As you had seen in the previous blog, how to convert binary into a decimal number and decimal into binary. If you have not read our these blog, then go to this link “How to Convert Binary to Decimal Number” and “How to Convert Decimal to Binary”

So, today we will see “how to convert binary into octal number system”. Before we start, let take a recap about Binary and Octal number.

**Binary number:** A binary number is a number that uses the digit only two-digit “0” and “1” and its base is 2. It is known as binary numbers. Here are some **examples of binary numbers are**: 101, 011, 1001, 1101, etc.

**Octal number:** A octal number is a number that uses the digit 0 to 7(0,1,2,3,4,5,6,7) and its base is 8. It is known as Octal Number. Here are some **examples of octal numbers are**: 12_{8}, 75_{8}, 256_{8}, etc.

For more details about this topic go to this link “Computer Number System”

For better understanding let start with the example.

**Example 1:** Convert the binary number 101_{2} into Octal?

**SOL:**

**Step 1:** Firstly we have to convert 101_{2} into the decimal number. Let’s convert

= 1 x 2^{2} + 0 x 2^{1} + 1 x 2^{0}

= 5_{10}

**Step 2:** Now, we have to convert the number 5_{10} into Octal form. Let’s convert

To covert this number, so we have to divide the decimal number by 8.

Decimal No. ÷ by 8 | Quotient | Remainder |
---|---|---|

5 ÷ 8 | 0 | 5 |

Hence, the octal number is **5 _{8}**.

**Example 2: ** Convert the binary number 10110011_{2} into Octal.

**Sol:**

**Step 1:** Firstly, we have to convert 10110011_{2} into decimal form.

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

= 179_{10}

**Step 2:** Now, we have to convert the number 179_{10} into Octal form. Let’s convert

To covert this number, so we have to divide the decimal number by 8.

Decimal No. ÷ by 8 | Quotient | Remainder |
---|---|---|

179 ÷ 8 | 22 | 3 |

22 ÷ 8 | 2 | 6 |

2 ÷ 8 | 0 | 2 |

Now, write the remainder downward to upward manner = 263

Hence, the octal number is **263 _{8}**.

**Example 3:** Convert the Binary number **10111001001 _{2} **into an

**Octal?**

**SOL:**

**Step 1:** Firstly, we have to convert **10111001001**_{2} into decimal form.

(10111001001)₂ = (1 × 2¹⁰) + (0 × 2⁹) + (1 × 2⁸) + (1 × 2⁷) + (1 × 2⁶) + (0 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (0 × 2²) + (0 × 2¹) + (1 × 2⁰)

= (1481)₁₀

**Step 2:** Now, we have to convert the number 1481 into Octal form. Let’s convert

To covert this number, so we have to divide the decimal number by 8.

Decimal No. ÷ by 8 | Quotient | Remainder |
---|---|---|

1481 ÷ 8 | 185 | 1 |

185 ÷ 8 | 23 | 1 |

23 ÷ 8 | 2 | 7 |

2 ÷ 8 | 0 | 2 |

Now, write the remainder downward to upward manner = 2711

Hence the Octal number is **(2711) _{8}**

**Example 4:** Convert the Binary number **(1000010111111) _{2}** into Octal?

**SOL:**

**Step 1:** Firstly, we have to convert **1000010111111 _{2}** into decimal form.

=**(1000010111111)₂** = (1 × 2¹²) + (0 × 2¹¹) + (0 × 2¹⁰) + (0 × 2⁹) + (0 × 2⁸) + (1 × 2⁷) + (0 × 2⁶) + (1 × 2⁵) + (1 × 2⁴) + (1 × 2³) + (1 × 2²) + (1 × 2¹) + (1 × 2⁰)

= **(4287)₁₀**

**Step 2:** Now, we have to convert the number **(4287)₁₀** into Octal form. Let’s convert

To covert this number, we have to divide the decimal number by 8.

Decimal No. ÷ by 8 | Quotient | Remainder |
---|---|---|

4287 ÷ 8 | 535 | 7 |

535 ÷ 8 | 66 | 7 |

66 ÷ 8 | 8 | 2 |

8 ÷ 8 | 1 | 0 |

1 ÷ 8 | 0 | 1 |

Now, write the remainder downward to upward manner = 10277

Hence the Octal number is** (10277) _{8}**.

Now, we are going to solve the decimal points question and see how they solve it.

**Example 6:** Convert the Binary number** (100.01) _{2}** into Octal?

**SOL:**

**Step 1:** Firstly, we have to convert **(100.01) _{2}** into decimal form. Let’s convert

=(100.01)₂ = (1 × 2²) + (0 × 2¹) + (0 × 2⁰) + (0 × 2⁻¹) + (1 × 2⁻²)

= **(4.25)₁₀**

**Step 2:** Now, we have to convert the number **(4.25)₁₀** into Octal form. Let’s convert

In the decimal point question, we have to do multiply the decimal no. by 8 until the decimal is not finished.

