decibel

26 April 2005

Peter Winship pointed out an error in our original description of dBFS, which he quotes in his comment:

In the definition for dBFS, you write, “Full scale is the level at which the binary number describing the signal is 1's in all places; it can't get any larger.”

This is not always correct. Indeed, in the 2's complement representation of binary numbers, which has been for the past 20–30 years far and away the most common fixed-point representation, the number represented by all ones is in the center of the range of representable numbers. Positive full scale is a zero followed by all ones, and negative full scale is one followed by all zeroes.

A three-bit example of 2's complement representation:

base 10 | base 2 |
---|---|

3 | 011 |

2 | 010 |

1 | 001 |

0 | 000 |

−1 | 111 |

−2 | 110 |

−3 | 101 |

−4 | 100 |

Peter assisted in rewriting the definition, but is in no way responsible for any remaining error.

Copyright © 2005 Sizes, Inc. All rights reserved.

Last revised: 27 April 2005.