X

ADVERTISEMENT

ADVERTISEMENT

Table of Contents:

Binary is the simplest type of numerical system that only uses two digits of 0 and 1 (i.e. base value 2). Digital electronics have both states (0 or 1). In modern computer engineers, networking and communication specialists, and other professionals, the binary numbers are therefore preferred.

On the other hand, octal number is a 10-value number with only 8 symbols: 0, 1, 2, 3, 4, 5, 6 and 7.

Octal system allows large binary numbers to be converted into smaller and more compact groups. A binary number can be converted to an octal number in different ways. Use direct or indirect methods to convert. Simply put, if you do it manually, you would do it with three steps. First, you must convert a binary to another basic system (for example, decimal or hexadecimal). Then in octal number that you need to convert.

However, binary to octal converter is an easiest way to convert binary to octal without converting binary to decimal first, then to octal.

**Let’s understand it with examples:**

First convert this into decimal number = (10010110)_{2}

= 1x2^{7}+0x2^{6}+0x2^{5}+1x2^{4}+0x2^{3}+1x2^{2 }+ 1x2^{1 }+ 0x2^{0}

= 128+0+0+16+0+4+2+0

= (150)_{10}

Then, convert it into octal number

= (150)_{10}

= 2x8^{2}+2x8^{1}+6x8^{0}

= (226)_{8} is the answer.

Now let’s solve the same binary number to octal number using binary to octal converter.

See, it’s that easy to convert binary to octal by a converter.

There’s another direct way to convert binary to octal and that’s grouping. As the octal number system only has 8 digits (0 to 7) so any digit of the octal number system can be represented with only 3 bit below.

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

0 | 000 |

1 | 001 |

2 | 010 |

3 | 011 |

4 | 100 |

5 | 101 |

6 | 110 |

7 | 111 |

Thus, if you create a binary number for every three-bit group, you can replace each binary number of its octal numbers equivalent. This is the octal number of the number given. Note that you can add a number of 0' s for integer part in left-most bit (or most significant bit MSB) and add any number of 0's for fraction part to complete the group of 3 bit in rightest bit (or in least significant bit LSB) so that the value of the binary input number is not modified.

**Therefore, these are steps to convert a binary to an octal number:**

- Divine the binary numbers into three groups (from right) for integer part and start from left for fraction portion.
- Convert three digits into an octal digit for each binary group.
- This is simple algorithm in which the binary number needs to be grouped and its octal numbers replaced.

Convert binary number 1010111100 into octal number. As no binary point and no fractional number is here. So,

**00**1 010 111 100

**Bold 0s are added to complete the pair of three*

Therefore, Binary to octal is.

= (1010111100)_{2}

= (001 010 111 100)_{2}

= (1 2 7 4)_{8}

= (1274)_{8}

Now again, if we’ll convert this binary to octal using binary to octal converter, you won’t have to go through these steps. It can be done in one click. See the below image.

Similarly, Prepostseo also offers multiple conversion tools like octal to binary, decimal to octal, octal to decimal, decimal to binary, hex to binary, binary to hex, decimal to hex, hex to decimal, hex to octal, binary to decimal and text to binary.

Feedback