__Octal and Hexadecimal __

Decimal | Binary | Octal | Hexadecimal |

(base 10) | (base 2) | (base 8) | (base 16) |

0 | 0000 | 0 | 0 |

1 | 0001 | 1 | 1 |

2 | 0010 | 2 | 2 |

3 | 0011 | 3 | 3 |

4 | 0100 | 4 | 4 |

5 | 0101 | 5 | 5 |

6 | 0110 | 6 | 6 |

7 | 0111 | 7 | 7 |

8 | 1000 | 10 | 8 |

9 | 1001 | 11 | 9 |

10 | 1010 | 12 | A |

11 | 1011 | 13 | B |

12 | 1100 | 14 | C |

13 | 1101 | 15 | D |

14 | 1110 | 16 | E |

15 | 1111 | 17 | F |

16 | 10000 | 20 | 10 |

Fig 3 Conversion table for small numbers

__Reasons for using octal and/or hexadecimal __

__Reasons for using octal and/or hexadecimal__

Although they are stored in a computer in binary form, bit strings are often displayed by or entered into a computer in octal or hexadecimal form. This is because:

1- Binary strings are longer than their octal or hexadecimal equivalents. This means:

(a) Octal or hexadecimal strings do not take up much room when displayed.

(b) Binary strings take longer to type in.

2- Binary strings are difficult to recognize and remember.

3- As octal and hexadecimal are each based on a power of 2, they can be converted to and from binary easily.

## CONVERSION BETWEEN HEXADECIMAL AND BINARY (INTEGERS) Every hexadecimal digit corresponds to four bits of the equivalent binary number.

__Binary to hexadecimal __

__Method __

1- Starting at the right split the binary number into groups of four bits.

2- Convert each group of bits to hexadecimal.

__Worked question __

A location contains the value 1001101011 in binary.

How would this be displayed in hexadecimal?

| Comments | ||

10 | 0110 | 1011 | Starting at the right group into fours For each group write hexadecimal equivalent |

2 | 6 | B |

Answer 1001101011_{2}=26B_{16}

__Hexadecimal to binary __

__Method __

1- For each hexadecimal digit write the four-digit binary equivalent.

2- Ignore any zeros at the left.

__Worked question __

The address of a location is 2B6A in hexadecimal. What is it in binary?

2 | B | 6 | A | Comment |

0010 | 1011 | 0110 | 1010 | For each hexadecimal digit write the binary equivalent |

The address is 0010 1011 0110 1010

** Notes**:

1- In the example addresses may occupy 16 bits so the two 1s at the left were not discarded.

2 -The methods for converting between octal and binary are similar with each octal digit corresponding to three binary digits.