Power of 2 | 3 | 2 | 1 | 0 | . | -1 | -2 | -3 | -4 |
---|---|---|---|---|---|---|---|---|---|

8 | 4 | 2 | 1 | . | 0.5 | 0.25 | 0.125 | 0.0625 | |

Include? | 0 | 1 | 1 | 0 | . | 1 | 0 | 0 | 1 |

```
````sum = 4 + 2 + 0.5 +0.0625 = 6.5625`

Here
is another number: `00010100`

.
This expression represents
decimal `1.25`

.

Here is the familiar *binary addition algorithm*
performed with the two bit patterns, and the usual decimal
addition performed with their decimal equivalent.

fixed point | as decimal | |

01101001 | 6.5625 | |

00010100 | 1.2500 | |

01111101 | 7.8125 |

Of course, the question is, does the sum of the fixed point expressions (01111101) represent the sum of the decimal expressions (7.8125)?

Power of 2 | 3 | 2 | 1 | 0 | . | -1 | -2 | -3 | -4 |
---|---|---|---|---|---|---|---|---|---|

8 | 4 | 2 | 1 | . | 0.5 | 0.25 | 0.125 | 0.0625 | |

Include? | 0 | 1 | 1 | 1 | . | 1 | 1 | 0 | 1 |

You can satisfy your burning curiosity by adding up the included decimals in the table.