# Octal to Decimal and Decimal to Octal Conversion

Like binary and decimal number system octal is another type of number system. As the name suggests the base of this number system is 8, i.e. in this number system there are 8 digits which can be used, they are 0, 1, 2, 3, 4, 5, 6 and 7. The concept of octal number system came from the Native Americans as they used to count numbers not with their fingers but with the space between their fingers i.e. 8. The octal number system became quite popular in the 90s but in modern era the binary number system has replaced it due to its reliability although this number system is still used in some specific applications.

## Decimal to Octal Conversion

Any decimal number can be converted into octal number system by dividing it by the largest possible power of 8. The remainder then again divided by the largest possible power of 8, this method is repeated until the power of 8 is 1 and the remainder obtained is less than 8. The result is obtained by arranging the obtained quotients as they are acquired. The method will be clear by a simple example.Let us convert 130_{10}into octal number. First of all we have to divide it by the largest possible power of 8 i.e. 8

^{2}130 / 8

^{2}= 2 130 - 8

^{2}×2 = 2 2 / 8

^{1}= 0 2 - 0 = 2

2/8

^{0}= 2 So the octal equivalent of 130

_{10}is 202

_{8}

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## Octal to Decimal Conversion

Similarly any octal number can be converted into decimal number. The method is quite similar to the transformation of any binary number to decimal number, the only difference is that in this case the 2 s will be replaced by 8 and everything else i.e. the methods will remain same. So it is quite clear if we want to change any octal number into decimal number we have to start multiplying the digits of the number from right hand side with increasing powers of 8 staring from 0 and finally summing up all the products. The method will be clearer with an example.Suppose we want to convert 1238 into decimal number, so we have to follow the procedure as shown below
123_{8} = 1×8^{2} + 2×8^{1} + 3×8^{0} = 64 + 16 + 3 = 83.
So, the decimal equivalent of the number 123_{8} is 83_{10}