# most significant digit

The 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 $-1. 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 $k=\lfloor log_{b}n\rfloor$.

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 MostSignificantDigit 2013-03-22 16:52:20 2013-03-22 16:52:20 PrimeFan (13766) PrimeFan (13766) 4 PrimeFan (13766) Definition msc 11A63