Octal to Decimal Conversion with Examples

In this article, you will learn how to convert a number from the octal number system to the decimal number system, and you will also see an example of how to do so. However, before we get started, it will be beneficial for us to first understand these two different number systems.

  • Octal number: The octal number system has a base of 8, which means this system allows 8 digits to be used to form an octal number. Those 8 digits are 0, 1, 2, 3, 4, 5, 6, 7. For example: 213, 73, and 3023, etc.
    Therefore, we can say that a number that consists of 0, 1, 2, 3, 4, 5, 6, and 7 can be considered an octal number.
  • Decimal number: On the other hand, the decimal number system has a base of 10. Therefore, it has a total of 10 digits, which are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, which can be used to form a decimal number. For example: 230, 409, and 23022, etc.

Octal to Decimal Conversion Steps with an Example

If we use an example to help us understand the steps involved in converting from octal to decimal, we will be able to benefit from the information much more. As a consequence of this, I have chosen a number, 345, and interpreted it as an octal number. Pay close attention to the instructions provided in the following box, which will walk you through the process of converting this octal number into its decimal representation.

8n.......83      82      81      80
         512     64      8       1
                 3       4       5     (write octal digit from right side)
                 3*64    4*8     5*1
= (3*64) + (4*8) + (5*1)               (add all of the values in the preceding row)
= 192 + 32 + 5
= 229                                  (the equivalent decimal value)

You have to write the octal digit in such a way that the last octal digit will be written just below 80 or 1. Therefore, we have told you to write octal digits from the right side. Therefore, from the above box, the equivalent decimal value of the given octal number 345  is 229; That is to say, (345)8 = (229)10. In the fourth row, we have written the multiplication of an octal digit with its corresponding value in the second row.

We have to follow these rules given below to convert any octal number to the decimal system.

  1. Write down the given octal number.
  2. Write down the weight for different positions.
  3. To get the product, multiply each digit from the given octal number by the corresponding weight.
  4. Now add all the product values to get the decimal equivalent of the given octal number.

Octal to Decimal Example

Now let's take an example and apply all the above rules practically to understand them in a better and clearer way.

For example, we have to convert the number 315 given in the octal system into the decimal system. Alternatively, (315)8 = ( ? )10.

Now concentrate on the table given below, which shows how to apply all the rules listed above to convert octal to decimal.

3 1 5 Given Number
82 81 80 Weight

Now apply the rules in number 4 to get the result, which is

= 3*82 + 1*81 + 5*80

= 192 + 8 + 5

205 is the answer, or the decimal equivalent.

Therefore, (315)8 = (205)10.

Programs Created on Octal to Decimal Conversion

Computer Fundamentals Quiz

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