Using the knowledge that we have gained from the previous lessons, we first convert the binary number into decimal, and later we convert the decimal into octal number.

Let's first develop a chart containing all binary octal representations.

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

000 | 0 |

001 | 1 |

010 | 2 |

011 | 3 |

100 | 4 |

101 | 5 |

110 | 6 |

111 | 7 |

Now we will use this chart to convert the numbers easily.

Binary (base-2) to octal (base-8) conversion:

Step 1: From right (LSD or least significant digit) to left (MSD or most significant digit), divide the binary digits into groups of three.

Step 2: Convert each group of three binary digits into one octal digit.

Step 3: Combine all the resulting octal digits into a single octal number.

Step 2: Convert each group of three binary digits into one octal digit.

Step 3: Combine all the resulting octal digits into a single octal number.

Binary number: *1101110*_{2}

Or,*001* *101* *110*_{2}

Or,

Step | Binary | Octal |
---|---|---|

1 | 1101110_{2} | --- |

2 | 001_{2} 101_{2} 110_{2} | 1_{8} 5_{8} 6_{8} |

3 | 1101110_{2} | 156_{8} |

So, the octal representation: 156_{8}

Using the knowledge that we have gained from the previous lessons, we first convert the octal number into decimal, and later we convert the decimal into binary number.

Octal (base-8) to Binary (base-2) conversion:

Step 1: From left (MSD or most significant digit) to right (LSD or least significant digit), convert each octal digit into a 3-digit binary number.

Step 2: Combine all the resulting binary digits into a single binary number.

Step 2: Combine all the resulting binary digits into a single binary number.

Octal number: *156*_{8}

Step | Octal | Binary |
---|---|---|

1 | 156_{8} | 001_{2} 101_{2} 110_{2} |

2 | 156_{8} | 1101110_{2} |

So, the binary representation: 1101110_{2}