Table of Contents

Last modified on April 25th, 2024

An octal-to-binary conversion is done to convert an octal number (base 8) to its equivalent binary number (base 2). Here are the methods to convert an octal number to its binary counterpart.

The octal number system has 8 digits from 0 to 7, represented in their equivalent binary using 3 bits.

Let us convert (363)_{8} into its binary number.

**Step 1:** Grouping 363 into individual digits, we have 3, 6, and 3.

**Step 2:** Now, we find their corresponding binary numbers using the conversion table.

Octal Number | Binary Number |
---|---|

0 | 000 |

1 | 001 |

2 | 010 |

3 | 011 |

4 | 100 |

5 | 101 |

6 | 110 |

7 | 111 |

By converting each octal digit of (363)_{8} to their binary numbers, we get

Octal Value | 3 | 6 | 3 |

Binary Value | 011 | 110 | 011 |

Here, we observe that each octal digit gives us a 3-bit binary number. Otherwise, we add zeros to maintain the correct number of digits.

**Step 3: **Taking the values from the first to last, (363)_{8} equals (011110011)_{2} or (11110011)_{2}.

**For Fractional Octal Numbers**

Similarly, we convert the fractional octal numbers into their corresponding binary.

Now, converting (452.01)_{8} to its equivalent binary, we get

**For the Integral Part:**

4 → 100, 5 → 101, and 2 → 010

**For the Fractional Part:**

0 → 000 and 1 → 001

Thus, (452.01)_{8} = (100101010.000001)_{2}

**Convert (53) _{8} into binary using the conversion table.**

Solution:

Grouping 53 into individual digits, we have 5 and 3.

By converting each octal digit of (53)_{8} to the binary, we get

(5)_{8} = (101)_{2}

(3)_{8} = (011)_{2}

Placing the values from the first to last, (53)_{8} equals (101011)_{2}.

Octal Value | 5 | 3 |

Binary Value | 101 | 011 |

There is another way by which each digit in any octal number is represented to its corresponding binary number without using the octal-to-binary conversion table.

Let us convert an octal number (73)_{8} into its corresponding binary.

First, we convert 73 into a decimal number and then decimal to binary.

**Step 1: Octal to Decimal**

While converting (73)_{8} to its decimal number, we multiply each digit from the right by the corresponding powers of 8, as shown.

Octal Value | 7 | 3 |

Decimal Value | 7 × 8^{1} | 3 × 8^{0} |

Now, on adding the values, we get the decimal number

(7 × 8^{1}) + (3 × 8^{0}) = 56 + 3 = 59

**Step 2: Decimal to Binary**

Now, converting (59)_{10} into its corresponding binary, we get

Thus, (73)_{8} = (111011)_{2}.

**Convert (347) _{8} into its corresponding binary.**

Solution:

By converting (347)_{8} into its corresponding decimal, we get

(3 × 8^{2}) + (4 × 8^{1}) + (7 × 8^{0}) = 192 + 32 + 7 = 231

Now, by converting (231)_{10} into its corresponding binary, we get

Thus, (347)_{8} = (11100111)_{2}.

Last modified on April 25th, 2024