Then convert each digit of the hexadecimal number into 4 little bits of binary number whereas converting each group of three bits from least significant into a binary number.īut, there are two of the direct methods which are available for converting the decimal number into an octal number − Converting with Remainders and Converting with Division. = (1x2 6 + 1x2 5 + 0x2 4 + 0x2 3 + 0x2 2 + 1x2 1 + 0 x 2 0 ) 10 or (6 x 16 1 +2x16 0 ) 10īecause the bases of the binary and hexadecimal are 2 and 16, respectively, you get In the indirect method, we need to convert the decimal number into another number system (e.g., binary or hexadecimal), then we can convert them into binary numbers by converting each digit into binary numbers from hexadecimal and using grouping from the octal numeration system.Įxample − Convert the Decimal Number 98 into an Octal Numberįirst, convert it into a binary or hexadecimal number. There are various direct or indirect methods to convert a decimal number into an octal number( decimal to octal conversion method). Let’s learn how to convert decimal to octal. Sometimes, these two given methods, which is to say, the Euclidean Method of Successive division by 8 and the Method of successive multiplication by 8.Ĭonversion from Decimal to Octal Number System Now do the same with the fractional part of the number, that is to say, multiplying it with the number 8 until at last, it becomes null. Whatever result may come, its integer part becomes the first digit of the octal fraction. First, all you have to do is to multiply the decimal fraction by the 8. Method of Successive Multiplication by 8: This method is also useful for converting the Decimal fraction to the octal. The formation of the Octal numerals is done by the quotients, and it is written in the order, which is generated by the algorithms. By doing so, you are going to have reminders, what you have to do of these reminders is to divide the smaller powers of 8 in a successive manner, until at last you are left with 1. All you have to do here is to divide the original number by the power of 8, which is supposed to be the largest power of 8. There are many methods for converting the decimal to octal, a few of which are discussed here:Įuclidean Method of Successive Division by 8: As the name suggests this method comes from the Greek Mathematician Euclid. There is so much more to learn about the octal number system, and if you wish to learn about this system of numerals then click on this link. Now, let us look at the octal numeral system the same number which is 74, which means multiplying 8 with the 8, and then adding 8 to the power of 1 and then again adding 2. So it means 7 multiplied by 10 to the power of 1, and adding. So, let us take as an example of Seventy-four, 74. In the decimal system, as said above, each number has a base of ten.

So, 100 of the normal numeral system becomes 64 in the octal numeral system. Then again it is simple, 100 is 10 times 10, and in a similar manner, for the octal numeral system it becomes 8 times 8, that is to say, 65. If you might be wondering that if 10 is represented by 8 in the octal numeral system then what about 100. Now, coming to the Decimal, in the normal numeral system the decimal is always represented by 10, but in the octal numeral system, it is again represented by 8. So, what the number 10 represents in the normal numeral system is represented by 8 in the octal numeral system. In simple terms, this system takes 8 as a base of the calculation and not the number 10. So, in mathematics Octal is a numeral system, which is quite often referred to as Oct as well. It is the base 8 which has only 8 symbols as 0, 1, 2, 3, 4, 5, 6, and 7.īefore starting to learn to convert the decimal to octal, it would be better to first have a good idea regarding the Octal. Whereas the octal system is one of the number systems to represent numbers. It is the base 10 which has only a total of 10 symbols − 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The decimal system is the most familiar number system to the general public. In the case of the decimal to octal conversion method, we divide the amount by 8 and write the remainder within the reverse order to urge the equivalent octal number. In decimal to binary, we divide the amount by 2, in decimal to hexadecimal we divide the amount by 16. It is the same as converting any decimal number to binary or decimal to hexadecimal. Here we'll learn conversion from decimal to octal number. A number with base 8 is an octal number and variety with base 10 is a decimal number. We have to find out about both the amount systems first.

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