# Decimal to Octal

The public is most accustomed to the decimal system of numbers. Base 10 only has the following ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, and 8. At the same time, one of the number systems used to represent numbers is the octal system. Base 8 only has the following eight symbols: 0, 1, 2, 3, 4, 5, and 6.

We must first become familiar with both number systems before converting from decimal to octal. The octal number has a base of 8, whereas the decimal number has a base of 10. Here, we'll translate a decimal number into its octal equivalent. The process is identical to converting any decimal number to binary or hexadecimal.

We divide the number by 2 when converting it from decimal to binary and by 16 when converting from decimal to hexadecimal. To convert a decimal to an octal number, divide the value by 8 and write the remainders in the opposite order.

## Decimal System

The decimal numeral system is the most widely used and accepted system in daily life. It bases itself on the number 10. (radix). Consequently, it has ten symbols: The digits 0 through 9, namely 0, 1, 2, 3, 4, 5, 6, 7, and 9.

Many ancient civilizations used the decimal numeral system, which is one of the earliest numeral systems that is now known. The Hindu-Arabic numeral system solved the problem of representing considerable numbers in the decimal system. The Hindu-Arabic numeral system assigns positions to the digits of a number. This system uses powers of base 10 to calculate numbers, and the digits are raised to the nth power according to their placements.

### Consider the decimal number 2345.67 as an example:

- The number 5 is in the place of ones (100 equals 1), and the number 4 is in the place of tens (101)
- 3 is in the hundreds position (102)
- 2 is in the thousands position (103)

In the meantime, the digits 6 and 7 are in the tenths (1/10, which is 10-1) and the hundredths (1/100, which is 10-2) positions, respectively, after the decimal point.

Therefore, the following is another way to express the number 2345.67: (2 * 103) + (3 * 102) + (4 * 101) + (5 * 100) + (6 * 10-1) + (7 * 10-2)

## The Octal System

The base of the octal number system, often known as oct, is 8. (radix). It employs eight symbols since it is a base-8 numeral system: The digits 0 through 7, namely 0, 1, 2, 3, 4, 5, and 7. Although certain Native American tribes continued to use it up to the 20th century, the octal system gained popularity as a computer programming language in the early days of computing. This is because the octal system condenses the lengthy and intricate chains of binary displays utilized by computers.

The binary counting of groups of three is done primarily using the octal system: Three binary digits are represented by each octal number. For processors that use word sizes divisible by three, such as 6-bit, 12-bit, 24-bit, or 36-bit, the octal system became the ideal abbreviation of binary because 8 is 2 to the third power (23). Nowadays, hexadecimal is more commonly used than octal in most modern systems. However, understanding octal numbers are crucial when working with electronics.

## Steps to Convert Decimal to Octal

- To learn how to convert a decimal to octal, follow the instructions below:
- The specified decimal number in writing.
- The octal number is the same if the specified decimal number is less than 8.
- Divide the decimal number by 8 if it is more significant than 7.
- Note the leftovers that we obtain after division.
- Steps 3 and 4 should be repeated until the quotient is less than 8.
- Write the leftovers in reverse order now (bottom to top)
- The outcome is the octal number that corresponds to the specified decimal number.

## Decimal to Octal Table

Decimal |
Equivalent Octal Number |
Decimal |
Equivalent Octal Number |

0 | 0 | 9 | 11 |

1 | 1 | 10 | 12 |

2 | 2 | 11 | 13 |

3 | 3 | 12 | 14 |

4 | 4 | 13 | 15 |

5 | 5 | 14 | 16 |

6 | 6 | 15 | 17 |

7 | 7 | 16 | 20 |

8 | 10 | 17 | 21 |