- Decimal to Octal
- The Octal Number System and Its Applications
- What is Octal Used for?
- Declining Usage Due to Decimal and Hexadecimal
- Converting a decimal number to an octal number
- Therefore the octal representation of 148 is 224.Examples of converting decimals to octal numbers:

**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.