How to Convert Octal to Decimal

There are four main number systems in the world: the binary system, the octal system, the decimal system and the hexadecimal system. We will discuss these two systems first before we proceed to the octal number conversion to decimal.

Decimal and Octal Number Systems

Everyone knows the decimal number system. It is the main number system we use today, and has 10 discrete digits from 0 to 9. The octal system on the other hand has only 8 digits (hence the name octal). The numbers in an octal system are only from 0-7. That means, there is no 8 and 9 in a normal octal system.

Now, while the decimal system is the most commonly used number system for most of the counting that we have to do, where is the octal system used? The octal system is used mainly in computer programming languages. There is a relationship between the octal and the binary system, which makes it very useful while programming computers. It is also often used in place of the hexadecimal system (16 digits), as it has fewer digits.

Conversions Between the Two

It is one of the most commonly taught problem solving exercises in computer basics. An octal number can be converted to a decimal number using the following formula:

Decimal Form = Ʃ(a_i x 8ⁱ)

In this formula, 'a' is the individual digit being converted, while 'i' is the number of the digit counting from the right-most digit in the number, the right-most digit starting with 0.

For example:

Convert (765)₈ into decimal:

(765)₈ = (7 x 8²) + (6 x 8¹) + (5 x 8⁰)

= (7 x 64) + (6 x 8) + (5 x 1)

= 448 + 48 + 5

= 501

Hence (765)₈ = (501)₁₀

We'll take one more example with a four digit number:

Convert (1336)₈ to decimal:

(1336)₈ = (1 x 8³) + (3 x 8²) + (3 x 8¹) + (6 x 8⁰)

= (1 x 512) + (3 x 64) + (3 x 8) + (6 x 1)

= 512 + 192 + 24 + 6

= 734

Thus (1336)₈ = (734)₁₀

Try this exercise out with the following numbers:

(5467)₈

(6345)₈

(76534)₈

Answers:

1.2871
2.3301
3.32092

This is a very simple and common mathematics exercise for learning the basics of information technology. I hope you are now able to face it!