Decimal To Octal

To convert Decimal to Octal, enter the Decimal value and the converter will convert Decimal to Octal.

Last Update:


Decimal to Octal



The Octal Number System and Its Applications

Octal, also known as base-8, is a positional numeral system that uses eight unique digits from 0 to 7. While not as widely used today as decimal (base-10) or hexadecimal (base-16), octal still has some important applications in specific contexts.

What is Octal Used for?

  • Computer Programming and Digital Systems: Octal was more common in early computing to compactly represent binary data. Groups of 3 bits can be represented by a single octal digit. But hexadecimal is more common now due to alignment with 4-bit binary groups.
  • Unix File Permissions: In Unix-like systems, file permissions are often expressed in octal notation. Each octal digit denotes a permission set for owner, group, others. For example, 644 represents "rw-r--r--".
  • Networking and IP Addresses: IPv6 addresses can be written in octal, though hexadecimal or mixed notations are more common.
  • PDP-8 Computer: The PDP-8 minicomputer architecture used octal extensively for machine code and memory addressing based on 3-bit groups.
  • Historical Significance: Octal was more widely used in early computing because of hardware limitations. It represents an important part of computing history.

Declining Usage Due to Decimal and Hexadecimal

While octal was once more common, decimal and hexadecimal dominate modern computing. However, octal still has relevance when working with legacy systems and studying computing history.

In summary, octal plays a diminished but ongoing role in special applications like Unix permissions, historical systems, and IP addressing. Understanding it remains useful for programmers and computer engineers.
 

Converting a decimal number to an octal number

Divide the decimal number by 8.

Take the remainder from the division. This will be one digit of the octal number.

Divide the quotient by 8 again.

Save the remainder from this division as the next digit of the octal number.

Repeat steps 3 and 4, dividing the quotient by 8 each time, until the quotient is 0.

The octal number will be the remainder recorded in step 4 written in reverse order.

For example, to convert the decimal number 148 to octal:

148 divided by 8 gives a quotient of 18 and a remainder of 4.

18 divided by 8 gives a quotient of 2 and a remainder of 2.

2 divided by 8 gives a quotient of 0 and a remainder of 2.

The remainders are 4, 2, 2 in reverse order.

Therefore the octal representation of 148 is 224.

Examples of converting decimals to octal numbers:

Converting decimal 10 to octal

10 / 8 = 1 remaining 2

Part 1 / 8 = 0 remainder 1

The octet number is 12

 

Convert decimal 45 to octal

45 / 8 = 5 remaining 5

Section 5 / 8 = 0 remaining 5

The octet number is 55

 

Convert decimal 156 to octal number

156 / 8 = 19 remaining 4

19 / 8 = 2 remaining 3

2 / 8 = 0 remainder 2

Octet number 234

 

Convert decimal 233 to octal

233 / 8 = 29 remaining 1

29 / 8 = 3 remaining 5

3 / 8 = 0 remainder 3

Octet number 351

 

Convert decimal 999 to octal

999 / 8 = 124 remaining 7

124 / 8 = 15 remaining 4

15 / 8 = 1 remaining 7

1 / 8 = 0 remainder 1

Octet number 1747

The operation is to repeatedly divide the decimal number by 8, take the remainder as the next octal digit and divide the quotient again until 0 is reached. Octal numbers are remainders written in reverse order.

#octal #base-8 #decimal #base-10 #converter

We use cookies to enhance your experience on our website. The types of cookies used: Essential Cookies and Marketing Cookies. To read our cookie policy, click here.