Converting decimal to octal is straightforward and valuable across many applications. Understanding different number systems in computing is crucial for efficient operations. Converting numbers between systems enhances our ability to manipulate data effectively. Using methods like division or shortcuts makes decimal to octal conversion accessible to everyone.
Introduction
In computing, numbers are represented in binary, decimal, octal, and hexadecimal formats, each serving distinct purposes. While decimal is ubiquitous in daily life, octal and hexadecimal are predominant in computing. This article will detail the conversion process from decimal numbers to octal numbers.
Also Read: Convert Decimal To Octal
What is Decimal?
Decimal refers to the base-10 number system, which is the standard numeric system used widely in everyday life. In the decimal system, each digit can be from 0 to 9, and the value of a number is determined by its positional notation. For example, the number 354 in decimal represents:
35410 = 3 x 102 + 5 x 101 + 4 x 100
So, 35410 in decimal equals 354
What is Octal?
Octal is a number system that uses a base of 8. It includes digits from 0 to 7, where each digit's position represents a power of 8. For example, the octal number 5310 (53 in decimal) is represented as 658 in octal, where:
658 =6 x 81 + 5 x 80 = 6 x 8 + 5 x 1= 48 + 5 = 5310
Also Read: Converse of Pythagoras Theorem
Why do we need to convert decimals to octal?
We convert decimals to octal in computing for several reasons:
- Storage Efficiency: Octal numbers represent data more compactly than decimal or binary equivalents, saving storage space.
- Representation of Binary Data: Octal numbers are useful for representing and manipulating binary data, as each octal digit corresponds directly to a group of three binary digits (bits).
- Permissions in File Systems: Octal numbers are commonly used to represent file permissions in Unix-like operating systems, where each digit represents permissions for owner, group, and others.
- Historical Reasons: Octal was historically used in computing systems due to the ease of conversion to binary and its compact representation, though it's less common now compared to hexadecimal.
How to convert Decimals to Octal?
To convert a decimal number to octal, you can follow these steps:
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Divide the Decimal Number: Divide the decimal number by 8.
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Record Remainders: Keep track of the remainders from each division.
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Repeat Division: Continue dividing the quotient from the previous division by 8, recording remainders each time, until the quotient is 0.
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Read the Octal Number: The octal number is formed by arranging the remainders obtained from bottom to top (last remainder to first remainder).
Also Read: Continuity and Discontinuity
Here's a step-by-step example:
Let's convert the decimal number 12310 to octal.
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Divide 123 by 8:
- 123 / 8 = 15 remainder 3
So, the first remainder is 3.
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Divide 15 by 8:
- 15 / 8 = 1 remainder 7
So, the next remainder is 7.
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Divide 1 by 8:
- 1 / 8 = 0 remainder 1
The final remainder is 1.
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Arrange the remainders (from bottom to top):
- The remainders are 1, 7, and 3.
Therefore, 12310 converts to 1738 in octal.
So, 123 in decimal is equivalent to 173 in octal.
Frequently Asked Questions
Ans. To convert a decimal to octal, repeatedly divide the decimal number by 8 and record the remainders from bottom to top.
Ans. Convert 789.625 to octal by separately converting the integer part (789) and the fractional part (0.625), then combining them.
Ans. 673.23 as a decimal converts to 1241.17 in octal, with the integer part (673) and the fractional part (0.23) converted separately.
Ans. 24 decimal converts to 30₈ in octal by dividing 24 by 8, yielding a remainder of 0.