The decimal number system (also called base-ten numeral system) is the general system for signifying non-integer and integer numbers. On the other hand, the octal number system employs a base-8 number system (digits 0 to 7) These number systems are widely used in computing processes and are interconvertible.
The numbers that can be expressed in the decimal system are called the decimal fractions, which are the fractions of the form ‘a/10n’, in which, a is an integer, and ‘n’ on the other hand, is a non-negative integer. It is worthy of mention that the decimal system extends to infinite decimals.
Octal numbers can be made from binary numbers by clustering together, successive binary digits into classes of three (beginning from the right side)
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Decimal to Octal Conversion – Step by Step
We’d be discussing two methods here for the process of converting decimal to octal, one of them being the conversion with remainders while the other one with the division.
1- Converting with remainders
- Consider a decimal number, let’s say our number is 682, now we divide it with 8.
- After dividing and rounding the value, we get the number 85.
- Now find the remainder, with a scientific calculator, you can find the remainder with mod function, in this case, type, 682 mod 8 and you’ll get the number ‘2’
- Setting aside the remainder for now and going back to our division, what you do now is divide the answer of the first division with 8, so dividing 85 with 8, we get 10 ignoring the fraction.
- Repeating step 3, we get the remainder value for 85, that is ‘5’
- Now, repeat step 4 and divide 10 with 8 to get the value ‘1’ by ignoring the fractional value now find the mod of 10 for 8 and you get ‘2’
- This process repeats until you reach the final digit.
2- Converting with Division
- Let’s consider the decimal number ‘90’ for our example to convert with the division.
- List 8’s powers, (8, 82, 83)
- We ignore 83 as its product ‘512’ is greater than 90.
- We take 82 = 64 and divide 90 with 64, we get 1.40.
- Ignore the fraction to get ‘1’ multiply it with 64 = 64, now subtract 64 from 90 to get the remainder, which is, 90-64 =26.
- List this newly obtained value.
- Now repeat the previous steps for the new value:26 by first dividing it with 8 and following through with the rest of the steps.
How to convert decimal to octal with our calculator
Our calculator as mentioned earlier is extremely easy to use. The only thing that you have to do is input the decimal value and press ‘calculate’ and it will convert it in the octal as well as the hex value in a fraction of a second. Cheers!
The decimal number system is the fundamental basis of everyday mathematics while on the other end, the octal number system finds extensive use in computing processes. Together, these two number systems have great importance and enable numerous applications in our daily lives.