Decimal no. multiply by 2 | Answer |
---|---|

4.25 x 8 | 34 |

If you multiply 4.25 with 8 then you will get 34. It means the decimal is finish. So, now we can easily convert 34 into octal. Let’s convert

**Step 3:** Now, we have to convert **34** into octal.

Decimal No. ÷ by 8 | Quotient | Remainder |
---|---|---|

34 ÷ 8 | 4 | 2 |

4 ÷ 8 | 0 | 4 |

Now, write the remainder downward to upward manner = 42.

(Note: 42 is not our answer, Our answer is 4.2. This is because we have finished the decimal point by multiplying by 8 only at one time. It means we have to put a decimal only one time in after 2. So, our answer is **4.2**)

Hence the octal number is **(4.2) _{8}**

**Example 7:** Convert the Binary number** (1011.001) _{2}** into Octal?

**SOL:**

**Step 1:** Firstly, we have to convert **(1011.001) _{2}** into decimal form. Let’s convert

=(1011.001)₂ = (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) + (0 × 2⁻¹) + (0 × 2⁻²) + (1 × 2⁻³)

= **(11.125)₁₀**

**Step 2:** Now, we have to convert the number **(11.125)₁₀** into Octal form.

To convert this, firstly we have to multiply with 8 until the decimal is not finished.

Decimal no. multiply by 2 | Answer |
---|---|

11.125 x 8 | 89 |

If you multiply 11.125 with 8 then you will get 89. It means the decimal is finish. So, now we can easily convert 89 into octal. Let’s convert

**Step 3:** Now, we have to convert **89** into octal.

Decimal No. ÷ by 8 | Quotient | Remainder |
---|---|---|

89 ÷ 8 | 11 | 1 |

11 ÷ 8 | 1 | 3 |

1 ÷ 8 | 0 | 1 |

Now, write the remainder downward to upward manner = 131.

(Note: 131 is not our answer, Our answer is 13.1. This is because we have finished the decimal point by multiplying by 8 only at one time. It means we have to put a decimal only one time in after 1. So, our answer is **13.1**)

Hence the octal number is **(13.1) _{8}**

**Example 8:** Convert the Binary number** (1011011101.001101) _{2}** into Octal?

SOL:

**Step 1:** Firstly, we have to convert **(1011011101.001101) _{2}** into decimal form. Let’s convert

= (1011011101.001101)₂

= (1 × 2⁹) + (0 × 2⁸) + (1 × 2⁷) + (1 × 2⁶) + (0 × 2⁵) + (1 × 2⁴) + (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰) + (0 × 2⁻¹) + (0 × 2⁻²) + (1 × 2⁻³) + (1 × 2⁻⁴) + (0 × 2⁻⁵) + (1 × 2⁻⁶)

= **(733.203125)₁₀**

**Step 2:** Now, we have to convert the number ** (733.203125)₁₀** into Octal form.

To convert this, firstly we have to multiply with 8 until the decimal is not finished.

Decimal no. multiply by 2 | Answer |
---|---|

733.203125 x 8 | 5865.625 |

5865.625 x 8 | 46925 |

If you multiply 733.203125 with 8 then you will get 5865.625. It still not finished the decimal point, so we have to multiply this number with 8.

When we multiply the number 5865.625 with 8 then it’ll give us 46925. It means the decimal point is now is finish. So, now we can easily convert 46925 into octal. Let’s convert

**Step 3:** Now, we have to convert **46925** into octal. So, let’s convert it

Decimal No. ÷ by 8 | Quotient | Remainder |
---|---|---|

46925 ÷ 8 | 5865 | 5 |

5865 ÷ 8 | 733 | 1 |

733 ÷ 8 | 91 | 5 |

91 ÷ 8 | 11 | 3 |

11 ÷ 8 | 1 | 3 |

1 ÷ 8 | 0 | 1 |

Now, write the remainder downward to upward manner = 133515

(Note: As you know that 133515 is not our answer, Our answer is 1335.15. This is because we have finished the decimal point by multiplying by 8 at two time. It means we have to put a decimal two time in after 15. So, our answer is **1335.15**)

Hence the octal number is **(1335.15) _{8}**

## Conclusion:

I have told you that how to convert the binary number into octal number. If you do not understand, then tell me in the comment section so that I come with a new method for you. I know this method is a bit lengthy and the same is explained in easy way on other website. So, Don’t worry guys, I will come with the table method in the upcoming so that you can learn both the method.

So, that’s for today’s blog guys. We will meet again with the new topic, till then you read our old blog and tell me that if I have made any mistake in my content so please tell me in the comment section so that I will fix it as soon as possible. And, also give us your feedback about this website.

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