So, hey guys today we are going to discuss how to convert the octal number into binary. Before we start let take a recap about Binary and Octal number.

**Octal Number:** The octal number is an 8 base number system that uses the digit 0 to 8(0,1,2,3,4,5,6,7). These are known as Octal numbers. Here, are some examples of octal numbers are 12_{8}, 27_{8}, 143_{8}, 276_{8, }etc., and many other numbers.

**Binary Number:** The binary number is a 2 base number system that uses the digit only 0 and 1. These are known as Binary numbers. Here are some examples of binary numbers: 010_{2,} 10_{2}, 101_{2}, 10010_{2}

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 octal number **(10) _{8}** into Binary?

Sol:

**Step 1:** Firstly we have to convert the given number **10 _{8}** into a Decimal number. So, let’s see how to convert

= 1 x 8^{1} + 0 x 8^{0}

= 8_{10}

**Step 2:** Now, we have to convert the number 8_{10} into a Binary number. Let’s convert…

As In our blog ” How to Convert Decimal Into Binary Number System,” we discussed that how to convert it to binary…

Decimal No.÷ by 2 | Quotient | Remainder |
---|---|---|

8 ÷ 2 | 4 | 0 |

4 ÷ 2 | 2 | 0 |

2 ÷ 2 | 1 | 0 |

1 ÷ 2 | 0 | 1 |

Write all the remainder from downward to the upward manner

=1000

So, Our answer is **(1000) _{2}**

Hence, the conversion of octal number **10 _{8}** is

**(1000)**.

_{2}**Example 2:** Convert the Octal number **(74) _{8}** into Binary?

**Sol:**

**Step 1:** Firstly we have to convert the given number **74 _{8}** into a Decimal number. So, let’s see how to convert…

= 7 x 8^{1} + 4 x 8^{0}

= 56 + 4

= 60_{10}

**Step 2:** Now, we have to convert the number 60_{10} into a Binary number. Let’s convert…

Decimal No.÷ by 2 | Quotient | Remainder |
---|---|---|

60 ÷ 2 | 30 | 0 |

30 ÷ 2 | 15 | 0 |

15 ÷ 2 | 7 | 1 |

7 ÷ 2 | 3 | 1 |

3 ÷ 2 | 1 | 1 |

1 ÷ 2 | 0 | 1 |

Write all the remainder from downward to the upward manner

= 111100

So, our answer is (111100)_{2}

Hence, the conversion of octal number **74 _{8}** is

**(111100)**.

_{2}**Example 3:** Convert the Octal number **(531) _{8} **Into Binary?

**Sol:**

**Step 1:** Firstly we have to convert the given number **531 _{8}** into a Decimal number. So, let’s see how to convert…

= 5 x 8^{2} + 3 x 8^{1} + 1 x 8^{0}

= 320 + 24 + 1

= 345_{10}

**Step 2:** Now, we have to convert the number 345_{10} into a Binary number. Let’s convert…

Decimal No.÷ by 2 | Quotient | Remainder |
---|---|---|

345 ÷ 2 | 172 | 1 |

172 ÷ 2 | 86 | 0 |

86 ÷ 2 | 43 | 0 |

43 ÷ 2 | 21 | 1 |

21 ÷ 2 | 10 | 1 |

10 ÷ 2 | 5 | 0 |

5 ÷ 2 | 2 | 1 |

2 ÷ 2 | 1 | 0 |

1 ÷ 2 | 0 | 1 |

Write all the remainder from downward to the upward manner

= 101011001_{2}

So, our answer is (101011001)_{2}

Hence, the conversion of octal number **531 _{8}** is

**(101011001)**.

_{2}**Example 4:** Convert the octal number **(1624) _{8}**

` `

into Binary?**Sol:**

**Step 1:** Firstly we have to convert the given number **1624 _{8}** into a Decimal number. So, let’s see how to convert…

= 1 x 8^{3} + 6 x 8^{2} + 2 x 8^{1} + 4 x 8^{0}

= 512 + 384 + 16 + 4

= 916_{10}

**Step 2:** Now, we have to convert the number **(916) _{10}** into a Binary number. Let’s convert…

Decimal No.÷ by 2 | Quotient | Remainder |
---|---|---|

916 ÷ 2 | 458 | 0 |

458 ÷ 2 | 229 | 0 |

229 ÷ 2 | 114 | 1 |

114 ÷ 2 | 57 | 0 |

57 ÷ 2 | 28 | 1 |

28 ÷ 2 | 14 | 0 |

14 ÷ 2 | 7 | 0 |

7 ÷ 2 | 3 | 1 |

3 ÷ 2 | 1 | 1 |

1 ÷ 2 | 0 | 1 |

Write all the remainder from downward to the upward manner

= 1110010100

So, our answer is (1110010100)_{2}.

Hence, the conversion of octal number **916 _{8}** is

**(1110010100)**.

_{2}**Example 5:** Convert the Octal number **(3246) _{8}** into Binary?

**Sol:**

**Step 1:** Firstly we have to convert the given number **3246 _{8}** into a Decimal number. So, let’s see how to convert…

= 3 x 8^{3} + 2 x 8^{2} + 4 x 8^{1} + 6 x 8^{0}

= 1536 + 128 + 32 + 6

= 1702_{10}

**Step 2:** Now, we have to convert the number **(1702) _{10}** into a Binary number. Let’s convert…

Decimal No.÷ by 2 | Quotient | Remainder |
---|---|---|

1702 ÷ 2 | 815 | 0 |

815 ÷ 2 | 425 | 1 |

425 ÷ 2 | 212 | 1 |

212 ÷ 2 | 106 | 0 |

106 ÷ 2 | 53 | 0 |

53 ÷ 2 | 26 | 1 |

26 ÷ 2 | 13 | 0 |

13 ÷ 2 | 6 | 1 |

6 ÷ 2 | 3 | 0 |

3 ÷ 2 | 1 | 1 |

1 ÷ 2 | 0 | 1 |

Write all the remainder from downward to the upward manner

= 11010100110

So, our answer is (11010100110)_{2}

Hence, the conversion of octal number **1702 _{8}** is

**(11010100110)**.

_{2}## Conclusion:

Today I have told you that how to convert the octal number into a binary number. I hope you liked this blog, If is not then tell me in the comment section about why you don’t like the blog so that I will improve it as soon as possible for you.

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