# most significant digit

The most significant digit of a number $n$ written in a given positional base $b$ is the digit in the most significant place value, and has to be in the range $$. In the case of an integer, the most significant digit is the ${b}^{k}$’s place value, where $k$ is the total number of digits, or $k=\lfloor lo{g}_{b}n\rfloor $.

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 most significant digit might be placed at position 0 or 1 (for example, by Mathematica’s IntegerDigits function).

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

Title | most significant digit |
---|---|

Canonical name | MostSignificantDigit |

Date of creation | 2013-03-22 16:52:20 |

Last modified on | 2013-03-22 16:52:20 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 4 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11A63 |