4]
    • Note how numbers 8 and 9 don't have straight conversions. In octal, these numbers do not exist, since there are only 8 digits (0-7) in a base-eight system.
  2. Say you need to convert the binary number 10010.11 to an octal number. Normally, you work from right to left to group the numbers into sets of three. With the decimal, you work away from the point. So, for the numbers left of the decimal (10010), you start at the point and work left (010 010). For the numbers to the right (.11), you start from the point and work right (110). When adding zeros, always add them in the direction you're working. The final breakdown is 010 010 . 110.
    • 101.1 → 101 . 100
    • 1.01001 → 001 . 010 010
    • 1001101.0101 → 001 001 101 . 010 100
  3. You'll need the chart to work backward, as a simple "3" doesn't give you enough information to do the math unless you already know the octal system well and want to re-think each combination. Simply use the following chart to easily convert each octal digit into a set of three binary numbers, then ram them together:
    • 0 → 000
    • 1 → 001
    • 2 → 010
    • 3 → 011
    • 4 → 100
    • 5 → 101
    • 6 → 110
    • 7 → 111[5]
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Community Q&A

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  • Question
    How can I convert 40.12 into an octal number?
    Community Answer
    Community Answer
    See the wikiHow article on converting from decimal to octal for details.
  • Question
    How can I convert the 1111100001 binary number into an actual number?
    Community Answer
    Community Answer
    Group the binary number into the group of three's. Add an extra zero to the left of the number to complete the group of three. Then follow the above procedure.
  • Question
    Could you write the rules of converting a binary number into octal?
    Community Answer
    Community Answer
    First identify if it is a binary number. Always Group them into numbers of three. Add extra zero on extreme left to complete the group, don't add anywhere else.
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This article was co-authored by wikiHow Staff. Our trained team of editors and researchers validate articles for accuracy and comprehensiveness. wikiHow's Content Management Team carefully monitors the work from our editorial staff to ensure that each article is backed by trusted research and meets our high quality standards. This article has been viewed 724,708 times.
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Co-authors: 22
Updated: July 26, 2024
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Categories: Programming
Article SummaryX

1. Group the digits in sets of 3.
2. Add zeros if you have less than 3 of any number.
3. Add a "421" under group of 3 as a placeholder.
4. If there's a 1 above any placeholders, write the placeholder number down.
5. Add the new numbers in each set of three.
6. Place the newly converted answers together to form the octal number.
7. Add subscript 8 to complete the conversion.

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