# Binary Integers

Extracts from this document...

Introduction

Carl Cooper Unit 1

124146 30/04/2007

Method 1

Binary Integers

- Computer systems use one, two, and three, even four bytes (32 bits) to store a single integer.

Denary Integer | Binary integer |

1 | 00000000 |

2 | 00000001 |

3 | 00000010 |

4 | 00000011 |

5 | 1 |

6 | 1 |

Calculating denary integers represented by a binary integer

- Denary integers are worked out by using the unit 10.

10,000=104 | 1,000=103 | 100=102 | 10=101 | 1 | Denary integer |

4 | 7 | 0 | 9 | 2 | 47,092 |

Binary Integers

- In the same way binary integers can be worked out as numbers based on the number 2.
- Therefore 10010100 represents the denary number 148 and we can write the answer in the table:

Binary integer | Denary | |||||||

27 | 26 | 25 | 24 | 23 | 22 | 21 | 1 | |

1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 148 |

- 10010100 Binary = 1x128+0x64+0x32+0x8+1x4+0x2+0x1 Denary

Middle

23

22

21

1

0

0

1

1

1

0

1

0

58

- 00111010 Binary = 1x32+1x16+1x8+1x2=

= 32+16+8+2

= 58

- 11101111 =

Binary integer | Denary | |||||||

27 | 26 | 25 | 24 | 23 | 22 | 21 | 1 | |

1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 239 |

- 11101111 Binary = 1x128+1x64+1x32+1x8+1x4+1x2+1x1

= 128+64+32+8+4+2+1

= 239

- 01000011 =

Binary integer | Denary | |||||||

27 | 26 | 25 | 24 | 23 | 22 | 21 | 1 | |

0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 67 |

- 01000011 Binary = 1x64+1x2+1x1

Conclusion

Binary integer | Denary | |||||||

27 | 26 | 25 | 24 | 23 | 22 | 21 | 1 | |

1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 205 |

Denary integer

- Start on your left.
- Check whether the denary number 205 is greater that the number in the first column 128.
- In this case it is which means that we need 128 in the number, so place 1 in the column.
- 205 – 128 = 77
- 77-64 = 13
- Moving to the next column, check whether 13 is greater that the number in the next column 32.
- As it is not, we place 0 in the column.

This student written piece of work is one of many that can be found in our GCSE Phi Function section.

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