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How to Convert from Decimal to Octal

12/27/2013

Octal is base-8, with only numbers 0-7. While Decimal is base-10 with numbers 0-9. Learn to convert from Decimal to Octal, without using a calculator.



Edit Steps



  1. Write down the decimal number you want to convert to octal.





  2. Divide that number by 8. Treat the division as an integer division, that is, do not calculate the quotient in decimals - stop once a remainder is obtained.





    • Note down the remainder separately.







  3. Divide the quotient obtained by 8 and again note down the remainder separately.





  4. Repeat the process described above until a quotient less than 8 is obtained. During the process every time note down the remainder separately. Please note that we also need to separately note down the last quotient (the one which is less than 8) of the process.





  5. Arrange the remainders and the last quotient from Right to Left in order they were obtained, thus keeping the last quotient in the first place.





    • The desired octal value of the given decimal number is simply this sequence read normally (Left to Right).









EditMore examples


Don't get the steps above? Use this section as your second reference.



99



  1. 99 / 8 = 12 . 375 = 12 r 3 (3)

  2. 12 / 8 = 1 . 5 = 1 r 4 (34)

  3. 1 goes to the remainder list (341)

  4. Reverse 341, so, 143 is the final answer (The octal of 99 is 143)



363



  1. 363 / 8 = 45 . 375 = 45 r 3 (3)

  2. 45 / 8 = 5 . 625 = 5 r 5 (35)

  3. 5 goes to the remainder list (355)

  4. Reverse 355, so, 553 is the final answer (The octal of 363 is 553)



5210



  1. 5210 / 8 = 651 . 25 = 651 r 2 (2)

  2. 651 / 8 = 81 . 375 = 81 r 3 (23)

  3. 81 / 8 = 10 . 125 = 10 r 1 (231)

  4. 10 / 8 = 1 . 25 = 1 r 2 (2312)

  5. 1 goes to the remainder list (23121)

  6. Reverse 23121, so, 12132 is the final answer (The octal of 5210 is 12132)



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