As people we count in denary which is a number system with a base ten.

Computers count in binary which is a number system with a base two.

Computers use binary to present and manipulate data.

To convert a denary value into binary

Draw a table such as the one below:

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

If we are converting the number 155

first we minus the largest binary number that goes into 155. In this case we do 155-128 to get 27. In addition we make a note on the table like below:

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

1 |

We find the largest number that 27 can be subtracted by.

We cannot use 64

We cannot use 32

We subtract 27 by 16 to get 11 and make a note on the table:

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

1 | 1 |

We then subtract 11 by 8 to get 3 and make a note on the table:

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

1 | 1 | 1 |

We then find the largest number that 3 can be subtracted by :

We cannot use 8

We cannot use 4

We can subtract 3 by 2 to get 1 and make a note on the table

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

1 | 1 | 1 | 1 |

We then subtract 1 by 1 to get 0 and make a note on the table .

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

1 | 1 | 1 | 1 | 1 |

Finally we fill the blanks in with zeros:

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |

155 is equal to 10011011 in binary

To convert binary into denary

We will convert the binary number 01010011

Draw out the table below and fill the binary number

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 |

Add the numbers with the values 1 so

64+16+2+1=83

01010011 = 83