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There are four main number systems in the world: the binary system, the octal system, the decimal system and the hexadecimal system. Since this article deals with 'octal to decimal: how to convert', we will discuss these two systems first before we proceed to the octal number system conversion to decimal.

Decimal and Octal Number System

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.

Octal to Decimal: How to Convert

Octal to decimal conversion is one of the most commonly taught problem solving exercises in computer basics. So is there an octal to decimal formula? Yes, an octal number can be converted to a decimal number using the following formula:

Decimal Form = Ʃ(ai 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

To convert an octal number to decimal, write out the number to be converted, placing each digitunder the proper position


Next, multiply the decimal equivalent by the corresponding digit of the octal number; then, add thiscolumn of figures for the final solution:

Solution: 7438 is equal to 4831

Now follow the conversion of 265258 to decimal:

Solution: 11,60510 is the decimal equivalent of 26,5258To convert a fraction or a mixed number, simply use the same procedure

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โˆ™ 2010-11-21 09:09:56
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Q: How do you convert octal numbers to decimal numbers?
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