# least significant digit

The least significant digit of a number $n$ written in a given positional base $b$ is the digit in the least significant place value, and has to be in the range $$. In the case of an integer, the least significant digit is the 1’s place value, usually written to the right of the $b$’s place value. In the case of a transcendental number^{}, there is no actual least significant digit, but for computational purposes the rational approximation would have a least significant digit.

In an array of digits $k$ long meant for mathematical manipulation, it might be convenient to index the least significant digit with index 1 or 0, and the more significant digits with larger integers. (This enables the calculation of the value of a given digit as ${d}_{i}{b}^{i}$ rather than ${d}_{i}{b}^{k-i}$.) For an array of digits meant for text string manipulation, however, the least significant digit might be placed at position $k$ (for example, by Mathematica’s IntegerDigits function).

In binary, the least significant digit is often called the least significant bit.

Title | least significant digit |
---|---|

Canonical name | LeastSignificantDigit |

Date of creation | 2013-03-22 16:21:06 |

Last modified on | 2013-03-22 16:21:06 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 5 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11A63 |

Defines | least significant bit |