# Binary to Octal

## Binary System

The base of the binary numeral system is two (radix). It only has two numbers since it uses the base-2 numeral system: 0 and 1.

The binary system has been used for many reasons in ancient Egypt, China, and India. Still, in the modern era, it has taken on the role of the language of electronics and computers. This one is the most effective method for determining whether an electric signal is off (0) or on (1). Additionally, it serves as the foundation for the binary code that computers utilise to construct data. Binary numerals are used in even the digital text you are reading right now.

Despite appearances, reading a binary number is simple: Every digit in a binary number is raised to the power of 2, starting with the rightmost digit (20) since this is a positional system. Each binary numeral in the binary system denotes a single bit.

## 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 utilised 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.

## How to Convert Binary to Octal?

Since octal numbers are just streamlined copies of binary strings, converting from binary to octal is pretty simple. Just keep in mind that each octal digit corresponds to three binary digits. Therefore three binary digits will only result in one octal digit. Even though the process is much simpler than it seems, using a binary to octal conversion chart might help you save time.

**Step 1: **grouping the 0s and 1s into three sets. Beginning from the right, perform this. Add additional 0s to the leftmost group to create another group if it doesn't have enough numbers to form a set of three.

**Step 2:** Underneath each group, write 4, 2, and 1. The positions' weights are as follows (22,21,20).

**Step 3:** Convert each binary group of three into an octal digit. Multiply the 4, 2, and 1 by the number above.

**Step 4:** Include the items from each pair of three. Below the groups to which the sums belong, write the sums.

**Step 5:** From left to right, the digits you obtain from each group's sum will give you the octal number.

The simplest type of number system is binary, which employs two digits of 0 and 1. (i.e. the value of base 2). Binary numbers are most frequently used in modern computer engineering, networking and communication specialists, and other professions because digital electronics only has two states (0 or 1).

In contrast, the octal number system, which has a value of 10, uses just eight symbols (0, 1, 2, 3, 4, 5, 6, and 7).

## Conversion from Binary to Octal number system

The octal number system offers a practical method for breaking up huge binary numbers into smaller, more manageable groups. A binary number can be transformed into an octal number in various ways. Both direct and indirect techniques of conversion are available. You must first translate a binary into another base system (e.g., into decimal or hexadecimal). After that, you must convert it to an octal number.

## Binary Octal Conversion Chart Table

Octal Digit Value | Binary Equivalent |
---|---|

0 | 000 |

1 | 001 |

2 | 010 |

3 | 011 |

4 | 100 |

5 | 101 |

6 | 110 |

7 | 111 |