Conversion from one number base to another is a common task in mathematics and computer science. In this article, we will explore the methods and techniques for converting numbers from one base to another.

## CONVERSION BETWEEN BINARY, OCTAL, AND HEXADECIMAL NUMBER SYSTEM

Binary, octal, and hexadecimal are all number systems that are widely used in computer science and digital electronics. The base of binary is 2, octal is 8, and hexadecimal is 16. To convert numbers between these bases, we need to know the place values and the digits used in each system.

## BINARY TO OCTAL/HEXADECIMAL

To convert a binary number to octal or hexadecimal, we can first divide the binary number into groups of three or four digits, respectively. We can then convert each group to its corresponding octal or hexadecimal digit. The table below shows the conversion of binary digits to octal and hexadecimal digits:

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

000 | 0 | 0 |

001 | 1 | 1 |

010 | 2 | 2 |

011 | 3 | 3 |

100 | 4 | 4 |

101 | 5 | 5 |

110 | 6 | 6 |

111 | 7 | 7 |

To illustrate, let’s convert the binary number **101101010** to octal and hexadecimal:

### Binary to Octal

We group the binary number into groups of three digits: **101 101 010**. We then convert each group to its corresponding octal digit: **5 5 2**. The octal representation of **101101010** is therefore **552**.

### Binary to Hexadecimal

We group the binary number into groups of four digits: **0001 0110 1010**. We then convert each group to its corresponding hexadecimal digit: **1**** 6 A**. The hexadecimal representation of **101101010** is therefore **16A**.

**See also: CONVERSION FROM OTHER BASES TO BASE 10 WITH VIDEO – NUMBER BASES**

## OCTAL/HEXADECIMAL TO BINARY

To convert an octal or hexadecimal number to binary, we can simply convert each digit to its corresponding binary representation. The table below shows the conversion of octal and hexadecimal digits to binary:

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

0 | 000 | 0 | 0000 |

1 | 001 | 1 | 0001 |

2 | 010 | 2 | 0010 |

3 | 011 | 3 | 0011 |

4 | 100 | 4 | 0100 |

5 | 101 | 5 | 0101 |

6 | 110 | 6 | 0110 |

7 | 111 | 7 | 0111 |

8 | 1000 | ||

9 | 1001 | ||

A | 1010 | ||

B | 1011 | ||

C | 1100 | ||

D | 1101 | ||

E | 1110 | ||

F | 1111 |

To illustrate, let’s convert the octal number **247** to binary and the hexadecimal number **ABCD** to binary:

### Octal to Binary

We convert each octal digit to its corresponding binary representation: **2 4 7** becomes **010 100 111**. The binary representation of **247** is therefore **010100111**.

### Hexadecimal to Binary

We convert each hexadecimal digit to its corresponding binary representation: **A B C D** becomes **1010 1011 1100 1101**. The binary representation of **ABCD** is therefore **1010101111001101**.

**Still unclear, watch the detailed video below**

## CONCLUSION

Converting between different number bases is a fundamental skill in mathematics and computer science. By understanding the place values and digits used in each system, we can use the appropriate method to convert numbers from one base to another. Whether we are working with binary, octal, hexadecimal, or other non-digital bases, the basic principles of conversion remain the same.

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